Chapter 4 Risk and Rates of Return

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Chapter 4 Risk and Rates of Return . © 2005 Thomson/South-Western. 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; must sum to 1.0 (100%).

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Chapter 4Risk 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;
• must sum to 1.0 (100%).
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
Continuous versus Discrete Probability Distributions
• Continuous Probability Distribution:number of possible outcomes is unlimited, or infinite.

s

Risk

=

=

=

Coefficient of variation

CV

Return

ˆ

k

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
Risk Aversion and Required Returns
• 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 Risk and Return
• The goal of finance manager is to create

AN EFFICIENT PORTFOLIO: “Maximizes return

for a given level of risk or minimizes risk for a

given level of return”.

Portfolio Returns
• The weighted average expected return on the stocks held in the portfolio
• Expected return on a portfolio,
Portfolio Returns
• Realized rate of return, k
• The return that is actually earned
• Actual return usually different from expected return
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 size and risk
• Inc size of a portfolio  risk dec
• Risk dec to a certain point .. (Co. risk = 0)
• If we take all sec in the stock mkt as one portfolio (max size)  still some risk exist (Market Risk) = relevant risk = the contribution of a sec’s risk to a portfolio.
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.
Firm-Specific Risk versus Market Risk
• Relevant Risk:
• The risk of a security that cannot be diversified away, or its market risk.
• This reflects a security’s contribution to a portfolio’s total risk.
NO GOOD…

.. of thinking how risky a security is if helf in isolation – you need to measure its market risk … measure how sensitive it is to market … this sensitivityis called BETA

The Concept of Beta
• Beta Coefficient, b:
• A measure of the extent to which the returns on a given stock move with the stock market.
• b = 0.5: Stock is only half as volatile, or risky, as the average stock.
• b = 1.0: Stock has the same risk as the average risk.
• b = 2.0: Stock is twice as risky as the average stock.
Steps in deriving Beta
• Plot mkt ret (X) and asset ret (Y) at various point in time.
• Regression: the slope = beta
• The higher the beta the higher the risk
• Beta for the market = 1, all other betas are viewed in relation to this value.
• Beta may be +ve or –v, +ve is the norm
• Majority of betas fall between .5 and 2.
Portfolio Beta Coefficients
• The beta of any set of securities is the weighted average of the individual securities’ betas
• IF mkt ret inc by 10%, a port with a beta of .75 will experience a 7.5% inc in its return (.75 x 10)
• 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%.
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.

Required Rate of Return (%)

khigh = 22

kM = kA = 14

kLOW = 10

kRF = 6

Relatively Risky Stock’s Risk Premium: 16%

Market (Average Stock) Risk Premium: 8%

Risk-Free Rate: 6%

0 0.5 1.0 1.5 2.0

Risk, bj

Security Market Line - CAPM
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, and
• 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, and
• 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, bx,
• Stock X’s expected growth rate, gX, and
• Changes in expected dividends, D0.