Chapter 11 Risk and Rates of Return. Defining and Measuring Risk Risk is the chance that an...

transcript

Chapter 11

Risk and Rates of Return

Defining and Measuring Risk

• Risk is the chance that an unexpected outcome will occur

• A probability distribution is a listing of all possible outcomes with a probability assigned to each.

• Probability must sum to 1.0 (100%)

Probability Distributions

Either it will rain or it will not.There are only two possible outcomes.Outcome (1) Probability (2)

Rain 0.40 = 40%

No Rain 0.60 = 60%

1.00 100%

Probability Distributions

Martin Products and U. S. Electric

Martin Products U.S. Electric

Boom 0.2 110% 20%Normal 0.5 22% 16%Recession 0.3 -60% 10%

Probability of This State Occurring

State of the Economy

Rate of Return on Stock if This State Occurs

Expected Rate of Return

• Rate of return expected to be realized from an investment during its life

• Mean value of the probability distribution of possible returns

• Weighted average of the outcomes, where the weights are the probabilities 5

Expected Rate of Return

(1) (2) (3) = (4) (5) = (6)Boom 0.2 110% 22% 20% 4%Normal 0.5 22% 11% 16% 8%Recession 0.3 -60% -18% 10% 3%

1.0 km = 15% km = 15%

State of the Economy

Martin Products U. S. Electric

Return if This State Occurs (ki)

Product: (2) x (5)

Probability of This State

Occurring (Pr i)

Return if This State

Occurs (ki)Product: (2) x (3)

Continuous versus Discrete Probability Distributions• Discrete Probability Distribution:

Where the number of possible outcomes is limited (or finite).• Continuous Probability Distribution:

Where the number of possible outcomes is unlimited or infinite.

Discrete Probability DistributionsDiscrete Probability Distributionsa. Martin Products

Probability of Occurrence

b. U. S. ElectricProbability of Occurrence

-60 -45 -30 -15 0 15 22 30 45 60 75 90 110Rate of

Return (%)Expected Rate of Return (15%)

-10 -5 0 5 10 16 20 25Rate of

Return (%)Expected Rate

of Return (15%)

Probability Density

-60 0 15 110Rate of Return

(%)Expected Rate of Return

Martin ProductsMartin Products

U. S. ElectricU. S. Electric

Continuous Probability Distributions

Measuring Risk: The Standard Deviation• Expected rate of return:

The weighted average of the expected returns• Variance:

The weighted average of the squared deviations from the mean expected return

• Standard deviation:The square root of the variance

Measuring Risk: The Standard Deviation

Calculating Martin Products’ Standard Deviation

(1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6)110% 15% 95 9,025 0.2 1,805.0 22% 15% 7 49 0.5 24.5 -60% 15% -75 5,625 0.3 1,687.5

Payoff

ki(ki - k)

2Pr iProbability

Expected Return

kki - k (ki - k)

%3.59 517,3 Deviation Standard

0.517,3 Variance

Measuring Risk: Coefficient of Variation

• Standardized measure of risk per unit of return• Calculated as the standard deviation divided by

the expected return• Useful where investments differ in risk and

expected returns

k̂Return

Risk CV Coefficient of variation

Risk Aversion

• Risk-averse investors require higher rates of return to invest in higher-risk securities

Risk Aversion and Required Returns

• Risk Premium (RP):

• The portion of the expected return that can be attributed to an investment’s risk beyond a riskless investment

• The difference between the expected rate of return on a given risky asset and that on a less risky asset

Portfolio Risk and theCapital Asset Pricing Model• CAPM:

• A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium, where risk is based on diversification.

• Portfolio• A collection of investment securities

Portfolio Returns

• Expected return on a portfolio,

The weighted average expected return on the stocks held in the portfolio

Portfolio Returns

• Realized rate of return, k• The return that is actually earned• The actual return usually differs from the expected return.

Returns Distribution for Two Perfectly Negatively Correlated Stocks (r = -1.0) and for Portfolio WM:

Stock W

Portfolio WM

Stock M

Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM’:

Stock M

Stock M’

Stock MM’

Portfolio Risk

• Correlation Coefficient, r• Measures the degree of relationship between two variables.• Perfectly correlated stocks have rates of return that move in the

same direction.• Negatively correlated stocks have rates of return that move in

opposite directions.

