























































Period 
Growth Rate
Sales 
HPR 

Acct. 
% of sales 































. 







Options 



1 

5% 
1.05 

CGS 
60% 










An option is a contract between the
seller, or the writer of the option, and the buyer of the option. There are call and put options. A call option gives the buyer the option to
buy some prespecified asset, 

2 

5% 
1.05 

Sales % 
10% 


48 

investmentvaluationforyou.com 











like a share of stock,
or as stock options that are traded on major exchanges, 100 shares is the
usual contract amount. The option
contract allows the buyer to buy this asset at a prespecified 

3 

5% 
1.05 












price, the exercise
price, E, for a certain period of time, T.
It seems rather obvious to see that the lower the exercise price, the
price at which the buyer of the option can buy the underlying instrument, in
this 

4 

5% 
1.05 

Taxes % 
50% 












case 100 shares of
stock, the more the call option is worth.
When you buy an option, the most you can lose is the price of the
option. If you have an option to buy a
stock at $60 per share, and the market price 

5 

5% 
1.05 












of the stock is at $50
per share, and the option is at expiration, then it is going to expire
worthless, as most options do. However, when you buy an option, you can make
unlimited profit. Suppose the 

6 

5% 
1.05 


This site is a decision support
system (DSS) for investment analysis and portfolio management, corporate
finance, and commercial loan analysis. 










market price of the
stock goes to 68, and the option is at expiration, then the option would be
worth $8 per share. The longer time
till expiration, the more the option is worth. You can only lose the price 

7 

5% 
1.05 

A decision
support system is a model based system for processing data to assist in making decisions. This site has several valuation models 











of the option, but you
could make unlimited profit, if the price of the underlying instrument (100
shares of stock) moves in the right direction. The more time you have for this to happen, the more 

8 

5% 
1.05 

for
different types of investments, and provides the fomulas and the necessary
variable inputs for these models. We
will be estimating the 











the option is worth. It
is easy to see the price of an option at expiration. The call option is worth SE, the market
price of the stock minus the exercise price.
A put option is worth ES, the exercise price 

9 

5% 
1.05 

Longterm debt 
$ 400.00 

"present
value" of investments, and determining how this present value compares
to the price of the investment. If
the 











minus the stock
price. 

10 

5% 
1.05 

APR 

5.00% 

present
value that we have calculated is higher than the price, the investment is
under priced. This is what you are
looking for, or at least 



Data as of 02/01/18 








In the example below, if S=75 at
expiration, then the call option will be worth $15x100=$1500). If you had bought a call option when T=.241
(88 days till expiration) when the price of the call option 

11 

5% 
1.05 

Monthly % 

0.41667% 

an
investment that is fairly priced. A
different approach to this problem is to estimate the return of an
investment, and compare this estimated 



S&P 500 
2762.13 








was at 10.61, then you
would have made a profit of (1510.61)=4.61x100=$461. This represents a return of 4.61/10.61=43%
in 88 days(an annualized return of 180%).
If you owned the stock during this 

12 

5% 
1.05 

Monthly pmt. 
$ 1.67 

return
with thef the investment's "required return". The meaning of an investment's required
return will be explained later. 


D/P last 12 months 
1.79% 

154.39 

period, you would have
made the same profit, but your return would have been 7/68=10.3%, an
annualized return of 48%. What is
illustrated here is that the option is a highly leveraged investment 

13 

5% 
1.05 

This year, only the interest on
this $400 debt is being paid. The
principal ($400) remains the same throughout the year. 

Let me describe the layout of this web
site. I start off with some narrative
about capital markets which explains how a fundamental analyst goes 

D/P projected 
1.83% 

18.28 
17.89 

instrument, much more
than just owning the stock. You get a
big bang for your buck. You can make a
lot or loose a lot very quickly. Besides
being used for speculation, options can be used to 

about
analyzing common stock. This section
can get rather complicated, especially when discussing the Capital Asset
Pricing Model and the 

2822.249 

hedge your investments,
thereby lowering your risk. Let's say
you own 100 shares of the stock referred to below. If you could buy a put with an exercise
price of 68, and you bought the stock for 60 today, 

Shortterm debt 

underlying
mathematics. It definitely requires
some investment acumen, or at least some knowledge of the underlying
mathematics involved 



you could lock in a
profit of 8x100=$800. The put
guarantees that you can sell each share of stock at 68 in 88 days. There are options and futures for a variety
of commodities. They are traded
in 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
Total 

(Probability
and Statistics). 

S&P 500 EPS Est. 


organized exchanges,
mostly in Chicago. Lets say you’re a
farmer, and you have a crop of oranges that is going to be harvested in two
months. You are not sure what the
price of oranges will be in two months, 

Shortterm Debt 

$ 944.79 
783.75 
591.61 
401.33 
201.35 
33.99 

I will have a section on options and
futures, including a discussion of the BlackScholes option pricing formula,
as well as a look at some 

INDEX NAME 

Q1,'18 
Q2,'18 
Q3.'18 
Q4,'18 
EPS'18 
Price 
P/E 


and this presents some
risk for you. You know what the price
is on a put option on oranges that matures in two months at an exercise price
that you find acceptable, so you buy enough puts that will 






APR=10% 

0.0083333 
$ 7.87 
$ 6.53 
$ 4.93 
$ 3.34 
$ 1.68 
$ 0.28 

traditional
option trading strategies. We will
look at theories affecting the pricing of interest rate instrument futures
and the term structure of 

S&P 500 

$35.66 
$38.15 
$39.61 
$40.97 
$154.39 
2762.13 
17.89 


allow you to sell your
oranges when they are harvested, at a price that you find acceptable. These
puts you have bought you a guarantee of what price you will be able to sell
your oranges for. On the other side of 






Monthly %=0.8333% 




interest
rates. We will also look at bond
valuation, and it's implications for portfolio management. There will be a section about overall
portfolio 

S&P 500 Consumer
Discretionary 

$8.73 
$10.08 
$10.24 
$10.50 
$39.55 
$848.74 
21.46 


the transaction, you
have someone that wrote the puts who is speculating that orange prices will
go up, the options will expire worthless, and he will profit by keeping the
option premium that he took in 






Monthly HPR=1.008333 



management,
with recommendations for different asset allocations for different investment
objectives. 

S&P 500 Consumer
Staples 

$6.82 
$7.53 
$7.95 
$8.09 
$30.39 
$593.21 
19.52 


when he sold the
puts. The put options have functioned
as an insurance policy for the farmer, locking in the price that he can sell
his oranges for. Call options can also
act as insurance for someone 

Monthly pmt.(int. only) on LTD 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 20.00 

I also have a section that is designed
more for the corporate user. One
section deals with extensive fundamental analysis of the corporation, 

S&P 500 Energy 

$5.70 
$6.47 
$6.58 
$6.27 
$25.02 
$559.45 
22.36 


who needs to be able to
buy a particular asset in the future at a guaranteed price, while the person
selling the call option might just be a speculator, betting that the price of
this asset will go down, 

Int. on shortterm debt 

$ 7.87 
$ 6.53 
$ 4.93 
$ 3.34 
$ 1.68 
$ 0.28 

analysis
that might be suitable if you are not only a stock holder, but someone who is
actually involved in the management of the company. 

S&P 500 Financials 

$8.27 
$8.53 
$8.77 
$8.94 
$34.51 
$498.32 
14.44 


and he will profit by
being able to keep the option premium (the option price is sometimes called
the premium). Futures can also act as
a hedge to protect assets, and speculators can use futures 

Total int. 

$ 9.54 
$ 8.20 
$ 6.60 
$ 5.01 
$ 3.34 
$ 1.95 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 
$ 1.67 

There is
ratio analysis, Sources and Uses of Funds, breakeven analysis, calculations
and implications of degrees of operational and financial 

S&P 500 Health Care 

$14.55 
$15.16 
$15.37 
$15.30 
$60.38 
$1,019.21 
16.88 


to attempt to profit
from price changes in assets. If you
own a bunch of oranges, you could take a short position in the orange futures
market, thus hedging your oranges against any price changes in the 

leverage. 

S&P 500 Industrials 

$7.21 
$9.30 
$9.46 
$9.40 
$35.37 
$669.91 
18.94 


future. Usually, a farmer is just trying to grow
his crop and sell it for a known profit.
He does not want to speculate on price changes of his crop, that is
not his business. However, it is the
business of 

Finally, I have a section that is
designed to produce proforma financial statements (projected financial
statements). The user will input some 

S&P 500 Information
Technology 

$14.02 
$14.12 
$15.04 
$18.14 
$61.32 
$1,189.61 
19.40 


some people, options and
futures speculators who want to take on this risk. Thus options and futures markets are
born. I have shown you how
agricultural commodities are wellsuited for these 

Income Statement (000's) 

beginning
numbers, like projected sales figures, as well as assumptions about projected
growth rates, as well as % of sales for certain items. 

S&P 500 Materials 

$5.37 
$5.89 
$4.92 
$5.14 
$21.32 
$389.09 
18.25 


markets, and so there
are organized exchanges, where options and futures contracts on agricultural
commodities are traded. You can see
why most of these exchanges are located in Chicago, the 

1 
% of Sales 
2 
% of Sales 
3 
% of Sales 
4 
% of Sales 
5 
% of Sales 
6 
% of Sales 
7 
% of Sales 
8 
% of Sales 
9 
% of Sales 
10 
% of Sales 
11 
% of Sales 
12 
% of Sales 
13 
% of Sales 


Yr.Tot.(112) 
% of Sales 
Proforma
statements can be useful for internal planning, as well as indicating to
investors about the future prospects for this company. 

S&P 500
Telecommunication Services 
$3.62 
$3.77 
$3.76 
$3.43 
$14.58 
$169.13 
11.60 


place where the rail
roads from all over the Midwest come together and meet. Traditionally, agricultural commodities
from all over the Midwest would be transported by rail thru Chicago, and on
to the major 

Sales 

$1,500.00 
100% 
$1,575.00 
100% 
$1,653.75 
100% 
$1,736.44 
100% 
$1,823.26 
100% 
$1,914.42 
100% 
$2,010.14 
100.00% 
$2,110.65 
100.00% 
$2,216.18 
100.00% 
$2,326.99 
100.00% 
$2,443.34 
100.00% 
$2,565.51 
100.00% 
$2,693.78 
100.00% 
Sales 

$23,875.69 
100.00% 

If you are
starting a new business enterprise, and if you are seeking either debt or
equity financing, any potential investor is going to want 

S&P 500 Utilities 

$3.95 
$3.36 
$5.09 
$3.17 
$15.57 
$254.88 
16.37 


population centers in
the east. From Chicago, commodities
could be shipped thru the Great Lakes, on thru the Erie Canal, and then by
rail or trucks to the major cities in the East. 

Cost of Goods Sold 

$ 900.00 
60% 
$ 945.00 
60% 
$ 992.25 
60% 
$1,041.86 
60% 
$1,093.96 
60% 
$1,148.65 
60% 
$1,206.09 
60.00% 
$1,266.39 
60.00% 
$1,329.71 
60.00% 
$1,396.20 
60.00% 
$1,466.01 
60.00% 
$1,539.31 
60.00% 
$1,616.27 
60.00% 
Cost of Goods Sold 

$14,325.41 
60.00% 

to see
proforma statements. Typically, if
you had a business plan, you would go to an accountant to prepare proforma
statements for any potential 
S&P 500 Real Estate 

$1.15 
$1.25 
$1.26 
$1.39 
$5.05 
$196.14 
38.84 

Anyhow, you can see why
agricultural commodity option and futures exchanges were in Chicago. Exchanges for trading options and futures
on stocks, bonds, stock indexes, and just about any 

Gross Profit 

$ 600.00 
40% 
$ 630.00 
40% 
$ 661.50 
40% 
$ 694.58 
40% 
$ 729.30 
40% 
$ 765.77 
40% 
$ 804.06 
40.00% 
$ 844.26 
40.00% 
$ 886.47 
40.00% 
$ 930.80 
40.00% 
$ 977.34 
40.00% 
$1,026.20 
40.00% 
$1,077.51 
40.00% 
Gross Profit 

$ 9,550.28 
40.00% 

investors. However, this can be very expensive. With
"investmentvaluationforyou.com" you can produce your own proforma
statements. 

INDEX NAME 

Q1,'19 
Q2,'19 
Q3,'19 
Q4,'19 
EPS'19 
P/E 

financial asset you can
think of, as well as agricultural commodities, are mostly located in Chicago
or New York. Exchanges for options,
futures, stocks (like the OTC market), don't have to be 

Selling Exp.(Variable) 

$ 150.00 
10% 
$ 157.50 
10% 
$ 165.38 
10% 
$ 173.64 
10% 
$ 182.33 
10% 
$ 191.44 
10% 
$ 201.01 
10.00% 
$ 211.07 
10.00% 
$ 221.62 
10.00% 
$ 232.70 
10.00% 
$ 244.33 
10.00% 
$ 256.55 
10.00% 
$ 269.38 
10.00% 
Selling Exp.(Variable) 
$ 2,387.57 
10.00% 

Before I describe what this DSS does, I
would like to present some background information about capital markets. 

S&P 500 

$39.28 
$41.86 
$43.51 
$45.21 
$169.86 
16.61 

located in buildings,
but they can exist as a computer network, with buyers and sellers linked
together online. 

Gen. and Ad. Exp.(Fixed) 

$ 20.00 
1% 
$ 20.00 
1% 
$ 20.00 
1% 
$ 20.00 
1% 
$ 20.00 
1% 
$ 20.00 
1% 
$ 20.00 
0.99% 
$ 20.00 
0.95% 
$ 20.00 
0.90% 
$ 20.00 
0.86% 
$ 20.00 
0.82% 
$ 20.00 
0.78% 
$ 20.00 
0.74% 
Gen. and Ad. Exp.(Fixed) 
$ 240.00 
1.01% 

If
you would like to skip this material and proceed to analysis of the aggregate
stock market, page down about 11 times to row 505, and you 

S&P 500 Consumer
Discretionary 

$9.96 
$11.48 
$11.70 
$11.90 
$45.04 
18.84 

Pg. Dn. 

Depreciation 

$ 50.00 
3% 
$ 50.00 
3% 
$ 50.00 
3% 
$ 50.00 
3% 
$ 50.00 
3% 
$ 50.00 
3% 
$ 50.00 
2.49% 
$ 50.00 
2.37% 
$ 50.00 
2.26% 
$ 50.00 
2.15% 
$ 50.00 
2.05% 
$ 50.00 
1.95% 
$ 50.00 
1.86% 
Depreciation 

$ 600.00 
2.51% 

will get
into analysis of the aggregate market (S&P 500), as well as analysis of
the individual economic sectors. We
will then get into 

S&P 500 Consumer
Staples 

$7.35 
$8.12 
$8.59 
$8.74 
$32.80 
18.07 

E.B.I.T. 

$ 380.00 
25% 
$ 402.50 
26% 
$ 426.13 
26% 
$ 450.93 
26% 
$ 476.98 
26% 
$ 504.33 
26% 
$ 533.04 
26.52% 
$ 563.20 
26.68% 
$ 594.85 
26.84% 
$ 628.10 
26.99% 
$ 663.00 
27.14% 
$ 699.65 
27.27% 
$ 738.14 
27.40% 
E.B.I.T. 

$ 6,322.71 
26.48% 

some
analysis of individual stocks. 

S&P 500 Energy 

$6.00 
$6.97 
$7.29 
$7.18 
$27.44 
20.40 

Interest 

$ 9.54 
1% 
$ 8.20 
1% 
$ 6.60 
0% 
$ 5.01 
0% 
$ 3.34 
0% 
$ 1.95 
0% 
$ 1.67 
0.08% 
$ 1.67 
0.08% 
$ 1.67 
0.08% 
$ 1.67 
0.07% 
$ 1.67 
0.07% 
$ 1.67 
0.06% 

Interest 

$ 44.64 
0.19% 

An important area of academic research
in finance has been in the area of the efficiency of capital markets. 

S&P 500 Financials 

$9.33 
$9.62 
$9.81 
$10.02 
$38.78 
12.85 




E.B.T. 

$ 370.46 
25% 
$ 394.30 
25% 
$ 419.53 
25% 
$ 445.92 
26% 
$ 473.63 
26% 
$ 502.38 
26% 
$ 531.38 
26.43% 
$ 561.53 
26.60% 
$ 593.19 
26.77% 
$ 626.43 
26.92% 
$ 661.34 
27.07% 
$ 697.99 
27.21% 

E.B.T. 

