Chapter 6Chapter 6

The Meaning and The Meaning and Measurement of Risk and Measurement of Risk and

ReturnReturn

Chapter ObjectivesChapter Objectives Define and measure the expected rate of return of an

individual investment Define and measure the riskiness of an individual

investment Compare the historical relationship between risk and

rates of return in the capital markets Explain how diversifying investments affect the

riskiness and expected rate of return of a portfolio or combination of assets

Explain the relationship between an investor’s required rate of return and the riskiness of the investment

Rate of ReturnRate of Return

Determined by future cash flows, not reported earnings

Expected Rate of ReturnExpected Rate of Return

Weighted average of all the possible returns, weighted by the probability that each return will occur

RiskRisk

Potential variability in future cash flowsThe greater the range of possible events that

can occur, the greater the risk

Standard Deviation of ReturnStandard Deviation of Return

Quantitative measure of an asset’s riskinessMeasures the volatility or riskiness of

portfolio returnsSquare root of the weighted average

squared deviation of each possible return from the expected return

Real Average Annual Rate of Real Average Annual Rate of ReturnReturn

Nominal rate of return less the inflation rate

Risk PremiumRisk Premium

Additional return received beyond the risk-free rate (Treasury Bill rate) for assuming risk

Risk and DiversificationRisk and Diversification

Diversification can reduce the risk associated with an investment portfolio, without having to accept a lower expected return

Annual Rates of Return Annual Rates of Return 1926 to 20001926 to 2000

Security Nominal Standard Real Risk

Average Deviation Average Premium

Annual of Returns Annual

Returns Returns

Common Stocks 13.0 % 20.2 % 9.8 % 9.1 %

Small Cmpy Stk 17.3 % 33.4 % 14.1 % 13.4 %

L-T Corp bonds 6.0 % 8.7 % 2.8 % 2.1 %

L-T Govt bonds 5.7 % 9.4 % 2.5 % 1.8 %

Interm. Govt bonds 5.5 % 5.8 % 2.3 % 1.6 %

U.S. Treasury Bills 3.9 % 3.2 % 0.7 % 0 %

Inflation 3.2 % 4.4 %

DiversificationDiversification

If we diversify investments across different securities the variability in the returns declines

Total Risk or VariabilityTotal Risk or Variability

Company-Unique Risk (Unsystematic)

Market Risk (Systematic)

Company-Unique RiskCompany-Unique Risk

Unsystematic riskDiversifiable --

Can be diversified away

Market RiskMarket Risk

SystematicNon-diversifiableCan not be eliminated through random

diversification

Market RiskMarket Risk

Events that affect market risk

Changes in the general economy, major political events, sociological changes

Examples:

Interest Rates in the economy

Changes in tax legislation that affects all companies

BetaBeta

Average relationship between a stock’s returns and the market’s returns

Measure of a firm’s market risk or the risk that remains after diversification

Slope of the characteristic line—or the line that measures the average relationship between a stock’s returns and the market

BetaBeta

A stock with a Beta of 0 has no systematic risk A stock with a Beta of 1 has systematic risk

equal to the “typical” stock in the marketplace A stock with a Beta greater than 1 has systematic

risk greater than the “typical” stock in the marketplace

Most stocks have betas between .60 and 1.60

Portfolio BetaPortfolio Beta

Weighted average of the individual stock betas with the weights being equal to the proportion of the portfolio invested in each security

Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market

Asset AllocationAsset Allocation

Diversification among different kinds of assets

Examples:

Treasury Bills

Long-Term Government Bonds

Large Company Stocks

Required Rate of ReturnRequired Rate of Return

Minimum rate of return necessary to attract an investor to purchase or hold a security

Considers the opportunity cost of funds

Opportunity CostOpportunity Cost

The next best alternative

Required Rate of ReturnRequired Rate of Return

k=kfr + krp

Where:

k = required rate of returnkfr = Risk Free Rate

krp = Risk Premium

Risk-Free RateRisk-Free Rate

Required rate of return for risk-less investments

Typically measured by U.S. Treasury Bill Rate

Risk PremiumRisk Premium

Additional return expected for assuming risk

As risk increases, expected returns increase

Risk Premium = Required Return – Risk Free rate

krp = k - kfr

Where: k = required rate of return kfr = Risk Free Rate

krp = Risk Premium

If required return is 15% and the risk free rate is 5%, then the risk premium is 10%. The 10% risk premium would apply to any security having a systematic risk equivalent to general market or a Beta of 1. If beta is 2, then risk premium = 20%.

Capital Asset Pricing ModelCapital Asset Pricing Model

Equation that equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the systematic risk

CAPM

CAPMCAPMCAPM suggests that Beta is a factor in

required returnskj = krf + B(market rate – risk free rate)Example:Market risk = 12%Risk Free rate = 5%5% + B(12% - 5%)If B = 0 Required rate = 5%If B = 1 Required rate = 12%If B = 2 Required rate = 19%