chapter 7: risk and return - textbook media · risk and rates of return beta = 1. market beta = 1....

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Risk and Return

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Learning Objectives

Define risk, risk aversion, and risk-return tradeoff.Measure risk.Identify different types of risk.Explain methods of risk reduction.Describe how firms compensate for risk.Discuss the CAPM.

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Expected Return

Expected return is the mean of the probability distribution of possible returns.Future returns are not known with certainty. The standard deviation is a measure of this uncertainty.

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Expected ReturnExpected return is the mean of the probability distribution of possible returns.Future returns are not known with certaintyTo calculate expected return, compute the weighted average of possible returns

whereμ = Expected returnVi = Possible value of return

during period iPi = Probability of V

occurring during period i

μ = Σ(Vi x Pi)

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Expected Return CalculationExample:

You are evaluating Zumwalt Corporation’s common stock. You estimate the following returns given different states of the economy

State of Economy Probability Return

Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%

= – 0.5%= 1.0%= 4.0%= 6.0%

k = 10.5%

Expected rate of return on the stock is 10.5%

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Risk and Rates of Return

Risk is the potential for unexpected events to occur.If two financial alternatives are similar except for their degree of risk, most people will choose the less risky alternative because they are risk aversei.e. they don’t like risk.Risk averse investors will require higher expected rates of return as compensation for taking on higher levels of risk.

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Measurement of Investment Risk

Example:You evaluate two investments: Zumwalt Corporation’s common stock and a one year Gov't Bond paying a guaranteed 6%.

Link to Society for Risk Analysis

100%

Return

Probability of Return

T-Bill

6%Return

10%

Probability of Return

Zumwalt Corp

5%

20%30%40%

10% 20%–5%

There is risk in owning Zumwalt stock, no risk in owning the T-bills

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Measurement of Investment RiskStandard Deviation (σ) measures the dispersion of returns. It is the square root of the variance.

Example:Compute the standard deviation on Zumwalt common stock. the mean (μ) was previously computed as 10.5%

σ = SQRT( Σ P(V - μ)2)

State of Economy Probability ReturnEconomic Downturn .10 5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%

(- - 10.5%)2 = .24025%

( - 10.5%)2 = .001%( - 10.5%)2 = .27075%

( - 10.5%)2 = .0605%

Σ = σ2 = varianceσ2 = .005725 = 0.5725%σ = SQRT of 0.005725σ = .07566 = 7.566%

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― Market related Risk - Risk due to overall market conditions

Stock price is likely to rise if overall stock market is doing well.

Risk and Rates of Return

– Firm Specific Risk - Risk due to factors within the firm

Risk of a company's stock can be separated into two parts:

Stock price will most likely fall if a major government contract is discontinued unexpectedly.

Diversification: If investors hold stock in many companies, the firm specific risk will be cancelled out.

Even if investors hold many stocks, cannot eliminate the market related risk

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Risk and Diversification– If an investor holds enough stocks in

portfolio (about 20) company specific (diversifiable) risk is virtually eliminated

# of stocks in Portfolio

Variability of Returns

Risk and Rates of Return

Market Related Risk

11# of stocks in Portfolio

Variability of Returns

Risk and Diversification– If an investor holds enough stocks in

portfolio (about 20) company specific (diversifiable) risk is virtually eliminated

Risk and Rates of Return

Firm Specific Risk

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Risk and Diversification– If an investor holds enough stocks in

portfolio (about 20) company specific (diversifiable) risk is virtually eliminated

Risk and Rates of Return

# of stocks in Portfolio

Variability of Returns

Total Risk

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Market risk is the risk of the overall market, so to measure we need to compare individual stock returns to the overall market returns.A proxy for the market is usually used: An index of stocks such as the S&P 500Market risk measures how individual stock returns are affected by this marketRegress individual stock returns on the returns of the market index

Risk and Rates of Return

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Risk and Rates of ReturnRegress individual stock returns on Market index

S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

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S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Jan 1999PepsiCo-0.37%S&P -1.99%

Risk and Rates of ReturnRegress individual stock returns on Market index

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S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Plot Remaining Points

Risk and Rates of ReturnRegress individual stock returns on Market index

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S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Best Fit Regression Line

Risk and Rates of ReturnRegress individual stock returns on Market index returns

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Risk and Rates of ReturnRegress individual stock returns on Market index returns

S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Slope = riserun

5.5%5%= = 1.1

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Market Risk is measured by Beta

Risk and Rates of Return

Beta is the slope of the regression (characteristic) line

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S&PReturn

PepsiCoReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Slope = 1.1 = Beta (β)

Risk and Rates of ReturnMarket Risk is measured by Beta– Beta is the slope of the regression (characteristic)

line

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Interpreting Beta

Risk and Rates of Return

Beta = 1Market Beta = 1Company with a beta of 1 has average risk

Beta < 1Low Risk CompanyReturn on stock will be less affected by the market than

average

Beta > 1High Market Risk CompanyStock return will be more affected by the market than

average

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kj = kRF + βj ( kM – kRF )

Security Market Line

where:Kj = required rate of return on the jth securityKRF = risk free rate of returnKM = required rate of return on the marketBj = Beta for the jth security

The Capital Asset Pricing ModelInvestors adjust their required rates of return to compensate for risk.The CAPM measures required rate of return for investments, given the degree of market risk measured by beta.

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CAPM Example

Suppose that the required return on the market is 12% and the risk free rate is 5%.

kj = kRF + βj ( kM – kRF )

Security Market Line

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Beta1.51.0.50

15%

10%

5%Risk Free Rate

CAPM Example

Suppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + βj (12% – 5% )

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Beta1.51.0.50

15%

10%

5%

Risk & Return on market

CAPM ExampleSuppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + βj (12% – 5% )

Risk Free Rate

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Beta1.51.0.50

15%

10%

5%

CAPM Example

Suppose that the required return on the market is 12% and the risk free rate is 5%.

SML

Connect Points forSecurity Market Line

Market

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Beta1.5.50

15%

10%

5%

SML13.4%

1.0 1.2

If beta = 1.2kj = 13.4

CAPM Example

Suppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + βj (12% – 5% )

Market