$ 6,278.07 
26.29% 

"An
efficient capital market is one in which security prices adjust rapidly to
the infusion of new information, 

S&P 500 Health Care 

$15.82 
$16.41 
$16.63 
$16.39 
$65.25 
15.62 



Taxes 

$ 185.23 
12% 
$ 197.15 
13% 
$ 209.76 
13% 
$ 222.96 
13% 
$ 236.82 
13% 
$ 251.19 
13% 
$ 265.69 
13.22% 
$ 280.76 
13.30% 
$ 296.59 
13.38% 
$ 313.22 
13.46% 
$ 330.67 
13.53% 
$ 348.99 
13.60% 

Taxes 

$ 3,139.03 
13.15% 

and
current market prices fully reflect all available information that is
relevant."^{1} Many studies have been conducted
concerning the efficiency 

S&P 500 Industrials 

$8.35 
$10.42 
$10.51 
$10.43 
$39.71 
16.88 



Net Income 

$ 185.23 
12% 
$ 197.15 
13% 
$ 209.76 
13% 
$ 222.96 
13% 
$ 236.82 
13% 
$ 251.19 
13% 
$ 265.69 
13.22% 
$ 280.76 
13.30% 
$ 296.59 
13.38% 
$ 313.22 
13.46% 
$ 330.67 
13.53% 
$ 348.99 
13.60% 

Net Income 

$ 3,139.03 
13.15% 

of capital
markets, and the empirical results indicate that capital markets are more or
less efficient for a vast majority of investors. 

S&P 500 Information
Technology 

$15.09 
$15.22 
$16.38 
$19.70 
$66.39 
17.91 



The
efficient market hypothesis (EMH) has important implications for technical
and fundamental analysis. Let me
define both of these types of financial analyses. 
S&P 500 Materials 

$6.32 
$6.41 
$5.51 
$5.59 
$23.83 
16.33 



Balance Sheet (000's) 

Technical
analysts operate on the premise that stock price movements take place in
trends that persist for a period of time. 

S&P 500
Telecommunication Services 
$3.66 
$3.77 
$3.83 
$3.64 
$14.90 
11.35 



Beg. 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

The trader
has a system that, given a certain signal,
can detect the beginning of a
price movement and profit on the movement yet to come. 

S&P 500 Utilities 

$4.06 
$3.56 
$5.14 
$3.64 
$16.40 
15.54 



Assets 

This
signal can be found in the action of the market itself. The belief that future prices can be
predicted by examining past trading data 

S&P 500 Real Estate 

$1.25 
$1.35 
$1.42 
$1.54 
$5.56 
35.20 



Current Assets 

is in
direct contrast with the efficient market hypothesis , which states that the
information dissemination process is extremely quick, 

INDEX NAME 

Q1,'16 
Q2,'16 
Q3,'16 
Q4,16 
EPS'16 




Cash 

$ 400.00 
$ 100.00 
$ 100.00 
$ 100.00 
$ 100.00 
$ 100.00 
$ 108.69 
328.66 
508.91 
$ 699.97 
$ 902.38 
$1,116.70 
$1,343.52 

and most
investors receive the information at about the same time. If current stock prices fully reflect all
relevant information, as the EMH contends, 

S&P 500 


$23.97 
$25.70 
$28.69 
$27.90 
$106.26 




" 
The BlackScholes Option Pricing Formula 

Accounts Rec. 


$ 

$1,500.00 
$1,575.00 
$1,653.75 
$1,736.44 
$1,823.26 
$1,914.42 
$2,010.14 
$2,110.65 
$2,216.18 
$2,326.99 
$2,443.34 
$2,565.51 

then any
technical trading system that depends on past trading data should be totally
useless. By the time the information
is made public, the resulting price change 
S&P 500 Consumer
Discretionary 

$7.70 
$8.56 
$8.54 
$8.50 
$33.30 






C= 
SN(d)1EertN(d2) 



Inventory 

$ 900.00 
$ 945.00 
$ 992.25 
$1,041.86 
$1,093.96 
$1,148.65 
$1,206.09 
$1,266.39 
$1,329.71 
$1,396.20 
$1,466.01 
$1,539.31 
$1,616.27 

has already
taken place. 

S&P 500 Consumer
Staples 

$5.71 
$6.30 
$6.79 
$6.53 
$25.33 


$2,821.37 

T= 
88 days or .241 of a year 
d1= 
(ln(S/E)+(r+˝σ2)T)/σ√T 

Total Current Assets 

$1,300.00 
$2,545.00 
$2,667.25 
$2,795.61 
$2,930.39 
$3,071.91 
$3,229.20 
$3,605.19 
$3,949.27 
$4,312.35 
$4,695.38 
$5,099.35 
$5,525.30 

Fundamental analysts contend that stocks
have a basic, intrinsic value that is determined by the levels of underlying
economic variables such as 

S&P 500 Energy 

($2.71) 
($2.06) 
$0.87 
$0.41 
($3.49) 


$2,762.13 




d2= 
d1σ√T 

Net Fixed Assets 

$ 800.00 
$ 750.00 
$ 700.00 
$ 650.00 
$ 600.00 
$ 550.00 
$ 500.00 
$ 450.00 
$ 400.00 
$ 350.00 
$ 300.00 
$ 250.00 
$ 200.00 

earnings,
earnings growth, and levels of risk. If the analyst can do a superior job of
estimating these variables, he can acquire undervalued stocks and 
S&P 500 Financials 

$5.47 
$5.46 
$7.00 
$5.86 
$23.79 


0.1964 


C=Call option price 

Total Assets 

$2,100.00 
$3,295.00 
$3,367.25 
$3,445.61 
$3,530.39 
$3,621.91 
$3,729.20 
$4,055.19 
$4,349.27 
$4,662.35 
$4,995.38 
$5,349.35 
$5,725.30 


earn
aboveaverage returns. Let me stress
that the analyst must project the future value of these variables in order to
determine the present value of a particular stock. 
S&P 500 Health Care 

$10.49 
$10.94 
$10.69 
$10.32 
$42.44 


S= 
68 

S=Stock price 





Simply
examining past data is unlikely to produce any aboveaverage returns. While advocates of fundamental analysis do
believe 

S&P 500 Industrials 

$5.88 
$7.14 
$7.50 
$6.55 
$27.07 


ab 

E= 
60 

E=Exercise price 

Liabilities 










that
capital markets are pretty efficient, they do realize that the price
mechanism is not always perfect. Over
bought or over sold conditions 

S&P 500 Information
Technology 

$8.03 
$8.27 
$9.23 
$12.45 
$37.98 


T= 
0.241 
√T= 
0.490918 
T=Time till expiration 






Current Liabilities 



















do occur,
producing temporarily overvalued or undervalued stocks. While advocates of fundamental analysis do
believe that market price 

S&P 500 Materials 

$1.67 
$4.91 
$3.73 
$2.71 
$13.02 


12 

σ√T= 
0.795271 
r= 
6% 

r=riskless interest rate 




Accounts Payable 

$ 900.00 
$ 945.00 
$ 992.25 
$1,041.86 
$1,093.96 
$1,148.65 
$1,206.09 
$1,266.39 
$1,329.71 
$1,396.20 
$1,466.01 
$1,539.31 
$1,616.27 






and
intrinsic value can differ, they also believe that the market will eventually
recognize this discrepancy and correct it.
Fundamental analysis involves several levels 
S&P 500 Telecom.
Services 

$2.80 
$1.92 
$2.60 
$2.54 
$9.86 


56 

0.632456 
σ= 
0.4 
σ^{2=} 
0.16 
σ=Standard deviation 






Accrued Exp. 

$ 

$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 
$ 20.00 





of
investigation, beginning with aggregate market analysis, and then moving on
to sector and industry analysis, and then company analysis. The analyst will attempt to estimate 
S&P 500 Utilities 

$3.66 
$2.68 
$4.93 
$2.40 
$13.67 



0.316228 
C= 
SN(d_{1})Ee^{rt}N(d_{2}) 

σ^{2}=the variance 




Total Current Liabilities 


$ 900.00 
$ 965.00 
$1,012.25 
$1,061.86 
$1,113.96 
$1,168.65 
$1,226.09 
$1,286.39 
$1,349.71 
$1,416.20 
$1,486.01 
$1,559.31 
$1,636.27 





future
aggregate stock market earnings per share, and with the dividend yield and the projected
growth rate, the value of the market.
The way to determine if 
S&P 500 Real Estate 

$2.55 
$1.51 
$1.48 
$1.83 
$7.37 

σ^{2}= 
0.16 
C= 
68N(d_{1})60e^{.06(.241)}N(d_{2}) 






Long Term Debt 



$400.00 
$400.00 
$400.00 
$400.00 
$400.00 
$400.00 
$400.00 
$400.00 
$350.00 
$300.00 
$250.00 
$200.00 
$150.00 





the
aggregate market looks attractive is to try to determine if the current
market is over or underpriced, or if it seems to be fairly priced. If the aggregate 
INDEX NAME 


Q1'17 
Q2'17 
Q3'17 
Q4'17 
EPS'17 



d_{1}= 
(ln(S/E)+(r+˝σ^{2})T)/σ√T 

ln68/60= 
0.125163 






Subtotal Liabilities 



$1,300.00 
$1,365.00 
$1,412.25 
$1,461.86 
$1,513.96 
$1,568.65 
$1,626.09 
$1,686.39 
$1,699.71 
$1,716.20 
$1,736.01 
$1,759.31 
$1,786.27 





market
seems to be underpriced according to your analysis, then this would imply
that an aboveaverage return could be earned in the market. 

S&P 500 


$28.82 
$30.51 
$31.33 
$33.47 
$124.13 



d_{1}=ln(68/60)+(.06+.5*.16).241/.4*.491 
SN(d_{1})= 
53.72 







Short Term Debt 



$ 

$ 944.77 
$772.62 
$ 591.60 
$401.33 
$ 201.33 
$ 

$ 

$ 

$ 

$ 

$ 

$ 






This type
of analysis should be done before industry or company analysis is
attempted. The technique we will use
to estimate market values 

S&P 500 Consumer
Discretionary 

$8.05 
$8.71 
$8.86 
$8.93 
$34.55 



N(d_{1})=N(.808)=.790 
d_{1}= 
(.125+.034)/.196=.808 
e^{.rt}= 
0.98564 

43.11207 





Total Liabilities 



$1,300.00 
$2,309.77 
$2,184.87 
$2,053.46 
$1,915.29 
$1,769.98 
$1,626.09 
$1,686.39 
$1,699.71 
$1,716.20 
$1,736.01 
$1,759.31 
$1,786.27 




is the
present value of dividends approach. Specifically, we will apply the basic dividend valuation
model (which I will describe below), 

S&P 500 Consumer
Staples 

$5.99 
$6.72 
$7.17 
$7.40 
$27.28 



N(d_{2})=N(.612)=.729 
d_{2}= 
d_{1}σ√T 

Ee^{rt}= 
59.1386 






Equity 




















to
the aggregate stock market. This
technique is referred to as a micro analysis of the aggregate market. This formula is also used for individual
stocks, portfolios of stocks like sectors or industries, 
S&P 500 Energy 

$3.88 
$2.75 
$3.73 
$4.29 
$14.65 



d_{2}= 
.808.196 

Ee^{rt}N(d_{2})= 
43.1121 

43.1121 




Common Stock 



$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 
$800.00 




and
the aggregate market, or a proxy thereof, like the S&P 500. What follows is the present value of
dividends model. 

S&P 500 Financials 

$6.83 
$6.98 
$6.14 
$6.78 
$26.73 




d_{2}= 
0.612 

C= 
10.6079 

10.60793 






Retained Earnings 



$ 

$ 185.23 
$ 382.38 
$ 592.15 
$ 815.11 
$1,051.92 
$1,303.11 
$1,568.80 
$1,849.56 
$2,146.16 
$2,459.37 
$2,790.04 
$3,139.03 





P=D_{1}/(ig) 

i=D_{1}/P+g 

S&P 500 Health Care 

$10.52 
$11.78 
$11.37 
$12.05 
$45.72 



C= 
10.60793 





Total Equity 


$800.00 
$985.23 
$1,182.38 
$1,392.15 
$1,615.11 
$1,851.92 
$2,103.11 
$2,368.80 
$2,649.56 
$2,946.16 
$3,259.37 
$3,590.04 
$3,939.03 


P=price 



S&P 500 Industrials 

$6.37 
$8.02 
$8.05 
$6.74 
$29.18 



Total Liabilities and
Equity 

$2,100.00 
$3,295.00 
$3,367.25 
$3,445.61 
$3,530.39 
$3,621.91 
$3,729.20 
$4,055.19 
$4,349.27 
$4,662.35 
$4,995.38 
$5,349.35 
$5,725.30 


D_{1}=dividend in year 1 



S&P 500 Information
Technology 

$10.30 
$10.81 
$12.20 
$16.24 
$49.55 



Hedge ratio= 
h=N(d_{1}) 








i= the estimated rate of
return 

_{} 

S&P 500 Materials 

$4.62 
$4.89 
$4.10 
$4.05 
$17.66 



h=.790 

Sources and Uses of Funds 






g=long term growth rate of earnings
and dividends 

S&P 500 Telecom.
Services 

$2.70 
$2.80 
$2.74 
$1.92 
$10.16 







Sources 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

You can
transform this formula into the pragmatic earnings multiplier model as
follows: 

S&P 500 Utilities 

$3.75 
$3.06 
$4.66 
$3.31 
$14.78 









Net Income 


$ 185.23 
$ 197.15 
$ 209.76 
$ 222.96 
$ 236.82 
$ 251.19 
$ 265.69 
$ 280.76 
$ 296.59 
$ 313.22 
$ 330.67 
$ 348.99 


P/E_{1}= 
D_{1}/E_{1} 

_{} 

S&P 500 Real Estate 

$1.37 
$1.29 
$1.56 
$1.45 
$5.67 



The BlackScholes formula gives the price of this call option at
10.61. If the market price of the
option is different than this, then significant profit opportunities exist
for investors. The strategies 

Depreciation 

$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 
$ 50.00 


(ig) 

for reaping these profits will be
discussed later. 

Increase in Liabilities 



$ 60.30 
$ 13.32 
$ 16.49 
$ 19.81 
$ 23.30 
$ 26.97 


E_{1}=earnings in year 1 



Finding a mispriced option is just the start of the arbitrage
strategy. Arbitrage means making
riskless profit. You take a position
in the option, and also a position in the underlying stock, The 

Decrease in Cash 

$ 300.00 




The P/E
ratio is the earnings multiplier. It
is determined by: 

investor now has a hedge against
stock price movements. The hedge ratio
tells you how much the price of an option changes, given a 1 point change in
the underlying stock. The hedge ratio 

Increase in Short Term Debt 

$ 944.77 

1. The expected dividend payout ratio, D_{1}/E_{1} 

is h=N(d_{1}). N(d_{1}) is part of the first term in the BlackScholes formula, N(.)
is the cumulative normal distribution function, whose values are given in the
table below. 

Increase in Accounts Pay. 

$ 45.00 



2. The estimated rate of return on the stock,
i 

N(d1)=ΔC/ΔS, where Δ (delta) means change.
The negative sign means that the option and the stock are held in
opposite positions. Once a mispriced
option is discovered, the investor 

Increase in Accrued Exp. 

$ 20.00 

3. The expected rate of growth of earnings and
dividends for the stock, g. 

can form a riskless
hedge by buying N(d1) shares of stock for each option written. The option and the stock are held in
opposite positions, thus the minus sign in front of N(d_{1}). 

Total 

$1,545.00 
$ 247.15 
$ 259.76 
$ 272.96 
$ 286.82 
$ 301.19 
$ 375.99 
$ 344.08 
$ 363.08 
$ 383.03 
$ 403.97 
$ 425.96 

The
difficult parameters to estimate are i and g, or more specifically, the
spread between i and g. 
However, it can be shown that D_{1}/P=(ig). Therefore, 

If the option is
overpriced, then a short position is taken in the option (it is written),
and a long position is taken in the stock.
Long means buy, short means
sell. In the above example 

Uses 



you
can use the indicated dividend yield to estimate (ig). 

h=N(.808)=.790 is the
hedge ratio. This means that if the
stock changes by one point, the call option will change a little less than ,8
points. However, the hedge ratio holds
only for small 

Increase in Accounts Rec. 

$1,500.00 
$ 75.00 
$ 78.75 
$ 82.69 
$ 86.82 
$ 91.16 
$ 95.72 
$ 100.51 
$ 105.53 
$ 110.81 
$ 116.35 
$ 122.17 

P/E_{1}= 
D_{1}/E_{1}= 
M, the multiplier 


changes in the price of
the underlying instrument. If the
underlying instrument (Stock) changes by 5 or 10 points, the ratio will not
assure the riskless hedge will be maintained.
The ratio 

Increase in Inventory 

$ 45.00 
$ 47.25 
$ 49.61 
$ 52.09 
$ 54.70 
$ 57.43 
$ 60.30 
$ 63.32 
$ 66.49 
$ 69.81 
$ 73.30 
$ 76.97 


(ig) 



must be reevaluated and
adjusted whenever the stock price changes significantly. Also, as time to expiration goes down, the
price of the option goes down, and the hedge must again 

Decrease in Liabilities 

$ 124.90 
$ 131.41 
$ 138.18 
$ 145.30 
$ 143.90 

P= 
E_{1} x 
D1/E1 

be adjusted. The solution for N(d_{1}) and N(d_{2}), N(∙) is the cumulative normal distribution function,
and the tables showing the N(d) for each d is shown 3 pages down. 