Portfolio Risk

• Risk Reduction• Combining stocks that are not perfectly correlated will reduce the

portfolio risk through diversification.• The riskiness of a portfolio is reduced as the number of stocks in

the portfolio increases.• The smaller the positive correlation, the lower the risk.

Firm-Specific Risk versus Market Risk

• Firm-Specific Risk:• That part of a security’s risk associated with random outcomes

generated by events, or behaviors, specific to the firm.

• Firm-specific risk can be eliminated through proper diversification.

Firm-Specific Risk versus Market Risk

• Market Risk:• That part of a security’s risk that cannot be eliminated through

diversification because it is associated with economic, or market, factors that systematically affect all firms.

The Concept of Beta

• Beta Coefficient, • A measure of the extent to which the returns on a given

stock move with the stock market.• = 0.5: Stock is only half as volatile, or risky, as the

average stock.• = 1.0: Stock has the same risk as the average risk.• = 2.0: Stock is twice as risky as the average stock.

Portfolio Beta Coefficients

• The beta of any set of securities is the weighted average of the individual securities’ betas

The Relationship Between Risk and Rates of Return

stock j on thereturn of rate k̂ thj expected

stock j on thereturn of rate k

stock j on thereturn of rate k̂th

required

expected

return of rate k

stock j on thereturn of rate k̂

freerisk

required

expected

premiumrisk market k-k RP

return of rate freerisk k

stock j on thereturn of rate required k

stock j on thereturn of rate expected k̂

stock j on the premiumrisk k-k RP

premiumrisk market k-k RP

return of rate k

stock j on thereturn of rate k̂

thjRFMj

freerisk

required

expected

Market Risk Premium

• RPM is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

• Assuming:• Treasury bonds yield = 6%• Average stock required return = 14%• Then the market risk premium is 8 percent:

• RPM = kM - kRF = 14% - 6% = 8%.31

Risk Premium for a Stock

• Risk Premium for Stock j = RPj = RPM xj

The Required Rate of Return for a Stock

• Security Market Line (SML):• The line that shows the relationship between risk as measured by beta

and the required rate of return for individual securities.33

jstock for return of rate k j required

jRFMRF

RP k k

Security Market Line

jRFMRFj kk k k:SML

khigh = 22

kM = kA = 14

kLOW = 10

kRF = 6

Risk, j0 0.5 1.0 1.5 2.0

Required Rate of Return (%)

Risk-Free Rate: 6%

Safe Stock Risk Premium: 4%

Market (Average Stock) Risk Premium: 8%

Relatively Risky Stock’s Risk Premium: 16%

The Impact of Inflation

• kRF is the price of money to a riskless borrower.• The nominal rate consists of:

• a real (inflation-free) rate of return• an inflation premium (IP)

• An increase in expected inflation would increase the risk-free rate.

Changes in Risk Aversion

• The slope of the SML reflects the extent to which investors are averse to risk.

• An increase in risk aversion increases the risk premium and increases the slope.

Changes in a Stock’s Beta Coefficient• The Beta risk of a stock is affected by:

• composition of its assets• use of debt financing• increased competition• expiration of patents

• Any change in the required return (from change in beta or in expected inflation) affects the stock price.

Stock Market Equilibrium

• The condition under which the expected return on a security is just equal to its required return

• Actual market price equals its intrinsic value as estimated by the marginal investor, leading to price stability

Changes in Equilibrium Stock Prices• Stock prices are not constant due to changes in:

• Risk-free rate, kRF,

• Market risk premium, kM – kRF,

• Stock X’s beta coefficient, x,

• Stock X’s expected growth rate, gX, and

• Changes in expected dividends, D0.

Physical AssetsVersus Securities• Riskiness of corporate assets is only relevant in terms of its

effect on the stock’s risk.

Word of Caution

• CAPM• Based on expected conditions• Only have historical data• As conditions change, future volatility may differ from past

volatility• Estimates are subject to error

Chapter 11 Risk and Rates of Return. Defining and Measuring Risk Risk is the chance that an...

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