The Capital Asset Pricing Model

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The Capital Asset Pricing
Model

Curriculum using the IEM



Prepared for the Fall 1999 IEM*IDEA/FIPSE Conference

By Thomas A. Rietz

November 1999


The Iowa Electronic Markets



2

Teaching Objectives

The Capital Asset Pricing Model

Apply the CAPM to determine
expected stock returns

Students should be able to:

1.

Find betas for stocks

2.

Understand and compute betas for stocks

3.

Determine appropriate risk free rates and market risk premiums

4.

Apply the CAPM to determine expected asset returns

Evaluate actual stock perform
ance

Students should be able to:

1.

Determine actual stock returns over specified periods

2.

Compare actual returns to CAPM required returns to evaluate performance

Implement investment /trading strategies

Based on sound financial analysis, students should be ab
le to turn expectations into actions.

Important Aspects of the Assignment



Students replicate analysis from the lecture.



Students start with specific directed tasks and slowly forces students to expand and generalize
their knowledge.



Students build on previ
ous knowledge and experience.




3

Lecture Outline

The Capital Asset Pricing Model (CAPM)

1.

Introduction

2.

The Feasible Set and Efficient Frontier

3.

Investor Utility Maximization

4.

The CAPM Asset Pricing Equation

5.

Applying the CAPM

6.

Notes on Estimating Betas

7.

Summary



4

CAPM Assignment

Introduction to the IEM

The Iowa Electronic Market (IEM for short) is a computerized market on which financial contracts can
be traded (bought or sold). For this assignment, we will be using a series of contracts based on three
popular com
panies, Apple Computers (AAPL), IBM (IBM) and Microsoft (MSFT), and an important
index called the S&P500 index. Shares of the firms trade over the counter (NASDAQ) and on the New
York Stock Exchange (NYSE). Similarly, a daily index value is determined for
the S&P500 based upon
the stock prices of the 500 companies that compose of it.

The contracts we will use are based on the shares of Apple computers, IBM and Microsoft, and on the
value of the S&P500. These contracts are listed on the IEM under the mark
et label “Computer Industry
Returns Market” or “Comp_Ret” for short. These contracts are described briefly later in this note and in
more depth in the IEM Trader’s Manual. Detailed descriptions of these markets are available at the IEM
website:

http://www.biz.uiowa.edu/iem/markets/computer.html


Objectives

The objectives of the IEM assignments are to help you apply class concepts in a "real world,"
unstructured way to learn how to:

1.

Apply the

CAPM to determine expected stock returns

2.

Evaluate actual stock performance

3.

Implement investment /trading strategies

Opening an IEM Account

All students need to open an account with the Iowa Electronic Market. This involves a minimum deposit
of ____ dolla
rs. Funds remaining in your account are refundable at the end of the semester.

You can open an IEM account over the internet. To do so, go to the sign
-
up webpage:

http://iemweb.biz.uiowa.edu/signup/

and follow the instructions given to you by your instructor. (DO NOT use forms other than those given
to you by your instructor. Using other forms may result in fees or decreased deposits in your account.)

After filling out your signup forms, you may n
eed to deposit cash with the IEM office (W283 PBAB,
phone 335
-
0881). Your instructor will give you details about any deposits you need to make.


5

Accessing the IEM

You can access the IEM through its website address:

http://www.biz.uiowa.edu/iem/

The IEM market has several contracts trading under it. The contracts of interest for our course are the
Computer Industry Returns Market (Comp_Ret, for short).

You access your trading account from the market pages or direc
tly at:

http://iemweb.biz.uiowa.edu/


Computer Industry Returns Contracts

The Computer Industry Returns Contracts consist of a series of contracts. Every month, existing
contracts in the series are liquidated and

payments are made as described below. Then, new
contracts are created as described below. These events occur on the Monday after the exchange
-
traded options for the underlying stocks expire (the Monday after the third Friday of each month).

The liquida
tion values for the contracts in this market are determined solely by the rates of return of
Apple Computers Common Stock (AAPL), IBM Common Stock (IBM), Microsoft Common Stock
(MSFT) and the S&P500 index (SP500). Whichever of these has the highest rate of

return as specified
below will payoff $1.00 per share. The remaining contracts will payoff zero. Thus, to do well in this
market, you will need to understand what determines real stock market returns.