Increase in Cash 

$ 

$ 

$ 8.69 
$ 219.97 
$ 180.25 
$ 191.06 
$ 202.41 
$ 214.32 
$ 226.82 


(ig) 

The variables that are
the inputs to the formula need to be estimated. The stock price, the exercise price, and
the time to maturity can be found in the option quotation. The time to maturity is 

Total 

$1,545.00 
$ 247.15 
$ 259.77 
$ 272.96 
$ 286.82 
$ 301.18 
$ 376.00 
$ 344.08 
$ 363.08 
$ 383.03 
$ 403.97 
$ 425.95 

P= 
E_{1} x
M 

calculated by taking the
number of calendar days until maturity, and then dividing it by 365 to
express it in annual terms. We need to
find the riskfree interest rate for borrowing and lending during 

You can
think of the multiplier as the value you are assigning to the stream of
earnings. Changes in earnings or
changes in the multiplier will affect the price. 

the period of the
option. Since these rates usually
differ, an average of the two can used.
The duration of the interest rate used should be as close as possible
to the time of expiration 

We will use the Standard & Poor's
500 as a proxy for the aggregate stock market. The S&P 500 is a marketweighted index
of 500 leading companies 

of the option. If the option has 3 months till expiration,
then a 3 month interest rate should be used.
Tbill rates are generally too low.
They are lower than the borrowing rate for anyone 

in leading
industries of the U.S. economy. Each
company in the index is weighted by it's total market capitalization, which
is the price x the number 

except the U.S.
government (which guarantees repayment).
Certificate if deposit rates are good to use, or rates for top quality
commercial paper. The price of the
option does not 

Ratio Analysis 

of shares
issued, authorized, and outstanding.
The S&P 500 includes about 75% of U.S. equities. Fortunately, Standard & Poor's provides
per share 

change a whole lot when
the interest rate changes. The
volatility of the stock price is the most difficult input to estimate. A good first approximation of the
volatility of the stock is to look 

4 

Liquidity Ratios 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
Total 

earnings
data for the S&P 500, which works
quite well for our micro analysis of the aggregate market. We are going to estimate the earnings and
dividends per share 

at past data. Price observations over the past several
months should be used. If we go back
too far, the returns will be less reflective of the future volatility of the
stock. 

Current Ratio 

Current Assets/Current
Liabilities 

2.64 
2.63 

for
the S&P 500 for the upcoming year, as well as the growth of earnings and
dividends for the upcoming year. We
will then be able to calculate the expected return 

The measure of volatility that is used
in the formula is the variance (σ^{2}) of returns. Let's assume we have endofweek quotes for
20 weeks. In order to change prices
into ratesofreturn 

Acid Test 

Cash+Marketable
Securities+Accounts Receivable/Current Liabilities 

1.66 
1.65 

for
the S&P 500, and then the value of the S&P 500. Standard & Poor's estimates future
earnings per share for the S&P 500 to be as follows: 

we have R_{k}=S_{k}/S_{k1}. S_{k}=the stock price at the end of the kth week. We get the natural log of the return to get
the continuously compounded return.
Now we calculate the mean of 

Profitability Ratios 




Estimates of EPS for the
S&P 500 

the return, m=1/20
Σ ln R_{k.
}ln R_{k
}is the natural log of R_{k. }We calculate the variance by by summing (ln R_{k}m)^{2} over all periods, then
dividing by(N1). We divide by (N1)
to account for the 

Return on Assets 

Net Income/Total Assets 

0.06 
0.059 
0.061 
0.063 
0.065 
0.067 
$ 0.066 


12 Month Operating
Earnings Per Share 

degrees of freedom. 

Return on Equity 

Net Income/Equity 

0.19 
$ 0.06 


2018 estimate=154.39 

The hedge ratio = h = N(d1). The hedge ratio in our example is
,790. If the market price of the call
option is below the formula price, it is underpriced. In this case you would 

Financial Leverage Ratios 




2019 estimate=169.86 

buy 1 option contract
(which controls 100 shares of stock) , and short sell 79 shares of stock,
using the remaining balance to invest at the NRFR. If the option is overpriced, you would 

Aftertax % cost of
interest Interest exp.Tax
shield Created/Amount borrowed 

0.01 


The
required return on common stocks is a function of the economy's"
real" riskfree rate (RFR), the expected rate of inflation (I), and the
risk premium for common 

sell, or write1 option
contract, buy 79 shares of the stock with the proceeds of the the option
sale, and borrow the remaining amount at the NRFR. In either case, an arbitrage profit 

% Total debt of total
assets 
Total debt/Total assets 

0.70 

stocks. The "real" RFR is combined with
the expected inflation rate to arrive at the nominal riskfree rate
(NRFR). The relationship is actually
multiplicative, but 

is possible. 

Capitalization ratio 

Longterm debt/Longterm
debt+Equity 

0.29 

just adding
the two rates together serves as a good approximation. 

Applications of the
Option Pricing Formula 

Interest coverage 

E.B.I.T./Interest 

39.83 

Nominal rates are the rates that you
actually observe in the market place.
The current yield to maturity of a government bond equal to your
investment planning 

"We begin by estimating the variables that go into the
formula. The interest rate should be
the riskfree borrowing and lending rate over the period of the option. Since these rates 

Burden coverage 

Profit before fixed
charges and taxes/Fixed charges+principal payments 

13.54 

horizon
should serve as a good proxy for the current nominal riskfree rate. The current risk premium of the expected
return of the market E(R_{m}) over the NRFR 

typically differ, we can use an
average of the two. The treasury bill
rate will typically underestimate the correct rate (it is below everyone's
borrowing rate but the US government). 

Efficiency Ratios 



needs
to be estimated. If ten years is your
planning horizon, then the yield on 10 year treasury bonds on 02/02/18 was
2.87%. (see section on The Capital
Asset Pricing Model). 

The Certificate of
Deposit rate or the rate of top quality commercial paper. The interest rate used in the formula
should be the same duration as the the option whose value you 

Return on Assets 

Net Income/Total
assets=Net income/Sales*Sales/Total assets 

0.06 

We must
now determine the risk premium for common stocks. "A study by Ibbotson and Sinquefield
estimated the equity risk premium as the difference 

are trying to
determine. The option price is not
very sensitive to small changes in the interest rate. Volatility in the formula is shown by the
standard deviation of the underlying 

Accounts receivable
turnover 
Sales/Accounts receivable 

1.00 

in
the annual rates of return for common stocks and treasury bills. They found that from 19261978, the
geometric mean of this risk premium was 6.2%."^{2} 

instrument. There are several ways to estimate the
standard deviation of the underlying instrument. You can use past data to estimate the
current standard deviation. 

Days sales outstanding 
Accounts receivable/Sales
for year/360 

360.00 

We could
say that during this period, the average risk premium for common stocks over
the 90 day Tbill rate was 6.2%. If we
assume that the current risk premium of the stock market 

First you convert prices
to rates of return. Rk=Sk/Sk1. S_{k}=stock price at the end of kth week. We then get the natural log of the return
to approximate the continuously 

Inventory turnover 

Sales/ending inventory 

1.59 

is
similar now, then we can estimate the investor's required return for the
stock market. The 3 month Tbill rate now is about 1.59%, so 7,79% would be
the expected 

compounded return. Next we calculate the mean of the return,
m=1/20Σln Rk. The variance is
then calculated by summing (ln R_{k}m)^{2} over all the periods, then dividing by 

Return on equity 

Net
Income/equity=Sales/Total assets*Net income/Sales*Total assets/equity 
0.19 

return
of the market E(R_{m}). As I will show you, the E(R_{m}) for the upcoming year
is more than twice that amount. 

(N1). We divide by (N1) to take account of the
degrees of freedom in the calculation of the variance in order the get an
unbiased estimate. Also, we do not
have to use 

"The intrinsic determinants of the
aggregate market risk premium are the business risk (BR), financial risk
(FR), and liquidity risk (LR) of the aggregate market. 


52 weekly
intervals. Monthly, biweekly, or even
daily data can be used. Remember that
we are using past data to predict future data. The variance does change over time, 

Sources and Uses of Funds
Statement 

The market
measure of this risk is the variance of returns, σ^{2}, for the stock
market."^{3} Both of these methods are trying to
determine the same thing, the 

so the more recent the
data, the more likely that it will be reflective of what the current data
is. The more entries that are used,
the more precise the sample will be.
Sometimes 

Sources of funds 

level of
risk in the stock market, and thus the investors' required rate of return for
the market, i. 

the time of day that the
observations are taken may be different, and the shorter the interval the
more this can matter. This can make
daily observations less dependable.
With 

Net Income 

These
intrinsic determinants cause volatility in the market, which is measured by
the variance of returns for the market, σ^{2}. 

weekly observations this
problem becomes less significant.
Twenty weekly observation seems to be a good compromise amongst these
considerations. 

Plus depreciation 

4.1666667 

The
required return on common stocks can be summarized as follows: 

The use of time series
analysis produces a forecast of the variance that is much more accurate than
just using a direct application of the historical data. If we also use 

Funds provided by
operations 


i=f(NRFR, BR, FR, LR) 

P/O ratio =Div./Op. Earn. 

2/1/2018 

firm, industry, and
market data along with time series analysis, we obtain a forecast that is
even more accurate than just using time series analysis alone. 

Increase in liabilities 


or 

Ret. rate =1PO ratio 
S&P close of: 


2762.13 

The forecasted data
produces results that match the actual data quite closely, and thus produces
a forecast of future results that are about as accurate as we are able 

Increase in common stock 


i=f(NRFR), σ^{2}) 

Dividend yield (last 12
months: Jan, '18) 
1.79% 

to obtain. 

Total 

This reads
"i is a function of NRFR, BR, FR, and LR or i is a function of NRFR and
σ^{2}". 

Dividend yield (current
indicated rate) 
1.83% 

Another method of producing a forecast of
future volatility is the use the variance that is implied by plugging the
option's price and other statistics into the option formula, 

Uses of funds 

The growth rate of dividends and
earnings, g, is a function of the retention ratio, b, and the return on
equity, ROE. 



and seeing what variance
is implied by the option formula. We
are using the formula to supply an estimate of the variance, and the same 

Dividends 

g=b x
ROE. ROE can be broken down as
follows: 

P/O ratio= 
32.8% 



estimate of the variance
is required as an input to the formula.
It seems that the reasoning here is kind of circular. However, obtaining the implied variance
does give us an idea 
Increase in cash 

ROE=Net
Income/Equity=Net Income/Sales x Sales/Total Assets xTotal Assets/Equity 

b= 
67.2% 

of what the market sees
as the variance of the underlying instrument.
It fits the actual data fairly well, and does not require data
collection, as the other method does, so it may be easier. 

Increase in accounts
receivable 

ROE=(Profit
Margin)(Total Asset Turnover)(Leverage) 

2766.6667 

Taking an average of the
implicit volatilities of several options may be the best way to determine
what the market's opinion of the variance is.
Also, differing tax rates for different investors 

Increase in inventory 

b
= the retention ratio, the % of earnings that are retained, or 1(D_{1}/E_{1}) 

means there may not be
one price that eliminates profit opportunities for all investors. Uncertainty in interest rates and variance
cause uncertainty in the correct option price and 

Net addition to total
fixed assets 

D_{1}/E_{1} =payout ratio 
ROE can be increased by increasing
profit margin, total asset turnover, or leverage. However, increasing leverage will inrease
financial risk. 

the correct hedge
ratio. 

Currently,
the retention ratio for the S&P 500 is about 67.3%, and the most recent
ROE was 15.4%. This makes for a
projected growth rate of about 10.4%. 

The arbitrage strategy involves
maintaining a dynamic hedge. The
position of the stock relative to the option must be constantly adjusted as
the time to maturity decreases and as 

A net increase in any
asset account is a use of funds, a decrease is a source. A net increase in any liability or equity
account is a source, a decrease is 

The
expected dividend yield for the upcoming year for the S&P 500 is
1.83%. We know from the present value
of dividend model that investors' expected rate of return for the S&P 500
is as follows: 

the price of the stock
changes. Each adjustment will require
transaction costs. Empirical evidence
by Galai (1975) suggests that even a 1%
transaction cost will eliminate any 

a use. 

P=D_{1}/ig 

Estimated return (i) with
long term growth rate of 13.4% 

Note:This 13.4% long term growth rate is larger than the 

profit potential from
following the hedging strategy for a typical investor. Even a floor trader whose transaction costs
are very low, after considering the implicit costs involved (i.e. exchange 

i=D_{1}/P+g 

P/E= 
18.28 

i=.0183+.134 

10.4% growth rate calculated by using b x ROE. 

seat cost, etc.) it may make the strategy impractical. The questioni is can an investor profit
from use of the option pricing formula?
The formula is widely known and used.
A majority 

Breakeven Analysis 

i=.0183+.104 

10 yr. TBond=2.87% 

i=.1523 
Risk Premium of E(R_{m}) less TBond yield = 
0.1236 

of market makers on the
option exchanges subscribe to option services who use the option pricing
model. The price of an option
calculated with the pricing model is wellknown information. 

Breakeven units=Total
fixed expenses/selling price per unitvariable expense per unit. FE/SPPUVEPU. 

i=.1223 

Dividend yield=D/P 
D/P=(ig) 
ig= 
0.0183 

An option that is
mispriced will be acted on immediately by a large group of investors, and
this will change the price to it's correct level. In retrospect, it is the option model's
popularity 

Breakeven dollars of
sales=FE/1(VE/S). 

The
S&P 500 was at 2821.37 on 02/02/18, with the estimated EPS for 2018 at
$154.39 (the estimated dividend is $50.63).
The estimated dividend yield (D/P) for the S&P 500 is 1.83% 

that prevents it's
profitable use. When just a small
group of investors has the informatiion that the model provides, then it can
be used profitably by this small group.
Hovever, when 

and
the long term growth rate of earnings (and dividends) was estimated to be
13.4%. These numbers indicate an
expected return of 15.2%.. The risk premium over the 10 year bond is 12.4%. 

everyone knows about the
formula, any mispricings quickly disappear.
The formula has become part of the market's information set. Then why are there mispriced options
according 

Fixed versus variable
expenses 

The
90 day TBill yield was about 1.59%, making the risk premium of the E(R_{m}) less the TBill yield
about 13.7%, more than double what we decided the "normal" premium
had ben (6.2%) between 

to the formula. It is because the formula is not the only
information in this set. There are
other firm, industry, or market indicators that investors consider in
determining the market price 

Ex.1 
Ex.2 

1926
and 1978. The P/E ratio (the
multiplier) was 18.28%. The P/E ratio
for the S&P 500 has been going up for the past 5 years because prices
have been increasing at a faster rate 

of the option. Investors, floor traders, or market makers
combine the information in the set, one of which is the formula, and
determine the market price of the
option. 

Sales 

200000 
200000 

than
EPS have. 

When some new
information enters this set, the market price of the option changes very
quickly, and the only people to profit from this change (if the change is
positive) are the people who owned the option 

CGS 75% 

150000 
150000 


Modern Portfolio Theory
and the Capital Asset Pricing Model 

before this new
information is released. When there is
a divergence between the market price of an option and it's formula price,
this implies that the market believes that the 

Gross margin 

50000 
50000 

We will begin with an assumption that
investors are risk averse. This means
that given a choice of two assets that have the same expected return, 

formula's price is not
correct. 

Variable expense 20% 
0 
40000 

the
investor will select the asset with the lowest level of risk. This means that there should be a positive
relationship between expected return 

The BlackScholes option formula makes
some assumptions that are unrealistic.
The original formulation does not allow for dividends. This formulation needs to be adjusted 

Fixed expense 

46000 
6000 

and
risk. For a given level of risk,
investors prefer higher returns to lower returns. Similarly, for a given
level of return, investors prefer less 

because dividend
payments usually make the price of the stock drop. If the option is not payout protected, a
drop in the price of the stock implies a drop in the option price. The holder 

E.B.I.T. 

