Review Risk and Return. r = expected rate of return. ^

Review

Risk and Return

.P = rn

1=iii

r

r = expected rate of return.^

stand-alone risk

An asset’s risk can be analyzed in two ways:

(1) on a stand-alone basis, where the asset is considered in isolation, and

(2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio.

Thus, an asset’s stand-alone risk is the risk an investor would face if he or she held only this one asset.

Probability distribution

Rate ofreturn (%) 50150-20

Stock X

Stock Y

Which stock is riskier? Why?

30

Measuring Stand-Alone Risk: Standard deviation σ

1- Standard deviation σ ( absolute mean of risk)

Standard deviation measures the stand-alone risk of an investment.

The larger the standard deviation, the higher the probability that returns will be far below the expected return.

Standard deviation σ

.

Variance

deviation Standard

1

2

2

n

iii Prr

Measuring Stand-Alone Risk: The Coefficient of Variation2- The coefficient of variation CV (an

alternative measure of stand-alone risk.)

CV = σ/ r^ It shows the risk per unit of return It provide a more meaningful basis for

comparison When the expected return on two

alternatives are not the same.

Portfolio Return, rp̂

^ ^rp = wirin

i = 1

.

Variance

deviation Standard

1

2

2

n

iipip Prrp

Two-Stock Portfolios

Two stocks can be combined to form a riskless portfolio if = -1.0.

Risk is not reduced at all if the two stocks have = +1.0.

In general, stocks have 0.65, so risk is lowered but not eliminated.

Investors typically hold many stocks.

What happens when = 0?

Type of Risk

• Systematic Risk

No diversifiable Risk = Market Risk war, inflation, recessions, and high

interest rates. Since most stocks are negatively affected

by these factors, market risk cannot be eliminated by diversification.

Type of Risk

• Unsystematic Risk

diversifiable Risk Caused by such random events as

lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm.

Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.

Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.

Stand-alone Market Diversifiable risk risk risk

= + .

Capital AssetPricing Model (CAPM) an important tool used to analyze the

relationship between risk and rates of return .

The primary conclusion of the CAPM is this: The relevant risk of an individual stock is its contribution to the risk of a well-diversified portfolio

The risk that remains after diversifying is market risk, or the risk that is inherent in the market, and it can be measured by the degree to which a given stock tends to move up or down with the market.

Capital AssetPricing Model (CAPM)

ri expected rate of return on the ith stock. ri required rate of return on the ith stock.

rRF risk-free rate of return. In this context,

rRF is generally measured by the return on long-term U.S. Treasury bonds.

bi beta coefficient of the ith stock. The beta of an average stock is bA = 1.0

^

Capital AssetPricing Model (CAPM) rM required rate of return on a portfolio consisting of all

stocks, which is called the market portfolio. rM is also the required rate of return on an average (bA = 1.0)

stock. RPM = (rM - rRF)

risk premium on “the market,” and also on an average (b = 1.0) stock.

RPi = (rM - rRF) bi = (RPM)bi

Security Market Line (SML)

Required return = Risk-free return + Premium for risk. the relationship between the required return

and risk is called the Security Market Line (SML).