Contracts will be designated by a ticker symbol and a
letter denoting the month of contract liquidation.
Thus, the contracts traded in this market for liquidation in month “m” are:

Code

Underlying Asset

Liquidation Value

AAPLm

IBMm

MSFTm

SP500m

Apple Computers

IBM

Microsoft

S&P 500 Market Index


$1.00 if AAP
L Return Highest

$1.00 if IBM Return Highest

$1.00 if MSFT Return Highest

$1.00 if SP500 Return Highest


In these contract codes, “m” refers to the month of expiration as given by the following table:

Month

Designation

Month

Designation

Month

Designation

January

February

March

April

a

b

c

d

May

June

July

August

e

f

g

h

September

October

November

December

i

j

k

l


For AAPLm, IBMm and MSFTm, the dividend
-
adjusted rate of return is computed based on closing
stock prices of the underlying listed firm between

the third Friday in the liquidation month and the third
Friday in the previous month. For these purposes, closing prices as reported in the Midwest edition of
the Wall Street Journal are used. In particular, this return is calculated as follows. First,

the raw return
on the underlying stock is computed (as the closing price on the third Friday of the liquidation month,

6

minus the closing price from the third Friday of the previous month, plus any dividends on ex
-
dividend
dates). Then, we divide the raw
return by the closing stock price from the previous month to arrive at
the dividend
-
adjusted rate of return.

For the SP500 contract, the return is computed as the capital gains rate of return. To do this, subtract
the closing index value on the third Frid
ay of the previous month from the closing index value on the
third Friday of the liquidation month. Then, divide by the previous month’s closing index value.

Trading on the IEM

You can trade on the IEM in several ways. First, you can buy or sell unit port
folios. A unit portfolio is a
set of contracts such as AAPLm, IBMm, MSFTm and SP500m. You can always buy or sell such
portfolios for $1.00 each. Thus, when you start to trade and do not own any contracts, you can buy a
unit portfolio and then start to t
rade. (To do this, select the appropriate contract under “Buy Bundles” or
“Sell Bundles” in the “Market Order” drop down menu. Enter a quantity and press the “Market Order”
button.)

Second, you can buy or sell using a "market order." On the market scree
n, you will see that some
individuals have posted an order to buy or to sell a contract (e.g., MSFTi, the contract for September
liquidation in the Computer Industry Returns Market) at a specific price. If you believe that a posted
order represents a good

deal, you can buy or sell at the posted price. (To do this, select the
appropriate contract under “Buy at Best Ask” or “Sell at Best Bid” in the “Market Order” drop down
menu. Enter a quantity and press the “Market Order” button.)

Third, you can buy or
sell using a "limit order." To do so, you state the price at which you are willing to
buy or sell a contract and post a limit order on the screen. In doing so, you are waiting for someone
who is willing to buy or sell at your stated price. In this manner
, when your order executes, it will
execute at your stated price, not at somebody else’s. The negative is that the order may never execute
because nobody likes your price because it is too high or low. (To place a limit order, select the
appropriate contr
act under “Post a Bid” or “Post an Ask” in the “Limit Order” drop down menu. Enter a
price, quantity and expiration date and press the “Limit Order” button.)

Completing Your Assignments and Submitting Them

As you can see below, the IEM assignments are ext
ensive, multi
-
part assignments that draw together
many concepts from the class. It would be wise to work on the various parts of the assignments as we
go over the relevant topics in class. To prepare the assignments for submission, please use the
followi
ng guidelines:

1.

Each assignment must be typed. Label clearly each assignment with a cover page giving
your name, student number, and section number.

2.

Complete each part in a separate section clearly labeling them Part 1, Part 2, etc.

3.

Within each se
ction, give the requested information, including sources of information
gathered and equations used to calculate results.

4.

Turn in your completed assignment to your instructor on the date it is due.


7

CAPM Assignment

Part 1: Finding and Computing Returns


DUE: ___________

GOAL

In this part of the assignment, you will learn where to find current and historical prices and how to
compute returns

Current stock returns

The IEM Computer Industry Returns or MSFT (Microsoft) Price Level markets depend upon

the
following three stocks: AAPL, IBM, MSFT and the S&P500 index. The prices of these stocks and the
value of the S&P500 index are reported in the Wall Street Journal and in various places on
-
line (e.g.,
http://quote.
yahoo.com
).

Starting on the third Friday of ____________, record the closing prices each Friday for AAPL, IBM,
MSFT and the S&P500 index. (If you use a print source such as the Wall Street Journal, notice that,
typically, these prices will appear in the
following Monday’s edition.) Continue recording prices each
Friday through the third Friday in ________. Also, find out if any dividends are paid on the three stocks
AAPL, IBM and MSFT during any week. Report this information in a table labeled Table 1.

(Note:
While you are free to use any source, the contracts are liquidated based on Wall Street Journal
reported prices.)

For each Friday from ________ to ________, report the dividend adjusted return from the first recorded
date to the current date for

each stock calculated from the prices and dividends (if any) in Table 1.
Report these returns in Table 1 as well.