4000 
4000 

risk
to more risk. Although the definitions
of risk and volatility are different, for our purposes and in most financial
literature, the terms are 

of a call option may
want to exercise the option just before the stock goes exdividend so they
can capture the value of the stock before the decline. When evaluating an option, the 

Level of sales where
E.B.I.T.is the same under each alternative. 

used
interchangeably. "The basic
portfolio model, developed by Harry Markowitz, showed that the variance of
the rate of return was a meaningful 

possibility of an early
exercise must be taken into account.
If the dividend payout is known, you can replace the stock price with
the stock price minus the dividend in the formula. 

Sales.75Sales46000=Sales.95Sales6000 

measure of
risk under a reasonable set of assumptions, and derived the formulas for
computing the variance of the portfolio."^{4} 

If dividends are paid at
a continuous rate, rather than lump sums, then the formula can be
adjusted. Let the dividend yield be
ⱷ. If the stock price is $100
and the dividend is $5, 

Sales=200000 

While the expected rate of return for a
portfolio of assets is simply the weighted average of the expected rates of
return for each asset in the portfolio, the same 

then ⱷ=.05. In order to modify the BlackScholes
formula to include this rate, we replace S in the first term of the formula
with e^{}^{ⱷ}^{T}S, and we replace the
interest rate r in the d_{1} and 

is not
true for the variance of the rate of return for a portfolio of assets. Let us look at the simplest case, a
portfolio of two assets. First we will 

the d_{2} terms with rⱷ. These modificatios
reduce the stock price S by the amount of the dividend, and adjust the return
from the riskless hedging strategy accordingly."^{16} 

Degree of Operating
Leverage 

demonstrate
the computation of the standard deviation (the square root of the variance)
for an individual asset. 

The % change in net
income brought about by a 1% change in sales. 


σ.=the standard deviation= 
the √ of (Σ (R_{i}E(R_{i))}^{2} x P_{i}) 

Traditional Option Trading Strategies: Spreads and
straddles 

1% 

1% 

1% 

1% 


σ^{2}=the
variance 

I am goingto tell you
about a couple of basic option trading stragies. They hsve nothing to do with the option
pricing model. They are strategies
concerning your outlook on the 

Sales 
990 
1000 
1010 

1485 
1500 
1515 


R_{i}=the rate or return for i 

underlying instrument of
an option. They could be options on
stock, one of several stock index futures, many agricultural commodity
futures, Treasury Bill Futures, Treasury Bond 
Var. exp. 
742.5 
750 
757.5 

1113.75 
1125 
1136.25 


E(R_{i})=the
expected rate of return of i (the arithmetic average of possible returns) 

Futures, precious metals
futures, and others that I can not think of right now. Let's say you are bullish on a particlar
stock. We will use IBM stock and some
call options 

Fixed exp. 
100 
100 
100 

100 
100 
100 


Σ_{i}=the summation of each i 

on it. We will now create
a bull spread. 

Net Inc. 
147.5 
150 
152.5 

271.25 
275 
278.75 


P_{i}=the
probability of each possible rate of return 

7/30/2016 

Strike 
Price 

D.O.L.= 
1.67% 

1.36% 

In order to discuss the derivation of
the variance of a portfolio of assets, I need to present two basic concepts
in statistics, covariance and correlation. 

IBM Stock 
$160.96 




You can also calculate
D.O.L.with the following formula.
D.O.L.=Q(SPPUVEPU)/Q(SPPUVEPU)FE 

Covariance
is a measure of the degree to which two variables, in this case the returns
of two assets, move together over time.
A positive covariance 

Options 
Call 



Q=Volume in units 

means that
the variables tend to move in the same direction at the same time, and a
negative covariance means that they move in opposite directions. 

Exp. 
1/15/2017 



SPPU=Selling price per
unit 

Covariance
is an absolute measure. For two
assets, i and j, the covariance of monthly returns is as follows: 

Strike 
160 
165 
170 
175 
155 
150 



VEPU=Variable expense per
unit 


1/12 x Σ (R_{i}E(R_{i}))(R_{j}E(R_{j})) 

Price 
$ 7.20 
$ 4.95 
$ 3.21 
$ 2.02 
$ 10.05 
$ 13.45 

FE=Total fixed expenses 


R_{i}=return of asset i 

These optios have about
5˝ months till expiration. 




D.O.L. Sales=1000=1.67% 


R_{j}=return of asset j 

I will go long (buy) the
option with a strike price of 165, and write, or go short (sell) the option
with a strike price of 175. 

D.O.L. Sales=1500=1.36% 

The
correlation coefficient is a relative measure of the degree to which two
variables move together. The
correlation coefficient is defined as follows: 

Strike 
Price 


r=Cov_{ij}/σ_{i}σ_{j} 

165 
$ 4.95 

Degree of Financial
Leverage 


Cov_{ij}=the covariance of assets i and j. 

175 
$ (2.02) 

The % change in earnings
per share brought about by a 1% change in earnings before interest and taxes. 


σ_{i}=the standard deviation of asset i 

Net 
$ 2.93 

1% 

1% 

1% 

1% 


σ_{j}=the standard deviation of asset j 

My total investment is
$2.93. On 1/15/17, IBM Stock is at
175. The 165 strike finishes at $10,
and the 175 strike expires worthless.
My net profit is as follows: 

E.B.I.T. 
792000 
800000 
808000 

990000 
1000000 
1010000 

The
correlation coefficient can vary between 1 and 1. 1 means there is a perfect, positive linear
relationship between 2 variables, while 1 

Strike 
Price 


E.P.S. 
0.784 
0.8 
0.816 

1.18 
1.2 
1.22 

means that
the variables move in completely opposite directions. 0 means that there is no linear
relationship between the two variables. 

165 
$ 10.00 

D.O.F. 
2.00% 

1.67% 

A
correlation of 1 gives you the maximum benefits of diversification. In a portfolio with 2 assets, perfect
negative correlation produces a standard deviation 

175 
$ 


You can also calculate
the D.O.F. with the following formula.
D.O.F.=E.B.I.T./(E.B.I.T.F) 

of 0, a
riskfree portfolio. 

Net 
$ 10.00 

F=Annual interest expense 

The formula
for the standard deviation of a portfolio is as follows: 

Spread 
$ (2.93) 


σp=the
√σp2 = (Σ Wi2σi2 + 2 x ΣΣWiWjCovij) 

σ_{p}=the standard deviation
of a portfolio 

Total 
$ 7.07 
With IBM finishing at
$175, my profit is $7.07. If IBM
finishes at 176, my profit is still $7.07. 

You currently own a
company. You own 10 shares of
stock. The tax rate is 50%. E.B.I.T.is 200. E.P.S. is 10. 


W_{i}=the weight of each asset in the portfolio 

σ_{p}^{2}=the variance of a portfolio 

Strike 
Price 


Now 


W_{i}W_{j}=the weights of each pair of assets in the portfolio 

165 
$ 11.00 

E.B.I.T. 
200 

We
see from the formula that not only do the individual variances affect the
portfolio variance, but the covariance's between each individual asset
also 

175 
$ (1.00) 

Taxes 
100 

affect the
portfolio variance. In fact, it can be
shown that in a portfolio with a large number of assets, the variance of the
portfolio becomes the 

Net 
$ 10.00 

If IBM finishes at
$167.93, my profit is at: 

If IBM finishes at $160,
my profit is at: 
With this bull spread, you can make
a maximum of 
E.A.T.C.S. 
100 

summation
of the weighted covariances. This
means that when you add an asset to a portfolio with a large number of
assets, it is not the asset's 

Spread 
$ (2.93) 

Strike 
Price 

Strike 
Price 

$7.07 (the $10 difference in the
strike prices less 
E.P.S. 
10 

variance,
but the asset's covariance with all the other assets in the portfolio that is
important. 

Total 
$ 7.07 

165 
$2.93 

165 
$ 


the initial investment of
$2.93). You can lose a 
Shares 
10 

When assets with correlations of less
than one are combined into portfolios, we get the benefits of
diversification. If all the possible 

If IBM finishes at $175
or higher, I will get the maximum profit on this spread of $7.07. If IBM finishes at $174, my profit is as
follows: 

175 
$ 


175 
$ 


maximum of $2.93, (the $10
difference in the strike 
You can expand E.B.I.T.
by 160. It will cost 500. You can raise the money by issuing 10 new
shares of stock, or by borrowing the money. 

portfolios
of assets are shown on a graph where the xaxis is the standard deviation and
the yaxis is the expected return, we will get a curve on the 

2008 EPS 
2008 P/E 
2009 EPS 
2009 P/E 
2010 EPS 
2010 P/E 
2011 EPS 
2011 P/E 
2012 EPS 
2012 P/E 
2013 EPS 
2013 P/E 
2014 EPS 
2014 P/E 


Strike 
Price 


Net 
$ 2.93 

Net 
$ 


prices less the maximum profit of
$7.07). 

Stock 

Loan 

edge of
these groups of portfolios called the efficient frontier (see graphs
2,3). All the portfolios on the
efficient frontier are superior to all the other portfolios that 
S&P 500 
$49.51 
18.24 
$56.86 
19.61 
$83.77 
15.01 
$96.44 
13.04 
$96.82 
14.73 
$107.31 
17.22 
$113.01 
18.22 


165 
$9.00 

Spread 
$ (2.93) 

Spread 
$ (2.93) 

$7.07+$2.93=$10, the difference in
the strike prices. 
E.B.I.T. 
360 

360 

are not on
the efficient frontier. When I say
superior, I mean that every portfolio on the efficient frontier has a higher
expected return for a given 

Con. Disc. 
$5.28 
32.08 
$10.96 
21.45 
$18.20 
16.24 
$20.81 
14.83 
$22.27 
16.89 
$25.12 
21.1 
$27.70 
20.67 


175 
$ 


Total 
$ 


Total 
$ 


Interest 
0 

40 

level of
standard deviation, or a lower standard deviation for a given expected
return, compared to every portfolio that is not on the efficient frontier. 

Con. Stap. 
$17.17 
14.37 
$18.36 
14.94 
$19.45 
15.61 
$21.38 
15.69 
$22.59 
15.97 
$23.95 
18.48 
$24.16 
20.68 



Net 
$ 9.00 

Taxes 
180 

160 


r=0 

Energy 
$50.93 
7.59 
$17.26 
24.91 
$35.21 
14.39 
$47.94 
10.86 
$44.30 
12.03 
$42.35 
15.39 
$42.93 
13.66 



Spread 
$ (2.93) 

If IBM finishes at 165 or lower,both options will expirre
worthless, and I will lose my initial investment of $2.93. With a bull spread you buy an option at a
strike price, 

E.A.T.C.S. 
180 

180 


σ 
Return 
Weight 1 
Weight 2 

Stock 
E(Ri) 
σ^{2} 
σ 

Financials 
($21.24) 
7.95 
$4.40 
44.04 
$14.82 
14.49 
$16.23 
10.79 
$16.44 
13.46 
$21.07 
13.99 
$21.96 
15.18 



Total 
$ 6.93 

and then write an option with a
higher strike price, and thus at a lower price. You get to lower your investment (if you
just bought the IBM 165 you would have to pay 

E.P.S. 
9 

16 


0.0812 
0.18 
0.2 
0.8 

1 
0.1 
0.0049 
0.07 

Health Care 
$24.47 
12.64 
$26.40 
13.72 
$28.90 
12.62 
$31.08 
12.93 
$31.53 
14.68 
$32.43 
19.81 
$35.79 
22.13 


$4.95), but you give up the
potential of the possibility to make a lot of money (If IBM stock went to
$200, you would make $35.00). When you
buy a call option, you 

Shares 
20 

10 


0.0662 
0.16 
0.4 
0.6 

2 
0.2 
0.01 
0.1 

Industrials 
$21.18 
9.78 
$14.22 
17.09 
$18.41 
16.36 
$20.96 
13.95 
$22.28 
14.76 
$24.88 
18.19 
$26.83 
18.13 


Graph 1 

may lose the money you paid for the
option, but you can make the difference between what the stock is trading for now, and what
your exercise price is. If the stock 


0.061 
0.15 
0.5 
0.5 

Info. Tech. 
$16.12 
14.38 
$17.48 
21.21 
$26.25 
15.41 
$31.44 
13.04 
$32.69 
14.19 
$33.58 
17.44 
$36.99 
18.7 


Standard Deviation & Return when
r=0 
price goes way above the exercise
price, you can make a lot of money.
The amount of money you could make is only limited by how high the
stock price 

Stock (20 shares, you own
10) 

Loan 


0.058 
0.14 
0.6 
0.4 

Materials 
$8.09 
17.01 
$7.09 
28.18 
$13.33 
17.97 
$16.20 
13.07 
$14.67 
16.2 
$14.04 
20.78 
$15.86 
19.25 


goes. A put works the same way, but in reverse
(with a put, you are betting that the stock will go down). However, there is no limit on how high the 

E.B.I.T. 
E.A.T.C.S. 
E.P.S. 

E.B.I.T. 
Interest 
E.A.T.C.S. 
E.P.S. 


0.0595 
0.12 
0.8 
0.2 

Telecom. 
$8.21 
13.61 
$7.22 
15.88 
$7.36 
17.5 
$6.85 
18.95 
$3.38 
43.26 
$12.31 
12.63 
$7.21 
21.16 



price of a stock will go, but it
can only go down to 0. Therefore, if
you have a call and a put both with the same parameters, the 

100 
50 
2.5 

100 
40 
30 
3 

Here we
see how the standard deviation and the return are affected by changing the
weights of stock 1 and stock 2. The
correlation coefficient in 

Utilities 
$12.25 
12.08 
$11.50 
13.74 
$12.34 
12.92 
$12.47 
14.67 
$11.97 
14.85 
$12.15 
15.91 
$13.22 
18.16 


call will be worth a little more
than the put. Anyway, back to our
spread, you must realize that you have written an option, 

200 
100 
5 

200 
40 
80 
8 

this
scenario is 0 (see Graph1). 

Real Estate 
$1.79 
43.56 
$0.99 
95.13 
$1.32 
91.14 
$2.49 
52.33 
$3.13 
48.33 
$3.31 
44.95 
$5.34 
35.22 

a 175 call as part of the
spread. If you have written an option
and do not have it covered by a long position on an option or the stock, you 
2000 
1000 
50 

2000 
40 
980 
98 

"Capital market theory builds on
portfolio theory, resulting in a model that can be used to price all risky
assets. We end up with the 

2015 EPS 
2015 P/E 
2016 EPS 
2016 P/E 
2017 EPS 
2017 P/E 
2018 EPS 
2018 P/E 
2019EPS 
2019 P/E 

Prices 

will leave yourself open to
unlimited loss if the stock goes through the roof. However, you are long (bought) the 165
call as 

10000 
5000 
250 

10000 
40 
4980 
498 

Capital
Asset Pricing Model that will tell us how to determine the required rate of
return for all risky assets."^{5} If we look at the graph
of the 









12'15 
12'16 
12'17 

the other part of the spread, so
you are covered (what ever you lose on the short side, you will gain on the 165 call that
you 

200000 
100000 
5000 

200000 
40 
99980 
9998 

efficient
frontier, the riskfree asset is on the yaxis. It has a 0 standard deviation. The covariance between the riskfree asset
and any risky asset 

S&P 500 
$100.45 
20.35 
$106.26 
21.07 
$124.13 
21.54 
$154.39 
18.28 
$169.86 
16.61 

2043.94 
2238.83 
2673.61 

are long. With this spread, you are anticipating that
the stock will finish somewhere in a range (165175). Actually, if the stock 

The growth rate of
E.P.S. will always be greater than the growth rate of E.B.I.T. whenever
financial leverage is used. With
common stock, they will be equal. 

or
portfolio of risky assets is zero.
Therefore, the variance of this portfolio is as follows: 

Con. Disc. 
$30.44 
20.4 
$33.30 
19.46 
$34.55 
22.73 
$39.55 
21.46 
$45.04 
18.84 

621.02 
647.82 
785.33 

finishes at 175 or above, you will
make the maximum you can make, $7.07. 


