Copyright ©2003 South-Western/Thomson Learning

Chapter 5Analysis of Risk and Return

Introduction

• This chapter develops the risk-return relationship for individual projects (investments) and a portfolio of projects.

Risk and Return

• Risk refers to the potential variability of returns from a project or portfolio of projects.

• Returns are cash flows.• Risk-free returns are known with certainty.

– U.S. Treasury Securities

• Check out interest rates on the following URLs

– http://www.stls.frb.org/fred/data/irates.html– http://www.bloomberg.com/

Expected Return

• A weighted average of the individual possible returns

• The symbol for expected return, r, is called “r hat.”

• r = Sum (all possible returns their probability)

^

^

Let’s Analyze Risk

• Standard Deviation is an absolute measure of

risk.

• Z score measures the number of standard

deviations a particular rate of return r is from

the expected value of r. See table V page T5 and slide 6

• Coefficient of variation v is a relative measure

of risk.

• Risk is an increasing function of time.

^

Calculating the Z Score

• Z score =

• What’s the probability of a loss on an investment with an expected return of 20 percent and a standard deviation of 7 percent?

• (0% – 20%)/17% = –1.18 rounded

• From table V = 0.1190 or 11.9 percent probability of a loss

Target score – Expected value Standard deviation

Coefficient of Variation

• The coefficient of variation is an appropriate measure of total risk when comparing two investment projects of different size.

Risk-Return Relationship

Required return = Risk-free return + Risk premium

Real rate of returnRisk-free rate Expected inflation

premium

Check out the risk-free rate at this Web site:http://www.cnnfn.com/markets/rates.html

Expected Inflation Premium

• Compensates investors for the loss of purchasing power due to inflation

Risk Premium

• Maturity risk premium

• Default risk premium

• Seniority risk premium

• Marketability risk premium

• Business risk

• Financial risk

Term Structure of Interest Rates

• Expectations theory

• Liquidity premium theory

• Market segmentation theory

Characteristics of the Securities Comprising the Portfolio

• Expected return

• Standard deviation,

• Correlation coefficient

• Efficient portfolio

Efficient Portfolio

• Has the highest possible return for a given

• Has the lowest possible for a given expected return

^ rr

aa

c bc b RiskRiska and c are preferred to ba and c are efficient

Diversification

• The Portfolio effect is the risk reduction accompanying diversification.

Systematic

Risk

Unsystematic Diversifiable

CAPM: Only Systematic Risk is Relevant

• Systematic risk caused by factors affecting the market as a whole

undiversifiable– interest rate changes– changes in purchasing

power– change in business

outlook

• Unsystematic risk caused by factors unique to the firm

diversifiable – strikes– government

regulations– management’s

capabilities

Systematic Risk is Measured by Beta,

• A measure of the volatility of a securities return compared to the Market Portfolio

j,m

j,m

j Variance

Covarianceβ

• A regression line of periodic rates of return for security j and the Market Portfolio

• Search for (stock beta) on this search engine:

http://www.altavista.digital.com/

SML Shows the Relationship Between r and ß ^

r SML

rf

^

^

Required Rate of Return

• The required return for any security j may be defined in terms of systematic risk, j, the expected market return, rm, and the expected risk free rate, rf.

)ˆˆ(βˆfmjfj rrrk

^

^

Risk Premium

• (rm – rf)

• Slope of security market line

• Will increase or decrease with

– uncertainties about the future economic

outlook

– the degree of risk aversion of investors

^ ^

SML

^

^

^

1.0

Risk Premium = (9% – 6%) = 3%ka = 6% + 1.5(9% – 6%) = 10.5%

a10.5% ra

1.5

^

6% rf

r SML

9% rm

CAPM Assumptions

• Investors hold well-diversified portfolios

• Competitive markets

• Borrow and lend at the risk-free rate

• Investors are risk averse

• No taxes

• Investors are influenced by systematic risk

• Freely available information

• Investors have homogeneous expectations

• No brokerage charges

Major Problems in the Practical Application of the CAPM

• Estimating expected future market returns

• Determining an appropriate rf• Determining the best estimate of • Investors don’t totally ignore

unsystematic risk.• Betas are frequently unstable over

time.• Required returns are determined by

macroeconomic factors.

^

International Investing

• Appears to offer diversification benefits

• Returns from DMCs tend to have high positive correlations.

• Returns from MNCs tend to have lower correlations.

• Obtains the benefits of international diversification by investing in MNCs or DMCs operating in other countries

Risk of Failure is Not Necessarily Captured by Risk Measurers

• Risk of failure especially relevant– For undiversified investor

• Costs of bankruptcy– Loss of funds when assets are sold at

distressed prices– Legal fees and selling costs incurred– Opportunity costs of funds unavailable to

investors during bankruptcy proceedings.

High-Yield Securities

• Sometimes called “Junk Bonds”

• Bonds with credit ratings below investment-grade securities

• Have high returns relative to the returns available from investment-grade securities

• Higher returns achieved only by assuming greater risk.

• Ethical Issues next slide

Ethical Issues

• Growth in high-risk junk bonds

• Savings and loan industry

• Insurance industry