Historical stock returns

Download the third Friday to third Friday stock returns for AAPL, IBM, MSFT, the S&P500 and one
-
month Treasury Bill
s from the IEM website at:

http://www.biz.uiowa.edu/iem/markets/compdata/compfund.html



You will use these returns in later parts of this exercise.

Download 5 years worth of monthl
y stock prices and dividends from Yahoo's website as follows.

1.

Go to :
http://quote.yahoo.com

2.

Enter AAPL as the ticker symbol and press the "get quote" button.

3.

Select the "Chart" link.

4.

At the bottom of the chart, sele
ct the "monthly" tables link.

5.

Select the appropriate dates in the resulting table and press the "get historical data" button
with the "Monthly" radio button selected.

6.

At the bottom of the table, select the "download spreadsheet format" link.

7.

Save the resul
ting "csv" format file. You can load this into Excel for analysis.

8.

Select the "Dividend" radio button and press the "get historical data" button again to
download dividends.


8


Repeat this procedure for AAPL, IBM, MSFT and the S&P500 (ticker symbol ^spx).
You can also
download 3 month T
-
Bill rates using the ticker symbol "^irx". The T
-
Bill data is in the form of return
each month.

For each stock, each month, use Excel to compute the dividend adjusted return. Also, compute the
return to the S&P500. Save t
his data for use later.

Returns to IEM Contracts

Make at least one trade in the IEM Computer Industry Returns market between the ________ and
________. Choose one trade to use for the rest of this part.

Report the date of the trade, the contract traded
and the price. Attach a print out showing your trading
activity. (You can either submit a “Processed Orders” report or an ‘Order History” report. To get the
first report, make sure that the “confirm” box is checked on the trading screen. You will be as
ked to
“execute” the order. Upon execution, the “Processed Orders” report will appear. To get the second
report, go to “My Account” information select “view order history” and print the resulting report.)

Based on the date of your trade, what is the hol
ding periods (in days) to the contract buyer if each
contract is held to its liquidation date?

Calculate and report the return over this holding period to the contract buyer if the contract liquidates for
$1.

Also calculate and report the return over the h
olding period to the contract buyer if the contract
liquidates for $0.



9

CAPM Assignment

Part 2: Computing Betas




DUE: ___________

GOAL

In this part of the assignment, you will learn how to analyze stock returns. You will look at historical
averages
, standard deviations and correlations. You will learn how to find betas on line and how to
compute your own betas for stocks.

Historical Analysis of IEM Returns

Use the monthly IEM returns downloaded in part one for this part of the assignment. Analyze
these
returns by reporting the following information (all numbers can be computed in Excel):

1.

Report the historical average monthly return for each stock, the S&P500 index and T
-
Bills.
(Use the Excel "average" function.)

2.

Report the historical standard devi
ation in monthly returns for each stock, the S&P500 and T
-
Bills. (Use the Excel "stdev" function.)

3.

Report the correlation coefficient between monthly returns for each stock and T
-
bills with the
S&P500. (Use the Excel "correl" function.) These correlatio
n coefficients will be the raw betas
for the stocks computed from the "characteristic line" as discussed in class.

4.

Compute and report the adjusted betas from the correlation coefficients computed above.
(

adjusted

= 1/3 + 2/3x

raw
.)

Historical Analysis of Yahoo Returns

Repeat the analysis above using the five years of monthly returns collected from Yahoo in Part 1.

Looking up Betas

Look up betas for each stock on Yahoo using the following procedure:

1.

Go to
:
http://quote.yahoo.com

2.

Enter AAPL as the ticker symbol and press the "get quote" button.

3.

Select the "Profile" link.

4.

Page down to "Statistics at a Glance"

5.

These statistics include "beta."


Repeat this exercise for ea
ch stock.



10

Discussion

Compare and contrasts the betas you get from each method. How close are they? Why are they
different? How stable are the betas? Given the information you have, do you think that beta's are a
stable enough measure to use for the CA
PM?


11

CAPM Assignment

Part 3: Applying the CAPM




DUE: ___________

GOAL

In this part of the assignment, you will learn how to apply the CAPM to compute expected returns. You
will have to make decisions about the risk free rate, the market risk premium a
nd the appropriate betas.

Finding Risk Free Rates

Current risk free rates can be found online at various websites. The current 1 month treasury rate can
be found on the IEM at the website:

http://www.biz.uiowa.edu/iem/markets/compdata/compfund.html


You can also get risk free rates from Yahoo. The ticker symbol for 3 month T
-
bills is ^inx, 5 year notes
is ^fvx, 10 year notes is ^tnx and 30 year bonds is ^tyx.