σ_{p}^{2}=(1WRF)^{2}σ_{i}^{2} 

WRF=the weight of the riskfree
asset 

Con. Stap. 
$24.32 
21.31 
$25.33 
21 
$27.28 
21.53 
$30.38 
19.52 
$32.81 
18.07 

518.42 
531.79 
587.39 

If you think that the underlying instrument of an option, in this case
IBM stock, is going down (you are bearish on the 


WRF=weight of the riskfree asset 

Energy 
($13.71) 
32.7 
($3.49) 
158.91 
$14.64 
36.43 
$25.02 
22.36 
$27.43 
20.4 

448.44 
554.5 
533.41 

stock), then a bear spread might be
approriate. You can write the IBM 160
call for $7.20, and buy the 170 call for $3.21, for a net inflow 

A straight
line going from the riskfree asset on the yaxis to a point tangent to the
efficient frontier and beyond is the capital market line (CML). The point 
Financials 
$23.01 
13.98 
$23.78 
16.25 
$26.72 
17.36 
$34.52 
14.44 
$38.79 
12.85 

321.73 
386.53 
463.94 

of $3.99. Remember that
the stock is at $160.96 on 07/03/16.
These options have 5˝
months till expiration. 

of
tangency to the efficient frontier is the market portfolio, point M (See
graph 5, point M is .05, .068). Any
portfolio along the line from RFR to M 

Health Care 
$38.72 
21.52 
$42.45 
18.77 
$45.72 
20.92 
$60.39 
16.88 
$65.24 
15.62 

833.23 
796.91 
956.32 

Strike 
Price 

represents
some combination of investment in the riskfree asset and the market
portfolio. Point M means that 100% of
your wealth is invested in the 
Industrials 
$28.00 
16.56 
$27.07 
19.88 
$29.18 
21.86 
$35.38 
18.94 
$39.70 
16.88 

463.53 
538.07 
637.81 

160 
$ 7.20 

market
portfolio. Any portfolio on the CML
that is above point M represents investing 100% of your wealth in the market
portfolio, and then borrowing some % of 
Info. Tech. 
$37.97 
19 
$37.99 
21.27 
$49.55 
22.32 
$61.32 
19.4 
$66.40 
17.91 

721.48 
807.95 
1106.18 

170 
$ (3.21) 

your
wealth at the riskfree rate and also investing this in the market
portfolio. Suppose that the expected
riskfree rate is 6%, and the expected return on the 
Materials 
$8.49 
32.23 
$13.01 
23.99 
$17.66 
21.46 
$21.32 
18.25 
$23.82 
16.33 

273.64 
312.16 
378.94 

Net 
$ 3.99 

market is
12%. The expected return and the
expected standard deviation from a portfolio that is invested 50% in the
riskfree asset and 50% in the 

Telecom. 
$12.15 
12.34 
$9.86 
17.9 
$10.17 
16.34 
$14.58 
11.6 
$14.90 
11.35 

149.91 
176.61 
166.07 

My net inflow is
$3.99. There is no initial investment
like with the bull spread shown above, but an initial positive cash flow, and
you hope 

market
portfolio would be as follows: 

Utilities 
$11.25 
19.55 
$13.67 
18.05 
$14.78 
18.09 
$15.57 
16.37 
$16.41 
15.54 

220 
246.83 
267.37 

that no negative cash
flows occour later. 


E(R_{port})=WRF(RFR) + (1WRF)(E(R_{m})) 

Real Estate 
$5.45 
34.89 
$7.38 
25.78 
$5.67 
35.95 
$5.05 
38.84 
$5.57 
35.2 

190.22 
190.23 
203.86 

On 1/15/17 IBM finishes
at $160. Both options expire
worthless, and you keep your $3.99 inflow. 


=.5(.06) + .5(.12) 

Stan. Dev. 
Return 

Strike 
Price 


=.03 + .06 

$2,044.16 

$2,238.90 

$2,673.76 

$2,822.25 

$2,821.37 

0.0812 
0.18 

160 
$ 



=.09 

In the row above, the P/E ratios of the index and each sector of
the index for historical data is based
on year end prices (2015 thru 2017).
The P/E ratios 

0.0662 
0.16 

170 
$ 



E(R_{port})=the expected return of the portfolio 

of estimated data are based on
current prices (very small differences are based on rounding errors). 

0.061 
0.15 

Net 
$ 



E(R_{m})=the expected return of the market 

0.058 
0.14 

Spread 
$ 3.99 


E(σ_{p})=(1WRF)(σ_{m}) 

0.0595 
0.12 

Total 
$ 3.99 

160.96 


=.5σ_{m} 

If IBM finishes at 150,
you get the same result. 

3.99 


E(σ_{p})=the expected standard deviation of the portfolio 

Strike 
Price 

164.95 


σ_{m}=the standard deviation of the market 

160 
$ 


If you
invested an amount equal to 100% of your wealth in the market portfolio, and
then borrowed an amount equal to 50% of your wealth at the 

170 
$ 


riskfree
rate and also invested this in the market portfolio, the WRF would not be
positive, but a negative 50%. Your
expected return and 

Net 
$ 


expected
standard deviation would be as follows: 

Spread 
$ 3.99 


E(R_{p})=.5(.06) + 1.5(.12) 

Total 
$ 3.99 


=.03 + .18 

If IBM finishes anywhere
from $160 or below, you make your $3.99 profit on the spread. If IBM finishes at $161, your profit will
be as follows. 


=.15 

t 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

Strike 
Price 



E(σ_{p)}=1.5(σ_{m}) 

3 
0.0013 

160 
$ 1.00 


Risk and
return increase in a linear fashion along the CML, which is above and thus
superior to the original efficient frontier.
The CML is the 

2.9 
0.0019 
0.0018 
0.0018 
0.0017 
0.0017 
0.0016 
0.0015 
0.0015 
0.0014 
0.0014 

170 
$ 



"new"
efficient frontier. "The market
portfolio, point M, is the tangent portfolio that gives the highest portfolio
possibility line. Therefore, everybody 

2.8 
0.0026 
0.0025 
0.0024 
0.0023 
0.0023 
0.0022 
0.0021 
0.0021 
0.002 
0.0019 

Net 
$ (1.00) 


will want
to invest in this risky asset portfolio M, and borrow or lend to be somewhere
on the CML. Because all investors want
this portfolio M 

2.7 
0.0035 
0.0034 
0.0033 
0.0032 
0.0031 
0.003 
0.0029 
0.0028 
0.0027 
0.0026 

Spread 
$ 3.99 


as part of
their total portfolio, all risky assets must be in the portfolio. If a risky asset were not in this
portfolio, it would have no demand, and 

2.6 
0.0047 
0.0045 
0.0044 
0.0043 
0.0041 
0.004 
0.0039 
0.0038 
0.0037 
0.0036 

Total 
$ 2.99 


therefore
no value. When the market is in
equilibrium, all assets that are included in this portfolio are in proportion
to their market value. 

2.5 
0.0062 
0.006 
0.0059 
0.0057 
0.0055 
0.0054 
0.0052 
0.0051 
0.0049 
0.0048 

If IBM finishes at
163.99, then your profit is $0. 

The market
portfolio does not include only common stocks, but also bonds, options, real
estate, coins, etc. Because the market
portfolio 

2.4 
0.0082 
0.008 
0.0078 
0.0075 
0.0073 
0.0071 
0.0069 
0.0068 
0.0066 
0.0064 

Strike 
Price 


contains
all risky assets, it is a completely diversified portfolio."^{6} 

2.3 
0.0107 
0.0104 
0.0102 
0.0099 
0.0096 
0.0094 
0.0091 
0.0089 
0.0087 
0.0084 

160 
$ 3.99 


Let me talk about systematic and
unsystematic risk. Systematic risk is
the risk associated with the overall market.
This type of risk (i.e. volatility) 

2.2 
0.0139 
0.0136 
0.0132 
0.0129 
0.0125 
0.0122 
0.0119 
0.0116 
0.0113 
0.011 

170 
$ 



is caused
by macroeconomic variables that affect all risky assets. Unsystematic risk is the risk associated
with each individual company. In the 

2.1 
0.0179 
0.0174 
0.017 
0.0166 
0.0162 
0.0158 
0.0154 
0.015 
0.0146 
0.0143 

Net 
$ (3.99) 


market
portfolio, this unsystematic risk is diversified away, and only the
systematic risk remains. Since
unsystematic risk can be eliminated through 

2 
0.0228 
0.0222 
0.0217 
0.0212 
0.0207 
0.0202 
0.0197 
0.0192 
0.0188 
0.0183 

Spread 
$ 3.99 


diversification,
the investor can only expect to be compensated for the level of systematic
risk that he assumes. Every investor
wants to invest 

1.9 
0.0287 
0.0281 
0.0275 
0.0268 
0.0262 
0.0256 
0.025 
0.0244 
0.0239 
0.0233 

Total 
$ 



in
portfolio M, the market portfolio. The
only decision is the financing decision, which depends on your risk
preferences. If you are relatively
risk 

1.8 
0.0359 
0.0351 
0.0344 
0.0336 
0.0329 
0.0322 
0.0314 
0.0307 
0.03 
0.0294 

If IBM finishes at
$170,then your profit is $0. 

averse,
you will invest some of your wealth in the riskfree asset, and the remainder
in the market portfolio. If you are
more of a risk taker, you will 

1.7 
0.0446 
0.0436 
0.0427 
0.0418 
0.0409 
0.0401 
0.0392 
0.0384 
0.0375 
0.0367 

Strike 
Price 


invest all
of your wealth in the market portfolio.
If you want to take an even higher risk (and higher expected return)
position, you could also borrow some 

1.6 
0.0548 
0.0537 
0.0526 
0.0516 
0.0505 
0.0495 
0.0485 
0.0475 
0.0465 
0.0455 

160 
$ 10.00 


portion of
your wealth at the RFR and invest it all in portfolio M. Because the only relevant portfolio is the
market portfolio, the only important consideration 

1.5 
0.0668 
0.0655 
0.0643 
0.063 
0.0618 
0.0606 
0.0594 
0.0582 
0.0571 
0.056 

170 
$ 



is
a stock's covariance with the market portfolio (Cov_{im}). The ratio of a
stock's covariance with the market over the variance of the market is equal
to 

1.4 
0.0808 
0.0793 
0.0778 
0.0764 
0.075 
0.0735 
0.0721 
0.0708 
0.0694 
0.0681 

Net 
$ (10.00) 


beta
(B_{i}=Cov_{im}/σ^{2}_{m}), (B_{i}=beta of stock i). A beta of 1 means that the covariance of a
stock with the market is equal to the market variance. A beta of 

1.3 
0.0968 
0.0951 
0.0934 
0.0918 
0.0901 
0.0885 
0.0869 
0.0853 
0.0838 
0.0823 

Spread 
$ 3.99 


2 means
that the covariance of a stock with the market is twice the market
variance. The Capital Asset Pricing
Model (CAPM) is as follows: 

1.2 
0.1151 
0.1131 
0.1112 
0.1093 
0.1075 
0.1056 
0.1038 
0.102 
0.1003 
0.0985 

Total 
$ (6.01) 



E(R_{i})=RFR + Bi(E(R_{m})  RFR) 

1.1 
0.1357 
0.1335 
0.1314 
0.1292 
0.1271 
0.1251 
0.123 
0.121 
0.119 
0.117 

If IBM finishes at 175,
you lose: 


E(Ri)=the expected return of stock i 

1 
0.1587 
0.1562 
0.1539 
0.1515 
0.1492 
0.1469 
0.1446 
0.1423 
0.1401 
0.1379 

Strike 
Price 


"The
expected rate of return for a stock is determined by the RFR plus a risk
premium that is a function of the systematic risk of a stock (B_{i}), and 

0.9 
0.1841 
0.1814 
0.1788 
0.1762 
0.1736 
0.1711 
0.1685 
0.166 
0.1635 
0.1611 

160 
$ 10.00 

the
prevailing market risk premium (R_{m}  RFR). If we expect
the economy's RFR to be .08 and the return of the market (Rm) to be .14, then
the 

0.8 
0.2119 
0.209 
0.2061 
0.2033 
0.2005 
0.1977 
0.1949 
0.1921 
0.1894 
0.1867 

170 
$ 5.00 

expected
return for a stock with a beta of .7 would be as follows: 

0.7 
0.242 
0.2389 
0.2358 
0.2327 
0.2296 
0.2266 
0.2236 
0.2206 
0.2177 
0.2148 

Net 
$ (10.00) 


E(Ri)=.08 + .7(.14  .08) 

0.6 
0.2743 
0.2709 
0.2676 
0.2643 
0.2611 
0.2578 
0.2546 
0.2514 
0.2483 
0.2451 

Spread 
$ 3.99 


=.122 

0.5 
0.3085 
0.305 
0.3015 
0.2981 
0.2946 
0.2912 
0.2877 
0.2843 
0.281 
0.2776 

Total 
$ (6.01) 

Beta is a
normalized measure of systematic risk."^{7} As I stated before,
this systematic risk is the only risk that the investor can expect to be 

0.4 
0.3446 
0.34 
0.3372 
0.3336 
0.33 
0.3264 
0.3228 
0.3192 
0.3156 
0.3121 

If IBM finishes at $160
or below, you make a maximum profit of $3.99, (the $10 difference in the
strike prices less the maximum loss of $6.01). 

compensated
for. The relationship between the
expected return of a stock and it's beta is shown in graph 4. The diagonal line is the Security Market 

0.3 
0.3821 
0.3783 
0.3745 
0.3707 
0.3669 
0.3632 
0.3594 
0.3557 
0.352 
0.3483 

If IBM finishes at $170
or above, you lose a maximum of $6.01, (the $10 difference in the strike
prices less your initial inflow of $3.99). 

Line
(SML). The RFR, which is 5%, is where
the SML intersects the yaxis (point 0).
The M portfolio (point 1), with an expected return of 15% and a beta
of 1, 

0.2 
0.4207 
0.4168 
0.4129 
0.409 
0.4052 
0.4013 
0.3974 
0.3936 
0.3897 
0.3859 

$3.99+$6.01=$10, the
difference in the strike prices. 

is where
the SML intersects the horizontal and vertical lines. When markets are efficient and in
equilibrium, all assets or portfolios of assets should plot on the 

0.1 
0.4602 
0.4562 
0.4522 
0.4483 
0.4443 
0.4404 
0.4364 
0.4325 
0.4286 
0.4247 

SML. Any security that is above the SML is
underpriced because it's estimated return would be above what is required
from a security with this level 

.0 
0.5 
0.496 
0.492 
0.488 
0.484 
0.4801 
0.4761 
0.4721 
0.4681 
0.4641 

of
systematic risk. In contrast, any
security that is below the SML would be overpriced, because its estimated
return would be below what is required from a 

security
with this level of systematic risk. In
the example above, the required return is 12.2%. If the estimated return for the upcoming
period 

.0 
0.5 
0.504 
0.508 
0.512 
0.516 
0.5199 
0.5239 
0.5279 
0.5319 
0.5359 

is higher
than this, then the stock is underpriced.
Securities' markets are pretty much efficient, but not completely
efficient. There are times when 

0.1 
0.5398 
0.5438 
0.5478 
0.5517 
0.5557 
0.5596 
0.5636 
0.5675 
0.5714 
0.5753 

not
everyone is aware of all the relevant informationabout a security. If an analyst can derive estimates of
returns that are consistently superior to the 

0.2 
0.5793 
0.5832 
0.5871 
0.591 
0.5948 
0.5987 
0.6026 
0.6064 
0.6103 
0.6141 

aggregate
market's estimates, then he will be able to earn above average returns on a
riskadjusted basis. 

0.3 
0.6179 
0.6217 
0.6255 
0.6293 
0.6331 
0.6368 
0.6406 
0.6443 
0.648 
0.6517 

The systematic risk of an asset can be
calculated with a statistical methodology called linear regression, which
allows you to derive an asset's characteristic 

0.4 
0.6554 
0.6592 
0.6628 
0.6664 
0.67 
0.6736 
0.6772 
0.6808 
0.6844 
0.688 

line with
the market portfolio of the following form: 

0.5 
0.6915 
0.695 
0.6985 
0.7019 
0.7054 
0.7088 
0.7123 
0.7157 
0.719 
0.7224 


E(R_{it})=α_{i} + B_{i}R_{mt} + e 

0.6 
0.7257 
0.7291 
0.7324 
0.7357 
0.7389 
0.7422 
0.7454 
0.7486 
0.7517 
0.7549 



E(R_{it})=the expected rate of return for asset i during period t 

0.7 
0.758 
0.7611 
0.7642 
0.7673 
0.7704 
0.7734 
0.7764 
0.7794 
0.7823 
0.7852 


R_{mt}=the rate of return for the market portfolio during period t 

0.8 
0.7881 
0.791 
0.7939 
0.7967 
0.7995 
0.8023 
0.8051 
0.8078 
0.8106 
0.8133 


B_{i}=beta of asset i 

0.9 
0.8159 
0.8186 
0.8212 
0.8238 
0.8264 
0.8289 
0.8315 
0.834 
0.8365 
0.8389 


α_{i}=constant term for asset
i 

1 
0.8413 
0.8438 
0.8461 
0.8485 
0.8508 
0.8531 
0.8554 
0.8577 
0.8599 
0.8621 


e=random error term 

1.1 
0.8643 
0.8665 
0.8686 
0.8708 
0.8729 
0.8749 
0.877 
0.879 
0.881 
0.883 

The
characteristic line is the line of best fit through a scatter plot of rates
of return for asset i, coinciding with market rates of return over some past 

1.2 
0.8849 
0.887 
0.8888 
0.8907 
0.8925 
0.8944 
0.8962 
0.898 
0.8997 
0.9015 

time
period. The characteristic line is
positioned in such a way that the summation of (yi  Yi)^2 is minimized. It is located in such a way as to 

1.3 
0.9032 
0.9049 
0.9066 
0.9082 
0.9099 
0.9115 
0.9131 
0.9147 
0.9162 
0.9177 

minimize
the sum of the squares of the errors, thus it is called the leastsquares
method. 

