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 TradeoffThe typical investor would prefer

A) The highest return possible at a given risk level

B) 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) Investors maximize expected return and minimize risk

2) Trades do not affect prices

3) Expectations are homogeneous

4) No taxes or transaction costs

5) All borrowing and lending is at the risk free rate

6) 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 = return on stock iai = interceptbi = slope coefficienteit = error termt = time

bi = = i

Cov(Ri,Rm)

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

j = 1Ri = ai + bijIj + ei

R = realized rate of returna = interceptb = sensitivity of return to indexI = value of indexe = error termi = asset indicatorj = 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.)

n

j = 1E(Ri ) = Rf

’ + bij 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

PV = =n

t=1

Ct

(1 + r)t

CEQt

(1 + rf)tn

t=1

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

Example• Risk-free rate is 5%• Investment will pay $1 million in two years• Appropriate risk-adjusted rate is 12%

PV = = $797,1941,000,000

(1.12)2

PV =CEQ2

(1.05)2

CEQ2 = $878,906

• The ratio of CEQ2 to C2 is 87.89%

Certainty Equivalent ProblemAn 18th century ship-owner sends a vessel out on a 2-year 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