Capital Budgeting and Risk
•
•
•
•
•
•
•
Risk and Return
The Market Risk Premium
Capital Asset Pricing Model Considerations
Determining Beta
Arbitrage Pricing Model
Certainty Equivalents
Reeby Sports Case
Risk and Return
Historical returns 1900-2003 (nominal)
Treasury bills
4.1%
Government bonds
5.2%
Common stocks
11.7%
Risk-Return Tradeoff
The typical investor would prefer
A)
B)
The highest return possible at a given
risk level
The lowest risk possible for a given
level of return
One measure of risk is the standard deviation
of returns
Capital Asset Pricing Model
• Law of large numbers applied to investments
• A diversified portfolio reduces, but does not
eliminate, risk
• Investors require compensation for
systematic risk
CAPM Assumptions
1)
2)
3)
4)
5)
6)
Investors maximize expected return and
minimize risk
Trades do not affect prices
Expectations are homogeneous
No taxes or transaction costs
All borrowing and lending is at the risk
free rate
Assets are infinitely divisible
Problems with the CAPM
• How can beta be measured?
• What is the market portfolio?
• Does the CAPM explain stock returns?
– Fama and French, 1992, “The Cross-Section of
Expected Stock Returns,” Journal of Finance: Size
and book-to-market ratios explain stock returns better
than beta over the period 1941-1990
Asset Risk for a Diversified Investor
Rit = ai + biRmt + eit
Ri
ai
bi
eit
t
=
=
=
=
=
return on stock i
intercept
slope coefficient
error term
time
Cov(Ri,Rm)
bi =
= i
Var(Rm)
Rm = return on the market portfolio
Practical Issues in Determining β
• Use historical price movements, but what
frequency (daily, monthly, quarterly) and for
how long?
– Common practice, last 60 months
– Past may not predict future values
• What is the market portfolio?
–
–
–
–
–
–
Large US common stocks
All US common stocks
Global stocks
Stocks and bonds
Stocks, bonds and real estate
Role of human capital
Market Risk Premium for the CAPM
Often calculated as the difference between the
return on the market and the risk free rate
Varies from 4-10% depending on time period
and/or country
What is important is the expected value going
forward, not historical values
Arbitrage Pricing Model
• The APM is similar to the CAPM with
regard to classifying risk as either
diversifiable or nondiversifiable.
• The APM does not require investors to be
concerned only with market risk.
• The APM allows consideration of any
number of factors to influence the risk of an
investment.
Arbitrage Pricing Model
n
Ri = ai +
R
a
b
I
e
i
j
=
=
=
=
=
=
=
 b I +e
j=1
ij j
i
realized rate of return
intercept
sensitivity of return to index
value of index
error term
asset indicator
factor indicator
Applications of the APM
• Pre-specified factors
–
–
–
–
–
Market Return
Long term bond risk premium
Inflation rate
GNP growth
Any other hypothesized factor
Problem: joint hypothesis test
Applications of the APM (cont.)
• Factor analysis:
– Let the computer generate the factors
Problems:
– How many factors?
– What do the factors mean?
– What if conditions change?
Applications of the APM (cont.)
E(Ri ) = Rf ’ +
n
b 
j=1
ij
j
Rf ’ = zero systematic risk return
j = excess return for risk factor measured by index
Empirical Testing Issues
• CAPM
– Initial support; recent refutation
– Anomalies: size, Book-to-Market value,
seasonal
• APM
– Theory says nothing about factor identity or #
– Pre-determined factors vs. factor analysis
Risk and Discounted Cash Flow
• The risk-adjusted discount rate method
discounts for time and risk simultaneously
• Cannot handle situations where there is risk,
but no time discount
Example: Space launch coverage payable at
time of launch
Certainty Equivalent Method
• Discounts separately
– risk
– time value of money
Certainty Equivalent Method
• Rather than discounting future cash flows
by one risk-adjusted discount rate to
account for both time and risk, reduce the
future cash flow to account for risk and then
discount that value for time at the risk-free
rate
n
PV =

t=1
Ct
(1 + r)t =
n

t=1
CEQt
(1 + rf)t
Example
• Risk-free rate is 5%
• Investment will pay $1 million in two years
• Appropriate risk-adjusted rate is 12%
1,000,000
PV =
(1.12)2
= $797,194
CEQ2
PV =
(1.05)2
CEQ2 = $878,906
• The ratio of CEQ2 to C2 is 87.89%
Certainty Equivalent Problem
An 18th century ship-owner sends a vessel out on a 2year voyage. The value of the cargo will not be known
until it returns. The expected value of the cargo is
$144,000. The present value of the voyage is $100,000.
The risk-free rate is 5 percent.
Reeby Sports
• Work in groups of four to complete the case
handout
Reeby Sports
• What value did your group place on the stock?
• What percent of your stock value is PVGO?
• What advice would you give the company
about dividend payouts?
• What additional information do you need to
perform a more complete analysis?
Next Class
• Managing Risk
• Read Chapter 27 and the reading available
online