1.4 
0.9192 
0.9207 
0.9222 
0.9236 
0.9251 
0.9265 
0.9279 
0.9292 
0.9306 
0.9319 

y_{i}=value of y for
observation i 

1.5 
0.9332 
0.9345 
0.9357 
0.937 
0.9382 
0.9394 
0.9406 
0.9418 
0.9429 
0.9441 

Y_{i}=predicted value of y
for observation i 

1.6 
0.9452 
0.9463 
0.9474 
0.9484 
0.9495 
0.9505 
0.9515 
0.9525 
0.9535 
0.9545 

Consider
the following example of the computation of the beta coefficient for IBM in
1979 relative to the S&P 500 
E(R_{IBM})=1.1% 


1.7 
0.9554 
0.9564 
0.9573 
0.9582 
0.9591 
0.9599 
0.9608 
0.9616 
0.9625 
0.9633 

B=Cov_{IBM},_{m}/σ_{m}^{2} 

σ^{2}_{IBM}=14.73 
σ_{m}^{2}=13.786 
B=11.111/13.785 

E(R_{m})=1.04% 

1.8 
0.9641 
0.9649 
0.9656 
0.9664 
0.9671 
0.9678 
0.9686 
0.9693 
0.97 
0.9706 

B=beta 


σ_{IBM}=3.838 

σ_{m}=3.713 
B=.806 

1.9 
0.9713 
0.9719 
0.9726 
0.9732 
0.9738 
0.9744 
0.975 
0.9756 
0.9761 
0.9767 

Cov_{IBM},_{m}=the covariance or the
returns for IBM and the S&P 500 
r=Cov_{IBM,M}/σ_{IBM}σ_{m} 

α= 
1.93824 

2 
0.9772 
0.9778 
0.9783 
0.9788 
0.9793 
0.9798 
0.9803 
0.9808 
0.9812 
0.9817 

=11.111 

r= 
0.78 

α=E(R_{IBM})B*E(R_{m)} 

2.1 
0.9821 
0.9826 
0.983 
0.9834 
0.9838 
0.9842 
0.9846 
0.985 
0.9854 
0.9857 

σ_{m}^{2}=the variance of the returns for the market 




α=1.1(.806*1.04) 

2.2 
0.9861 
0.9864 
0.9868 
0.9871 
0.9875 
0.9878 
0.9881 
0.9884 
0.9887 
0.989 

=13.785 
σ_{m}=3.713 


Characteristic Line= 
R_{IBM}=1.94 + .806(R_{m}) 

2.3 
0.9893 
0.9896 
0.9898 
0.9901 
0.9904 
0.9906 
0.9909 
0.9911 
0.9913 
0.9916 

This is
the simple linear regression model, with the market returns as the
independent variable x, and the stock returns (IBM) as the dependent 

2.4 
0.9918 
0.992 
0.9922 
0.9925 
0.9927 
0.9929 
0.9931 
0.9932 
0.9934 
0.9936 

variable
y. This model measures the type and
extent of the relationship between variables.
Excel and Lotus both have a linear regression function 

2.5 
0.9938 
0.994 
0.9941 
0.9943 
0.9945 
0.9946 
0.9948 
0.9949 
0.9951 
0.9952 

that
automatically calculates the above values.
There are many services that calculate betas for stocks. Yahoo, for instance, gives you a beta for
each stock. 

2.6 
0.9953 
0.9955 
0.9956 
0.9957 
0.9959 
0.996 
0.9961 
0.9962 
0.9963 
0.9964 

The number of observations and the time
interval between them used to calculate the characteristic line varies
amongst services. Value Line 

2.7 
0.9965 
0.9966 
0.9967 
0.9968 
0.9969 
0.997 
0.9971 
0.9972 
0.9973 
0.9974 

Investment
Services uses weekly rates of return over a 5 year period. Other services use monthly rates of return
over a 5 year period. 

2.8 
0.9974 
0.9975 
0.9976 
0.9977 
0.9977 
0.9978 
0.9979 
0.9979 
0.998 
0.9981 

There is
no set limit on how many observations to use or the interval between them..
You want to use enough observations to get an accurate picture of the 

2.9 
0.9981 
0.9982 
0.9982 
0.9983 
0.9984 
0.9984 
0.9985 
0.9985 
0.9986 
0.9987 

characteristic
line, but not so many that you are going so far back in time that the company
may have changed a lot. Typically, the
S&P 500 is used 

3 
0.9987 

as
a proxy for the market portfolio when determining the characteristic
line. We must remember that we are
using historical data to estimate the future 

beta for
an asset. "Studies have shown that betas for individual stocks over
short periods are rather unstable, but the stability of portfolio betas over
longer 

periods
increased dramatically."^{8} 

N(d_{1})=N(.808)=.790 

If the estimated return of a stock is
equal to the expected return, then the stock will plot on the SML (Graph 4),
and it is properly valued. If the 

N(d_{2})=N(.612)=.729 

estimated
return is greater than the expected return, then the stock will plot above
the SML and it would be undervalued.
If the estimated return is 

less than
the expected return, then the stock would plot below the SML and it would be
overvalued. 


The expected return is synonymous
with the required return. It is the
return that the investor requires from a stock, a portfolio, or the 

market as
a whole. The CAPM shows how the systematic risk of an asset, Beta (B),
determines the investor's required rate of return and thus it's 

value. The separation theorem implies that
everyone will want to invest in this mythical market portfolio, the only
difference between investors is how 

they will
finance this investment. First of all,
there is no portfolio that contains all risky assets. Also, if you can not borrow at the RFR, how
can you attain a 

highrisk
portfolio? Although the mythical
"market" portfolio containing all risky assets (stocks, bonds, real
estate, coins, stamps, antiques, etc.) does not 

exist, an
investor can acquire a diversified portfolio of some of these assets that
would be highly correlated with the
market portfolio. It is possible 

to acquire
welldiversified portfolios of stock through large, balanced mutual
funds. These funds are highly
correlated the S&P 500 index. You
can also 

acquire
welldiversified portfolios of municipal, government, or corporate bonds
through fixedincome mutual funds. A
real estate investment trust (REIT) 

can
provide a diversified portfolio of real estate. If you can not borrow and leverage your
portfolio, and you want to have a portfolio with a beta of 1.3, 

you can
simply build a welldiversified portfolio of stocks with a weighted average
beta of 1.3. 

The question is whether or not the CAPM
can explain the returns of risky assets.
Is there a positive relationship between systematic risk (beta) and
return? 

"A
study by Sharpe and Cooper generally supports a positive relationship,
although it was not completely linear.
In the highest risk classes, there was 

a tendency
for returns to level off and even decline slightly. This study also shows that betas for
portfolios were stable."^{9} 

An investor wants to analyze the
performance of their investment portfolio,
whether they do their own analysis or have it done by a professional
money 

manager. If you do their own analysis, you want to
see if the time and effort spent was worth it in terms of results. If you paying a professional 

money
manager (through a mutual fund or an investment counselor), you need to
evaluate his performance and determine if the results are worth 

what he is
charging you. We will now take a look
at how we evaluate portfolio performance.
We will examine three composite performance measures 

that
determine risk and return. When
evaluating the performance of portfolio managers, we will consider two major
factors. First, we will look at the 

ability to
derive above averagereturns for a given riskclass. Also, we will look at the ability to
diversify, and thus eliminate all unsystematic risk 

from the
portfolio. Superior riskadjusted
returns can be achieved through superior timing or superior stock
selection. The "superior
analyst" can 

consistently
select stocks that plot above the SML (see graph 4). The level of diversification in a portfolio
can be determined by a portfolio's 

Stan. Dev. 
Return 

correlation
with the market portfolio, which is completely diversified. 

0.12 
0.22 

We will now take a look at different
methods of ranking portfolio managers' riskadjusted return performance. The first composite performance measure 

0.12 
0.21 

we will
look at is the Treynor method, developed by Jack Treynor in an article in the
"Harvard Business Review" ^{10} 
^{} 

0.12 
0.2 

The Treynor
performance measure (T) is as follows: 

0.12 
0.19 


T_{i}= 
R_{i}RFR 

0.12 
0.18 


B_{i} 

0.11 
0.21 


T_{i}=the Treynor performance measure for portfolio i during a given
time period 

0.11 
0.2 


R_{i}=the average rate of return for portfolio i during a given time
period 

0.11 
0.19 


RFR=the average riskfree rate
during a given time period 

0.11 
0.18 

Graph 2 


B_{i}=the beta of the portfolio i, which indicates relative
volatility and systematic risk 

0.11 
0.17 

The Efficient Frontier 

"
Another measure of portfolio performance is the Sharpe measure, developed by
William F. Sharpe that was designed to evaluate the performance of 

0.1 
0.19 

mutual
funds. The Sharpe measure is as
follows: 

0.1 
0.18 




Si= 
R_{i}RFR 

0.1 
0.17 



σ_{i} 

0.1 
0.16 



S_{i}=the Sharpe portfolio performance measure for portfolio i
during a given time period 

0.1 
0.15 



R_{i}=the average rate of return for portfolio i during a given time
period 
P 

0.09 
0.17 



RFR=the average riskfree rate
during a given time period 

0.09 
0.16 



σ_{i}=the standard deviation of portfolio i 

0.09 
0.15 


The
difference between the two measures is that the Treynor measure uses beta,
the systematic risk, as the denominator, while the Sharpe measure uses the 

0.09 
0.14 


standard
deviation, the total risk, as the denominator. "The Sharpe measure not only evaluates
a portfolio manager on the basis of return performance, but also 

0.09 
0.13 


measures
how well diversified the portfolio is.
If a portfolio is perfectly diversified, (i.e. does not contain any
unsystematic risk), the two measures would 

0.08 
0.14 


give
identical rankings, the total variance would equal the systematic
variance. In a welldiversified
portfolio such as a mutual fund, the two measures 

0.08 
0.13 


will give
very similar rankings. The Jensen
measure is another composite performance measure, and like the others it is
based on the Capital Asset 

0.08 
0.12 


Pricing
Model. If this model is empirically
valid, we can express the expectations formula in terms of realized rates of
return. 

_{} 

0.08 
0.11 



R_{jt}=RFR_{t} + B_{j}(R_{mt}  RFR_{t}) + U_{jt} 

0.08 
0.1 



R_{jt}=the realized rate of return on portfolio j during time period
t 

0.07 
0.11 



RFR_{t}=the riskfree rate during time period t 

0.07 
0.1 



B_{j}=the beta of portfolio j 

0.07 
0.09 


U_{jt}=random error term 

0.07 
0.08 

Subtract
the RFR_{t} from both
sides. 

0.07 
0.07 


R_{jt}  RFR_{t}=B_{j}(R_{mt}  RFR_{t}) + U_{jt} 



0.06 
0.07 

If a
portfolio manager is superior because he can forecast market turns or
consistently select undervalued securities, the risk premium he experiences 

0.06 
0.06 

will
exceed the premium implied by the model.
The superior portfolio manager will have consistently positive random
error terms. His actual returns will 

0.06 
0.05 

consistently
be above the expected returns. In
order to measure this superior performance,
we will have to allow for an intercept that measures these 

0.06 
0.04 

positive
residuals. This intercept is alpha,
and if it is positive, it measures how much the actual returns are above the
expected returns. 

0.06 
0.03 


R_{jt}  RFR_{t}=α_{j} + B_{j}(R_{mt}  RFR_{t}) + U 

0.05 
0.06 


α_{j}=alpha of portfolio j 

0.05 
0.05 

If a
regression of the portfolio j risk premium (Rjt  RFRt) and the market risk
premium (Rmt  RFRt) indicates a positive, statistically significant
intercept, 

0.05 
0.04 

then this
intercept shows how much the portfolio's riskadjusted return exceeds the
aggregate market's return. However, if
these residuals 

0.05 
0.03 

are
consistently negative, the alpha will be negative. This indicates an inferior portfolio
manager. His actual returns will
consistently 

0.05 
0.02 

be below
the expected returns. An alpha of zero
indicates that the portfolio manager has essentially matched the expected
return. 

The
correlation coefficient, R squared, is a good measure of
diversification. A correlation
coefficient of 1 means the portfolio is perfectly 

correlated
with the market. This portfolio is
just as diversified as the market is. 

The above mentioned portfolio
performance measures can be used to evaluate openend mutual funds. The return for each year for these funds 

Graph 3 

can be
calculated as follows. 

Eff. Fron. 

Stan. Dev. 
Return 





R_{it}= 
EP_{it} + Div_{it} + Cap Dist_{it}  Bp_{it} 

0.12 
0.22 




Bp_{it} 



0.11 
0.2 


R_{it}=the return for fund i during year t 


0.1 
0.19 


Ep_{it}=the ending price for fund i during year t 


0.09 
0.17 


Div_{it}=the dividend payment made by fund i during year t 


0.08 
0.14 


Cap Dist_{it}=capital gain distributions made by fund i during year t 


0.07 
0.11 


Bp_{it}=the beginning price for fund i during year t 


0.06 
0.07 

Mutual
funds provide a convenient way to achieve instant diversification in a
certain area. There are many
different types of mutual funds that invest 


0.05 
0.06 

in
different types of stocks and bonds.
Mutual funds may be very appealing to investors with neither the time
nor the inclination to do fundamental analysis 


themselves. They offer a wide variety of investments in
terms of risk and return. There are
two main types of mutual funds, closedend and 


openend
funds. Both of these types of mutual
funds begin like any other publicly held company, with an initial offering of
stock to investors. 


The
difference between these two types of funds is what they do after this. The closedend mutual fund, again like any
other publicly held company, 


has stock
that trades on a secondary market, and the price of it's shares depends on
supply and demand. When buying or
selling shares of a 


closedend
fund, the investor pays a regular trading commission. There are no additional shares offered
after the initial offering, and the company 


does not
repurchase shares on demand. The net
asset value (NAV) is the total market value of all the securities in the fund
divided by 


the number
of shares of the fund outstanding.
Surprisingly, the NAV and the market price of the fund's shares are
almost never the same. 


Typically,
the market price of the shares is 5 to 20 percent below the NAV. An openend mutual fund continues to sell
shares after the initial 


offering
is made. They sell shares at the NAV
of the fund, with or without a sales charge.
Also, they stand ready to buy back shares at the NAV 


at any
time, with or without a sales charge.
Openend mutual funds are either load or noload. A load fund charges a sales fee when the 

fund is
initially offered. This sales fee is
usually 7.5  8 percent of the NAV. If
we assume an 8 percent load, then an investor with $1,000 will 

only
receive $920 worth of securities. A
load fund typically will not charge a redemption fee, which means they redeem
their shares at the NAV. 

A load
fund is listed with a bid and an ask price.
The bid price is the redemption price, which is the NAV. The asking price is the NAV divided 

by .92,
assuming an 8 percent load. A noload
mutual fund does not charge a sales fee with the initial offering. There might be a small 

redemption
fee with these funds of onehalf of one percent. The bid price of a noload fund is the NAV,
which is the redemption price. 

The ask
price is also the NAV. Mutual funds
fall into several categories, depending on the type of securities they invest
in. There are 

funds that
invest only in common stock. Some
funds emphasize "growth" stocks.
These are stocks of companies that retain a lot of 

their
earnings (as opposed to paying a high dividend), thus creating capital gains
for the investor. Some funds
concentrate on stocks of companies 

that
payout a large percentage of their earnings as dividends. There are index funds that invest in a
cross section of stocks in a particular 

series,
such as the S&P 500. Their intent
is to match the return of the series.
There are mutual funds that concentrate on bonds, in order to 

produce
current income. Some invest solely in
highgrade corporate bonds, while others may hold a combination of different
grades of 

bonds. There are funds that concentrate on
municipal bonds, which are not subject to federal taxes. There are balanced funds, that invest 

in both
stocks and bonds. Finally, there are
money market funds, which invest in a variety of shortterm securities such
as treasury bills, bank 

certificates
of deposit, bank acceptances, and commercial paper. As you can see, there are mutual funds to
suit almost any need. 

There have
been a lot of studies that have examined the performance of mutual funds, and
the results have been very consistent. 

If you do
not consider the expenses of running the fund (gross returns), about half the
funds performed better than the market, and the 

other half
performed worse. This is what you would expect with random selection. If you consider the expenses of running the
fund (net returns), 

only about
onethird of funds do better than the market, and twothirds do worse. Also, funds were not consistent in their
performance. 