Determining the mark
et risk premium

Using the date from Part 1, subtract the monthly T
-
Bill rate from the S&P500 return. This is the monthly
market risk premium. What is the average monthly risk premium according to your IEM data?

Computing the Expected Return from the CAPM

Using the current monthly T
-
Bill rate from the IEM and the average monthly risk premium calculated
from IEM data above, compute the one
-
month expected return for each of the three stocks and the
S&P500 index using:

1.

Betas you calculated from IEM data in Pa
rt 2.

2.

Betas you calculated from Yahoo data in Part 2.

3.

Betas you looked up on Yahoo in part 2.


Discussion

What risk free rate do you think should be used in the CAPM? Does the time horizon (from 1
-
month T
-
bill rates to 30
-
year T
-
Bond rates) matter? What
seems most appropriate to you?

Do you think that the risk premium used is an adequate measure of the risk premium? Can you find
other sources for the risk premium from your book, course materials or the web?

What are the differences between the expected r
eturns computed using the various betas above?
How stable are these returns? Can you order the stocks from highest expected return to lowest? Does
the source of the beta matter?


12

CAPM Assignment

Part 4: Evaluating Securities



DUE: ___________

GOAL

In

this part of the assignment, you will learn how to use the CAPM to evaluate the historical
performance of assets.

Evaluation

Recall the average historical returns from Part 1 of the assignment.

Recall the CAPM predicted returns from Part 3 of the assignme
nt.

Subtract the CAPM predicted return from the historical average return of the stock. This is the amount
by which the stock outperformed (+) or underperformed (
-
) the required return as predicted by CAPM
over the historical time period. This is known a
t the stocks "alpha."

Graph the Security Market Line (relationship between beta and the expected return) using the one
-
month risk free rate and the risk premium from the IEM used in Part 3. On this graph, also graph the
average monthly return (from part 1
) and beta (from part 2) for each of the three stocks. The distance
that the stock lies above the Security Market Line is also the stocks "alpha."

According to the stocks' alphas, which stocks outperformed or underperformed historically? Can you
rank or
der their performance?

Discussion

Can you explain why each stock either outperformed or underperformed? Were there special
circumstances for any of the companies? Do you think the historical performance will continue? Do
you think any of the companies f
ace special circumstances now that will enable them to outperform in
the future? Are there any special circumstances that would cause them to underperform?



13

CAPM Assignment

Part 5: Implications and Actions



DUE: ___________

GOAL

In this part of the as
signment, you will use the CAPM to forecast returns for stocks and turn those
forecasts into actions on the IEM.

Prediction

Given all of your analysis in parts 1 to 4, predict what each stock's return and the SP&500 return will be
for the next month. Just
ify these predictions using the analysis techniques developed in class and in
this assignment.

Which of the stocks do you predict will have the highest return? How confident are you of your
prediction?

Implication

Given your predictions above, which IEM c
ontract (AAPLm, IBMm, MSFTm or SP500m) should be
priced the highest at the beginning of trading during the current trading month. Justify your prediction.
(Recall that the contract with the highest actual monthly return will liquidate at $1. The others
will expire
worthless. Thus, you need to predict which stock will have the highest monthly return in order to
determine which IEM contract will have the greatest likelihood of payoff. This contract should be priced
the highest.)


Actual IEM Prices

For ea
ch Friday that you report stock prices in Part 1, report the corresponding closing contract prices
on the IEM Computer Industry Returns and Microsoft Price Level markets in a table labeled Table 2.
(To access this information, use the “Market Info” button
, select the market and select the “Price
History” report. Alternatively, you can access a price history by selecting the “History” link on the
market’s webpage under the IEM address:
http://www.biz.uiowa.edu/i
em.
)

Compare your prediction to the actual price of the contracts at the beginning of trade in the current
month. Can you reconcile your predictions with actual prices?

Note how prices evolve through time and correlate IEM price changes with the returns
to date for the
stocks from Part 1.

Action

Make at least one additional trade in the IEM Computer Industry Returns market between the
________ and ________. Log your trades. For each trade, report the date of the trade, the contract
traded and the price
s. Attach a print out showing your trading activity. (You can either submit a
“Processed Orders” report or an ‘Order History” report. To get the first report, make sure that the

14

“confirm” box is checked on the trading screen. You will be asked to “exec
ute” the order. Upon
execution, the “Processed Orders” report will appear. To get the second report, go to “My Account”
information select “view order history” and print the resulting report.)

Justify each trade you make using:

1.

Your forecast returns

2.

The

actual returns do date

3.

IEM prices at that time and

4.

Any other information and analysis you wish to include.