If you had your own portfolio manager,
these are some of the functions you would want him to perform. First, you would want him to 

S&P 500 
Rm 
RIBM 
RmE(Rm) 
RIBME(RIBM) 

Points on characteristic
line (tab 1 page over for graph of characteristic line) 

determine
your riskreturn preferences and develop a portfolio that is consistent with
what you want. You would want him to
diversify your 

12 
96.11 

x 
y 

portfolio
to eliminate unsystematic risk, and monitor your portfolio to maintain
diversification, and make sure you remain in your desired risk class. 

1 
99.93 
3.97 
3.4 
2.93 
4.5 
13.185 

8.5849 
20.25 

10 
10 

You would
want him to attempt to achieve a riskadjusted performance that is superior
to the aggregate market (a positive, statistically significant 

2 
96.28 
3.65 
2.8 
4.69 
1.7 
7.973 

21.9961 
2.89 

9 
9.194 

alpha,
using the Jensen portfolio performance measure). Also, the portfolio manager needs to know
what your investment objectives are.
He 

3 
101.59 
5.52 
5.2 
4.48 
6.3 
28.224 

20.0704 
39.69 

8 
8.388 

needs to
know what your cash flow objectives are for your portfolio, and the
implications this may have on your tax situation. If you are a small 

4 
101.76 
0.17 
0.4 
0.87 
0.7 
0.609 

0.7569 
0.49 

2 
3.552 

investor,
you may not have the resources to buy 100 shares of 10 or 12 different issues
in order to achieve diversification.
In such cases, 

5 
99.08 
2.63 
3.3 
3.67 
2.2 
8.074 

13.4689 
4.84 

0 
1.94 

mutual
funds can provide diversification for an investment as low as $1000. The investor can acquire a portfolio that
is .9 correlated with the 

6 
102.91 
3.87 
2.8 
2.83 
1.7 
4.811 

8.0089 
2.89 

2 
0.328 

market
portfolio, and thus it is 90 percent diversified. 

7 
103.81 
0.87 
5.6 
0.17 
4.5 
0.765 

0.0289 
20.25 

8 
4.508 

The CAPM sounds good, but the test of
any theory should be how well it explains relationships that exist in the
real world. Two questions 

8 
109.32 
5.31 
0.4 
4.27 
1.5 
6.405 

18.2329 
2.25 

10 
6.12 

arise when
considering the CAPM. Is there are
positive relationship between beta and the rate of return on risky
assets. Also, how stable is 

9 
109.32 
0 
3.2 
1.04 
2.1 
2.184 

1.0816 
4.41 

beta, the
measure of systematic risk. As I
stated before, we are using past betas to estimate future risk. " A
study by Sharpe and Cooper 

10 
101.82 
6.86 
7.9 
7.9 
6.8 
53.72 

62.41 
46.24 

generally
showed that there is a positive relationship between beta and rates of
return, although it might not be completely linear."^{11} Specifically, 

11 
106.16 
4.26 
4.6 
3.22 
5.7 
18.354 

10.3684 
32.49 

rates of
return tend to level off for the highest risk classes. "This study, like others by Blume and
Levy, show stability in beta over time, 

12 
107.94 
1.68 
1.3 
0.64 
0.2 
0.128 

0.4096 
0.04 

especially
with larger portfolios (25 or 50 stocks).
Blume found that in portfolios
of 20 or more stocks, the correlation with the market, R squared, 

1.04 
1.1 

133.336 

165.4175 
176.73 

ranged
from .93 to .98."^{12} In general, most
studies show that portfolio betas are very stable over short and long
runs. These results are 

encouraging
for investors who want to use beta as a measure of future risk of a
portfolio. 

CovIBM,m=133.336/12=11.111 

r=CovIBM,m/σIBM*σm 
14.7275 

13.78479 

y=1.94 + .806x 
1.94 

Many portfolio managers use the S&P
500 as a market proxy. However, all of
the above mentioned performance measures are 

σ2m=∑((RmtE(Rm)2/N 

0.77969 

σ2IBM = 
14.7275 

0.806 

essentially
based on the CAPM which is based on the idea of a "market
portfolio", that is the point of tangency between the 

13.78479 

α=E(R_{IBM})BE(R_{m}) 

σIBM = 
3.837643 

2.09 

Markowitz
efficient frontier and the SML (see graph 6).
This theoretical "market
portfolio" should contain all risky assets in the economy, 

13.785 

1.1 

α=1.10.806(1.04) 

stocks as
well as bonds, gold, real estate, coins, stamps, etc. The fact that this "market
portfolio" does not in reality exist does not 

B=11.111/13.785 
0.83824 

1.93824 

negate the
usefulness or the CAPM. The analyst
must realize that the true SML could have a higher slope because the true
efficient frontier 

0.806021 

1.93824 

x 
y 

3.82 

could be
higher than the one that was derived by using the S&P 500 as a market
proxy. The portfolio manager might
want to adjust his performance 

σm=13.785.5 

2 
3.552 

0.039746 

targets to
account for this. 

3.712816 

1 
2.746 

I think that I have done enough
explaining, so lets do some actual analysis.
We will start with an analysis of the aggregate market. We will use 

E(RIBM)=1.94 + .806E(Rm) 

0 
1.94 

the
S&P 500 as a proxy for the market.
First, let's take a look at the last several quarters' payout ratio,
return on equity, and the growth rate for 

1.10176 

1 
1.134 



dividends
and earnings for the S&P 500, as well as some earnings estimates for the
S&P 500. It was demonstrated
earlier that with an ROE of 

2 
0.328 

Note: To see the scatter plot of
estimated returns for IBM and the S&P 500, page down. 


around
15%, and a retention ratio of 70%, the current annual growth rate of earnings
and dividends should be 10.5%. On
12/31/14, the expected 

3 
0.478 

The characteristic line that was
fitted from the scatter plot with the 


dividend
yield on the S&P 500 was 2.00%, and thus the expected return per share on
the S&P 500 was 12.5%. 

4 
1.284 

leastsquares method is a page over. 









5 
2.09 



2/1/2018 

Note: The annual growth rate in earnings of the
S&P 500 that is shown by the formula g=b x ROE 










S&P 500 
2763.13 

of 10.38%. The growth
rate for the S&P 500 shown 1 page dowm of 13.4% is the 5 yr. prog. annual 











OP EARN 
P/E 
Div. 
D/P 
D/E 
growth rate. This is the rate that is used in the
valuation model P=Div_{1/}/(ig). 












2018 EST 
154.39 
17.90 
50.630 
1.83% 
32.79% 













2019 EST 
169.86 
16.27 




































The
5 year average annual growth rate in earnings from 2018 to 2019 forecasted by
S&P (13.4%) is higher than the growth rate (10.4%)forecasted using b x
ROE. This is because 







this
formula only accounts for earnings growth that results from capital raised by
retaining earnings. It does not
account for growth that comes 







from
capital that comes from other sources, like taking on more debt. You can raise EPS by simply increasing the
% of total assets that are 







financed
by debt. However, this additional debt
increases the degree of financial leverage that the market has, and
consequently increases the 







level of
risk for the market. 







b=retention
ratio 






ROE=return
on equity 






"Let
me point out that the earnings estimates that we are using are bottom up
estimates. These are estimates that
are built from the Capital IQ consensus 






estimates
for specific issues, building from the bottom up to the index level
estimate. There are also estimates
known as top down estimates, which 
0.1523 





incorporate
economic and financial models to produce estimates, and do not come down from
the issue level. The earnings
estimates that I have been 






using in
"investmentvaluationforyou.com have been bottom up estimates. Actual numbers are always bottom up, while
estimates are bottom up or 





top
down. The current expected dividend
yield for the S&P 500 is 1.83%, and the current expected earnings and
dividend growth is approximately 





13.4%"^{13}. With i=D/p+g, we have i=15.23%, as I have
shown. 











Note: The above narrative begins 10 pages up and
continues about 4 more pages down. It
is a column beginning in the upper left hand corner of this spreadsheet, and
if you page down about 





15 pages
you will get to the end of this first section in this web site. If you have read to this point, continue
paging down to the end of this first section.
If you go to the top of this column of pages, 





you
will find S&P earnings estimates
for 2015 to the right. There
are earnings estimates for the index, as well as estimates for each sector of
the S&P 500. Immediately to the
right of this section you 


will
find the section about options. If you
page down from there you will get to the section about the "Black
Scholes Option Pricing Model. If you
page up 6 pages and over 1 page you will find a table 


showing
EPS and P/E for the S&P 500 for the years 20082015. If you page over again you will find Graph
1, showing the risk and return for a particular investment. If you page down 3 pages from there, you 


will
find several graphs that are referred to in the opening narrative (the first
column of pages). If you page down 1
page from Graph 3, you will find the results of a simple linear regression of the 


returns
of IBM and the S&P 500. 1 page
down from there is a scatter diagram of these returns, and 1 page over is the
resulting characteristic line from this regression. If you page down 2 times
from 



Riskadjusted performance
measurement methods 

there you will find Graph 4, and
page down 3 times to find Graph 5. 



Treynor 

Sharpe 

Jensen 



T_{i}= 
R_{i}RFR 

S_{i}= 
R_{i}RFR 
E(R_{j})=NRFR+[E(R_{m})NRFR] 



Β_{i} 

σ_{i} 



Review of formulas 



α=E(R_{i})B*E(R_{m}) 





Modern Portfolio Theory 

NRFR=nominal riskfree
rate 



Cov_{ij}= 
∑(R_{i}E(R_{i})) (R_{j}E(R_{j}))/n 



i=estimated return 



r= 
Cov_{im} 





h_{i}m 




Standard Deviation of a two asset
portfolio 


σ_{port}=√∑W_{i}^{2}σ_{i}^{2}+2∑∑W_{i}W_{j}Cov_{ij} 



a 
b 



Capital Asset Pricing
Model 


E(R_{i})=RFR+B_{i}(R_{m}RFR) 

NRFR=RFR 
NRFR= 
2.87% 

α=E(R_{i})B_{i}(E(R_{m})) 


B= 
Cov_{im} 

RP=E(R_{m})NRFR 
E(R_{m})= 
15.23% 

α=alpha 


σ_{m} 

RP= 
12.36% 

E(Ri)=expected return of
security i 


Beta is a normalized measure of
systematic risk 

E(Rm)=expected return of
the market 


S&P 500 


Present Value of
Dividends Model 

2/1/2018 



2/1/2015 


P= 
Div_{1} 
i= 
D/P+g 

Price 
2762.13 

P=Div_{1}/(ig) 
2762.13 
Price 
2762.13 

Beta 
Return 


(ig) 
D/P= 
(ig) 

Div_{1} 
50.63 

i=D/P+g 
15.23% 
P/E 
17.89 

0 
0.15 
Horizontal Line 


g= 
bxROE 

D/P 
1.83% 

EPS_{1}= 
154.39 

0.2 
0.15 





(ig) 
1.83% 

0.4 
0.15 


P= 
2762.13 

ROE 
15.4% 

g=b x ROE 
10.32% 
However, this g is the growth
generated from b X ROE. 

0.6 
0.15 


PO 
33% 

As I stated earlier, growth can come
from other sources, like 

0.8 
0.15 




b 
67% 



taking on more debt. S&P has the
5 year expected average annual growth 

Market 
1 
0.15 
Intersection of Diagonal,
Vertical, and Horizontal Lines 




g 
13.40% 

rate for the index over
the next 5 years to be 13.4% as of 02/02/18. 

1 
0.13 
Vertical Line 

I chose to use the Jensen measure
(α) and the Treynor measure because they both look at systematic
risk. Remember that since
nonsystematic risk 

1 
0.11 

can
be diversified away, the market will only compensate you for the systematic
risk that you assume. There is some
discrepancy in the rankings of 

1 
0.09 

the
two methods, however both methods agree on the top five sectors, and these
are the only sectors that have positive alphas. That does not mean 

1 
0.07 

that
you can't find stocks with forecasted positive alphas in the lower five
sectors, but you will find more stocks with forecasted positive alphas in the 

1 
0.05 

top
five sectors. We are now at the stage
where we can start looking at individual stocks. We want to determine the beta of a stock,
and then estimate 

1 
0.03 

the
return on the stock. We then determine
what the market's required return on this stock should be, and then select
stocks that have an estimated 

1 
0.01 

risk
adjusted return that is greater than their required return. 

SML 
Market 
1 
0.15 
Diagonal Line 

The investor must now decide what his
investment objectives are. Is the
investor looking for capital gains, or is he looking for stocks that payout 

0.8 
0.13 

most
of their earnings in dividends? The
type of stock selected is a function of the investor's overall goals for his
portfolio. The investor might be 

0.6 
0.11 

quite
wealthy, and he does not need current cash flow from his investments. This is the type of investor who wants
stocks that retain most of their 

0.4 
0.09 

earnings,
producing capital gains. Other types
of investors may need current income from their investments, and they look
for stocks that payout 

0.2 
0.07 

a
large portion of their earnings in dividends.
This type of investor might prefer to invest in bonds, which produce
interest payments (usually twice 

NRFR 
0 
0.05 

a
year). Remember, dividends and
interest payments are taxable when they are received (a small amount of
dividends are deductible, but the 

rest
are taxed). Capital gains are not
taxable until you sell the stock and realize the gain. Also, the tax rate on capital gains is
lower than it is 

on
regular income. If you already have
enough current income to live on, then you can just hang on to your stocks
and the capital gains will not 

be
taxed until you sell them. If you
never sell them, then you will never pay taxes on the capital gains. If you do finally sell the stock, you will 

have
to pay taxes on the capital gains, but chances are that if you wait long
enough your tax rate will decline. 

The individual investments in an
investor's portfolio are a function of the investor's overall wealth
position, his tax situation, income requirements, 


and
age. All these factors go into
determining the investor's risk tolerance.
Age alone is a big factor. If
you are young, have a job that provides you 

income
to cover your living expenses, you have a fairly high risk tolerance. You can withstand some volatility in your
portfolio's return. However, 

if
you are older, maybe retired, then your risk tolerance goes down. You can withstand less volatility, and you
may need to draw some income from 

your
portfolio. Bonds may be suitable. However, interest rates are so low these
days that you might want to try some stocks that have a high 



dividend
yield. S&P has a web site (it is
free). Select S&P 500, and then
click on additional information. Take
a look at the Dividend Aristocrat 

file. This file contains stocks that have 25
years of increasing dividends, with liquidity and market value
restrictions. The Index Earnings file 

is
where I get all my S&P 500 and individual sector earnings data. 




12/29/2017 


INDEX
NAME 


Price 
EPS_{1} 
P/E 
Div_{1} 
PO 
b 
D/P 
S&P 500 5 yr. Proj. Annual Growth % 

S&P 500 


2762.13 
$154.39 
17.89 
$ 50.53 
33% 
67% 
1.83% 
13.4% 




S&P
500 Consumer Discretionary 

785.33 
$39.55 
19.86 
$ 13.05 
33% 
67% 
1.66% 
19.88% 



S&P 500 
S&P 500 5YR 

S&P
500 Consumer Staples 

587.39 
$30.38 
19.33 
$ 10.03 
33% 
67% 
1.71% 
9.16% 



2018 EST 
PROJ ANNUAL 

S&P
500 Energy 

533.41 
$25.02 
21.32 
$ 8.26 
33% 
67% 
1.55% 
30.47% 



OPER P/E 
GROWTH % 

S&P
500 Financials 

463.94 
$34.52 
13.44 
$ 11.39 
33% 
67% 
2.46% 
10.64% 



18.28 
13.4 

S&P
500 Health Care 

956.32 
$60.39 
15.84 
$ 19.93 
33% 
67% 
2.08% 
10.88% 



21.46 
19.88 

S&P
500 Industrials 

637.81 
$35.38 
18.03 
$ 11.68 
33% 
67% 
1.83% 
11.23% 



19.52 
9.16 

S&P
500 Information Technology 

1106.18 
$61.32 
18.04 
$ 20.24 
33% 
67% 
1.83% 
13.92% 



22.36 
30.47 

S&P
500 Materials 

378.94 
$21.32 
17.77 
$ 7.04 
33% 
67% 
1.86% 
11.65% 



14.44 
10.64 

S&P
500 Telecommunication Services 

166.07 
$14.58 
11.39 
$ 4.81 
33% 
67% 
2.90% 
9.10% 



16.88 
10.88 

S&P
500 Utilities 


267.37 
$15.57 
17.17 
$ 5.14 
33% 
67% 
1.92% 
4.15% 



18.94 
11.23 

S&P
500 Real estate 

203.86 
$5.05 
40.37 
$ 1.67 
33% 
67% 
0.82% 
5.64% 



19.4 
13.92 


R_{i}=NRFR+Β(R_{m}NRFR) 
NRFR= 
2.87% 
Note: There was no
dividend info. for the sectors, so I assumed the same PO as index, and Div_{1}, b, and D/P could be
wrong 

18.25 
11.65 

i=D/P+g 

RP=R_{m}NRFR 
0.1523 

i=D/P+g 
P=Div_{1}/(ig) 

B*RP= 
0.1483 

R=Required return 
for the
sectors. 

11.6 
9.1 

15.230% 

E(R_{m})= 
15.23% 
D/P= 
2.03% 
D/P=(ig) 
α=E(R_{i})B(E(R_{m})) 
NRFR= 
0.0287 

RP=Risk premium 

16.37 
4.15 



RP= 
12.36% 
NRFR= 
2.87% 
g=ROE x b 
E(R_{m})=NRFR + RP 
E(R_{i})= 
0.1770 

NRFR=Nominal riskfree rate 

38.84 
5.64 

Graph 4 


i=Estimated return 



E(R_{i})=NRFR + (B x RP) 
E(R_{i})=..0287+(1.2 x .1236) 
PO=Pay out ratio 

1492.59% 

SML 


Β=Beta 

E(R_{m})= 
15.23% 
i= 
15.23% 
E(R_{m})=.0287.+.1236 
E(R_{i})=15.54% 

b=Retention ratio (1PO) 




P=Price 

E(R_{m})=Expected return of the market 


15.23% 
B= 
1.2 

g=growth rate of earnings and dividends 






α=Alpha 

Note: g=ROExb if there is no new debt or any
other factor 

Note: Expected return
and required return are 





σ=Standard deviation 

that has an affect on ROE and thus
g. The index has g=15%x70%=10.5%, 

synonymous in this context. 





R=Required return 

as compared to g=11.94% that S&P
has calculated. 



NRFR=5% 


INDEX
NAME 


i=D/P+g 
Β 
E(R_{s}) 
P 
α 
σ 



R_{m}=15% 


S&P 500 

15.23% 
1 
15.23% 
2762.13 
0.00% 
8.8 





S&P
500 Consumer Discretionary 

21.54% 
1.1 
16.47% 
785.33 
4.79% 
1.2 





S&P
500 Consumer Staples 

10.87% 
0.7 
11.52% 
587.39 
0.21% 
10.3 





S&P
500 Energy 

32.02% 
1.1 
16.47% 
533.41 
15.27% 
18.8 





S&P
500 Financials 

13.10% 
1.1 
16.47% 
463.94 
3.66% 
13.6 



S&P
500 Health Care 

12.96% 
1 
15.23% 
956.32 
2.27% 
11.7 



S&P
500 Industrials 

13.06% 
1.1 
16.47% 
637.81 
3.69% 
11.2 



S&P
500 Information Technology 

15.75% 
1.1 
16.47% 
1106.18 
1.00% 
12.7 



S&P
500 Materials 

13.51% 
1.2 
17.70% 
378.94 
4.77% 
14.4 



S&P
500 Telecommunication Services 

12.00% 
0.6 
10.29% 
166.07 
2.86% 
14.4 



S&P
500 Utilities 

6.07% 
0.3 
6.58% 
267.37 
1.50% 
13.8 



S&P
500 Real estate 

6.46% 
0.8 
12.76% 
203.86 
5.73% 
13.2 



Note: The stock valuation model (P=Div_{1}/(ig) or P/E= 
D/E 
P=Ex 
D/E 

D/E 
This is the multiplier
(M) 


(ig) 

(ig) 

(ig) 
P=ExM 

A word
about the stock valuation model. As I
stated earlier, g=ROExb. If i=ROE,
then the dividend payout ratio does not affect the price. If ROE is 

Point M, the market portfolio, is
(1,.15) is where all 3 lines intersect. 

greater
than i, then the higher the retention ratio (b), the higher the price. If ROE is less than i, then the higher the
dividend payout ratio is (i.e. the lower 

The point where the SML intersects
the yaxis is 5%, which is the NRFR. 

the
retention ratio is), the higher the price is.
The reverse is also true. 

In a lot
of the analysis in this site, I will use the shorter version of the valuation
model, simply to save space and time. 

INDEX
NAME 

Jenson 
α 
Rank 
T_{s} 
Rank 
Ss 
Rank 

S&P 500 



12.36% 

1.40% 

The Treynor method uses Beta as the
denominator, 

S&P
500 Consumer Discretionary 
4.79% 
2 
16.97% 
2 
15.56% 
1 
while the Sharpe method uses the
standard 



S&P
500 Consumer Staples 

0.21% 
5 
11.42% 
5 
0.78% 
6 
deviation (σ) as the
denominator. Beta is a measure 



S&P
500 Energy 

15.26% 
1 
26.50% 
1 
1.55% 
2 
of the systematic risk of a
portfolio, while σ is a 



S&P
500 Financials 

3.66% 
8 
9.30% 
8 
0.75% 
7 
measure of the total risk. If the two methods 



S&P
500 Health Care 

2.27% 
7 
10.09% 
7 
0.86% 
5 
give the same rankings, it shows
that the 



S&P
500 Industrials 

3.69% 
9 
9.26% 
9 
0.91% 
4 
portfolios are perfectly
diversified. If the rankings 



0.005 
0.035 

0.005 
0.035 

S&P
500 Information Technology 
1.00% 
6 
11.71% 
4 
1.01% 
3 
are close, then the portfolios are
fairly diversified. 



0.029 
0.045 

0.029 
0.045 

S&P
500 Materials 

4.77% 
10 
8.86% 
10 
0.74% 
8 
This is the case here. These are portfolios of 



0.051 
0.055 

0.051 
0.055 

S&P
500 Telecommunication Services 
2.86% 
3 
15.21% 
3 
0.63% 
9 
stocks in the same sector, which
would make 



0.065 
0.065 

0.065 
0.065 

S&P
500 Utilities 

1.50% 
4 
10.67% 
6 
0.23% 
11 
the returns of some of these stocks
correlated. 



0.071 
0.075 

0.071 
0.075 

S&P
500 Real estate 

5.73% 
11 
4.48% 
11 
0.27% 
10 

0.075 
0.085 

0.075 
0.085 

These
performance measures are usually used to rank the past performance of
portfolios such as mutual funds.
Remember that we are using these methods 

0.079 
0.095 

0.079 
0.095 

to
rank the projected returns of different sectors. The formula for determining the return for
a portfolio is the capital gains plus any dividends earned. 


R_{it}= 
EPit+Div_{it}+Cap.Dist._{it}BPit 


Bpit 

R_{it}=return on fund i
during year t 

Epit=ending
price for fund i during year t. 

Cap.Dist.it=capital
gain distributions for fund i during year t. 




Bpit=beginning
price for fund i during year t. 



The
Jensen performance measure is based on the Capital Asset Pricing Model as
follows. 








E(R_{j})=NRFR+B_{j}[E(R_{m})NRFR] 




NRFR= 
2.87% 
E(Rj)= 
17.70% 




RP= 
12.36% 
B_{j}= 
1.2 




E(R_{m})= 
15.23% 

E(R_{m})=the expected return of the market 





RP=E(R_{m})NRFR 

E(R_{j})=the expected return of stock or portfolio j 





NRFR= 
Nominal riskfree rate 
B_{j}=Beta of stock or portfolio j 





RP= 
Risk premium 





B_{j}= 
The Beta of security or portfolio j 



"We
can express the expectations formula in terms of realized rates of return. 



0.035 
0.005 

R_{jt}=NRFR+B_{j}[R_{mt}NRFR]+U_{jt} 



0.045 
0.029 

U_{jt}=Random error term 



0.055 
0.051 

Subtracting
the NRFR from both sides gives us 



0.065 
0.065 

R_{jt}NRFR=B_{j}[R_{mt}NRFR]+U_{jt} 



0.075 
0.071 

The risk
premium for the jth security or portfolio equals B_{j} times the market risk premium plus a random error term. If some portfolio managers 


0.085 
0.075 

are
superior, they will consistently achieve positive random error terms. They are consistently achieving returns
that are superior to the returns that 

0.095 
0.079 

would be
expected with the CAPM. It is
necessary to allow for an intercept (a nonzero constant) in this equation
that will take account of the 

positive
residuals. If we allow for a nonzero
constant alpha (α), the equation becomes 

R_{jt}NRFR=α+B_{j}[R_{mt}NRFR]+U_{jt} 

With this
equation, a positive and statistically significant α indicates the
ability to generate superior, riskadjusted returns. 

A superior
analyst is one that can achieve consistently positive alphas (α) in the
portfolios they manage. They are able
to generate superior 

returns
because they can forecast market turns or consistently select undervalued
securities. On the other hand,
consistently negative, statistically 

significant
alphas indicate inferior returns on a riskadjusted basis. 

It should be realized that these
performance measures are meant to be used as methods to analyze return per
unit of risk after the fact. 

We are
using them to analyze the estimated return of the aggregate market (S&P
500), as well as the different sectors of the market. 

Once we
have decided on some sectors that look attractive, we can then start looking
at individual stocks in these sectors. 

Analyzing individual stocks is the same
as analyzing the aggregate market or sectors of the market. You need to find out what the EPS for the
upcoming year is, as well as the 

dividends,
the expected growth rate of earnings and dividends, and some measure of the
risk of the stock. Let's look at a
couple of stocks to get a feel for this. 





IBM 


Price 
$ 157.37 

$ 157.38 

PO= 
36% 




Div_{1} 
$ 5.76 

next 12 months 


i= 
8.17% 
E(R_{IBM})= 
12.65% 


EPS_{1} 
$ 16.01 
P/E= 
9.83 


E(R_{m})= 
15.23% 


D/P 
3.66% 

RP=risk premium 
B= 
0.91 


(ig) 
0.0366 

RP=E(R_{m})NRFR 
NRFR= 
2.87% 

10 yr. TBond=NRFR 


g 
4.51% 

RP=.1523.0287 
RP= 
12.36% 

5.95% 


P=D/(ig) 
$ 157.38 

RP=12.36% 






i=D/P+g 
8.17% 

last 12 months 

Required rate of return 


EPS 
$ 11.90 
P/E= 
13.22 
P/O_{IB}_{M}= 
37% 

E(R_{IBM})=NRFR+B(R_{m}NRFR) 


Div. 
$ 4.40 

RP_{m} 
12.36% 

E(R_{IBM})=.0287+.91(.1523.0287) 


α=iB(R_{m}) 
α= 
5.69% 

E(R_{IBM})= 
14.12% 



IBM
is way overpriced. The required
return of a stock with B=.91 in this environment is 14.12%. The estimated return for IBM is only 8.17%. 









0.1236 




GM 

next 12 months 




Price 
$ 33.92 
P/E= 
7.73 




Div_{1} 
$ 1.20 
B= 
0.97 

PO= 
27% 




EPS_{1} 
$ 4.39 





D/P 
3.54% 

Required rate of return 




(ig) 
3.54% 

E(R_{GM)}=NRFR+B(R_{m}NRFR) 







g 
14.06% 

E(R_{GM})=.0287+.97(.1523.0287) 
E(R_{GM})= 
14.86% 




P=D/(ig) 
$ 33.90 




i=D/P+g 
17.60% 

α=.1760(.97*,1523) 





α= 
2.83% 



$ 33.90 

GM
is extremely underpriced. The required
return is 14.86%, while the estimated return is 17.60%. Referring to graph 4, this stock would plot
above the Security Market Line (SML). 



Price 
125.66 


Div_{1} 
2.08 


EPS_{1} 
9.74 


D/P 
1.66% 


(ig) 
1.66% 


g 


P=D/(ig) 
126.06061 


i=D/P+g 


P/E 
12.9 



0 

0.018 


0.01 

0.028 


0.02 
0.02 
0.038 


0.03 
0.038 
0.048 


0.04 
0.054 
0.058 


point M 
0.05 
0.068 
0.068 


0.06 
0.074 
0.078 


0.07 
0.078 
0.088 


0.08 
0.08 
0.098 


Note: This website is a work in progress. It is in no way completed. In fact, I will be adding new material once
a week, sometimes more. 

On the
first page of this site I have outlined the different topics that will be
discussed in the different sections of this site. There is still a lot 

more to
come. 

^{1} 
Frank K. Reilly,
"Investments" (1982): 152. 

^{2} 
Roger G. Ibbotson and Rex A.
Sinquefield, "Stocks, Bonds,
Bills, and Inflation: Historical
Return" {19761978) (Charlottesville, VA: Financial 


Analysts Research Foundation 1979). 

^{3} 
Frank K. Reilly,
"Investments" (1982): 262. 

^{4} 
Harry Markowitz, "Portfolio
Selection," "Journal of
Finance 7" (1952): 7791; and idem, "Portfolio SelectionEfficient
Diversification of Investments" 


(New York: John Wiley & Sons, 1959). 

^{5} 
William F. Sharpe, "Capital
Asset Prices: A Theory of Market
Equilibrium Under Conditions of Risk," "Journal of Finance 19
(1964): 425442; 


John Lintner, "Security
Prices, Risk and Maximum Gains from Diversification," "Journal of Finance 20 (1965):
587615; and J. Mossin, 


"Equilibrium in a Capital Asset
Market," "Econometrica
34" (1966): 768783. 

^{6} 
Frank K. Reilly,
"Investments" (1982): 591. 

^{7} 
IBID 595 

graph 5 

^{8} 
Robert A. Levy, "On the
Shortterm Stationarity of Beta Coefficients," Financial Analysts
Journal 27(1971): 5562. 

CML 

^{9} 
William F. Sharpe and Guy M.
Cooper, "RiskReturn Classes of New York Stock Exchange Common
Stocks: 19311977,"
"Financial 


Analysts Journal 28 (1972): 4654. 



^{10} 
Jack L. Treynor, "How to Rate
Management of Investment Funds," "Harvard Business Review"
(1965): 6375. 


^{11} 
William F. Sharpe and Guy M.
Cooper, "RiskReturn Classes of New York Stock Exchange Common
Stocks: 19311977,"
"Financial 


^{} 
Analysts Journal 28 (1972): 4654. 


^{12} 
Marshall E. Blume, "On the
Assessment of Risk," "Journal of finance 

NRFR=1.8% 


^{13} 
Howard Silverblatt, S&P Senior
Index Analyst, "S&P 500 EPS EST" Excel Spreadsheet, Standard
& Poor's Dow Jones indices website 

R_{m}=6.8% 


^{14} 
"The 2013 Economic Report of
the President" Figure 214, 71 


^{15} 
Howard Silverblatt,
S&P Senior Index Analyst, "S&P 500 EPS EST" Excel
Spreadsheet, Standard & Poor's Dow Jones indices website 


^{16} 
Richard M. Bookstaber,
Chapter 4, "Option Pricing and Strategies in Investing"
(1981): 4073. 


References 


Frank K.
Reilly, "Investments" (1982). 


Roger G.
Ibbotson and Rex A. Sinquefield, "Stocks, Bonds, Bills, and Inflation:
Historical Return" (19761978). 


Harry
Markowitz, "Portfolio Selection," "Journal of finance 7"
(1952). 


William F.
Sharpe, "Capital Asset Prices: A
Theory of Market Equilibrium Under Conditions of Risk," "Journal of
finance 19" (1964). 


John
Lintner, "Security Prices, Risk and Maximum Gains from Diversification,
"Journal of Finance 20" (1965). 


J. Mossin,
"Equilibrium in a Capital Asset Market," "Econometrica
34" (1966). 


Robert A.
Levy, "On the shortterm stationarity of Beta Coefficients,"
Financial Analysts Journal 27 (1971). 


William F.
Sharpe and Guy M. Cooper, "RiskReturn Classes of New York Stock
Exchange Common Stocks: 19311977,
Financial Analysts 


Journal 28
(1972). 

Jack L.
Treynor, "How to Rate Management of Investment Funds, "Harvard
Business Review" (1965) 

Standard
& Poor's Dow Jones Indices website, specifically the S&P 500
Earnings and Estimate Report spreadsheet prepared by 

Point M (the market portfolio) is
where the straight line (the CML) is tangent to the curved line (the old
efficient frontier), 

Howard
Silverblatt, S&P Senior Index Analyst 

M=.05,.068, the CML is the new
efficient frontier. 

"The
2013 Economic Report of the President"
Transmitted to the Congress March 2013. 


This site
was created by Lawrence I. Kurtz, BBA and MS, both with majors in finance,
Georgia State University, Atlanta, GA 

My email
is bark23@att.net 



Note: This website is a work in progress. It is in no way completed. In fact, I will be adding new material once
a week, sometimes more. 

On the
first page of this site I have outlined the different topics that will be
discussed in the different sections of this site. There is still a lot 

of material
to come. 





























































































