finance ch.8

Key Financial Concept Recall from Chapter One: Risk Requires a RewardThe purpose of this chapter is toShow how we measure riskQuantify the relationship between risk and reward
Return on an Investment Income plus Capital Appreciation (or Loss)Divided by Investment
Types of Return Realized Return – the return that actual has been earned or actually will be earned (The returns we have talked about so far.)Expected Return (based on anticipated income and anticipated capital appreciation)Realized return often differs from expected return.Required Return (the anticipated return necessary to get an investor to bear the risk associated with a particular investment
Expected Return The expected return is equal to the weighted average of the possible future returns:E(R) = (pr1 × R1) + (pr2 × R2) + … Each R represents a possible return.The weights are the probabilities of each possible return.Note: Weights must add to 1.0
Expected Return Example An investment has a 40% of chance of having a return of -100% (lose everything) and a 60% chance of having a return of +100% (double your money). What is the expected return?.40(-1.0) + .6(+1.0) = .20 or +20% = E(R)Always work in decimals.The only possible returns are -1.0 and +1.0.The probability of a -1.0 return is .40The probability of a +1.0 return is .60Weights add to 1.0: .40 + .60 = 1.0
Risk Risk is the uncertainty associated with earning the expected return.There is no risk in a world of certaintyDecisions must be made in the present, based on anticipated returns.Results (realized return) occur in the future.Risk means that results may differ from the anticipated returns.
Portfolios A portfolio is a collection of assets held for investment purposes.A diversified portfolio contains many different types of assets so that the risks unique to a particular asset (unsystematic risk) offset each other.
Sources of Risk Warning!What your text says about the sources of risk Two parts of TOTAL RISKUnsystematic risk (diversifiable) -depends on events that are unique to a particular firmSystematic risk (non-diversifiable) – depends on the firm’s exposure to economic-wide events. is very misleading. IGNOR IT!
Diversifiable Risk (Unsystematic Risk) Instability in a firm’s revenues or costs caused by events that only affect one firm such asChanges in managementStrikesLawsuitsUnsystematic risk is reduced through portfolio diversification.
Nondiversifiable Risk (Systematic Risk Risk arising from economic factors that affect all firms to some degree such asFluctuations in stock market prices / a change in the Dow Jones industrial averageChanges in interest ratesChanges in inflationChanges in the value of a foreign currencyChanges in commodity pricesThe tendency for a stock’s return and the return on the market to move together.Systematic risk is NOT reduced through portfolio diversification.
Nondiversifiable Risk (Systematic Risk) Firms will have high systematic risk if Their sales revenues depend heavily on the business cycle (choice of business)Their costs of production tend to be fixed rather than variable (choice of production method)They have more debt (choice of funding)Financial risk (amount of debt) is NOT diversifiable because firms with heavy use of debt financing are more likely to fail in an economic downturn
The Standard Deviation as a Measure of Risk SD is a measure of total risk (the sum of systematic risk and unsystematic risk)SD measures the dispersion (spread) of the possible returns around the expected return.The larger the standard deviation of an investment’s return, the larger the risk.
Rule of Thumb About 2/3 of the time (68%), the realized return will be within one standard deviation of the expected return.About 2/3 of the time, the realized return on Stock A will be between 14% and 16%.About 2/3 of the time, the realized return on Stock B will be between 11.7% and 18.3%
Portfolio Expected Returns The expected return on a portfolio is equal to the weighted average of the returns on the assets within the portfolio.E(RP) = (w1 × E(R1)) + (w2 × E(R2)) + … The return on a portfolio considers bothThe individual asset’s returnThe proportion of the portfolio that is invested in that asset.
Portfolio Standard Deviation The standard deviation of a portfolio is between zero and the weighted average standard deviation.0 < SDP < WASDForming a portfolio reduces (but does not eliminate risk) without reducing expected return (which is the reward for bearing risk)!
Risk Reduction Through Diversification Firm-specific factors of the assets within a well-diversified portfolio tend to offset.A diversified portfolio reduces unsystematic risk (and total risk)A diversified portfolio does NOT reduce systematic risk.
Beta Coefficients A beta coefficient is an index (measure) of an asset’s systematic risk.An asset’s beta depends on two factorsThe volatility (standard deviation) of an asset’s return relative to the volatility of the “market portfolio.”The linkage (correlation) between the return on the asset and the return on the “market portfolio.”
The “Market Portfolio” The “Market Portfolio” ought to be the portfolio of all tradable assets in the world.Returns on this true “Market Portfolio” would be impossible to measure.We estimate betas using a substitute, like the S&P 500, for the “Market Portfolio.”An asset’s estimated beta depends upon its standard deviation relative to the standard deviation of the S&P 500 and its correlation with the S&P 500.
Interpreting a Beta of 1.0 A beta of 1.0 indicates that an asset has the same systematic risk as the market (S&P 500) and the average stock and will tend to have the same returns as the market.When the market goes up by 10%, the stock with a beta of 1.0 will tend to go up by 10%When the market goes down by 10%, the stock with a beta of 1.0 will tend to go down by 10%
Interpreting a Beta Greater Than 1.0 An asset with a beta greater than 1.0 will tend to move in the same direction as the market, but move more than the market.When the market goes up by 10%, the high beta stock will tend to go up by more than 10%When the market goes down by 10%, the high beta stock will tend to go down by more than 10%Why would an aggressive investor prefer stocks with high betas during rising markets?
Interpreting a Beta Between 0 and 1.0 An asset with a beta between 0 and 1.0 will tend to move in the same direction as the market, but move less than the market.When the market goes up by 10%, the low beta stock will tend to go up by less than 10%When the market goes down by 10%, the low beta stock will tend to go down by less than 10%Most stocks have betas between 0.6 and 1.6.
Interpreting a Negative Beta An asset with a beta less than zero will tend to move opposite the market.When the market goes up, the negative beta asset will tend to go down.When the market goes down the negative beta asset with tend to go up.Negative betas are very rare in stocks.Investors invest in assets like gold in hopes of finding negative betas.
Portfolio Beta The beta of a portfolio is equal to the weighted average of the betas of assets within the portfolioβP = (w1 × β1) + (w2 × β2) + … The beta of a portfolio considers bothThe individual asset’s beta.The proportion of the portfolio that is invested in that asset.
Beta Stability Beta coefficients are computed with estimated data concerning the asset’s realized return.The numerical value of an asset’s beta are NOT stable over time.The beta of a portfolio tends to be much more stable that the betas of component assets.
Two Important Reasons for Diversifying a Portfolio Diversification reduces the portfolio’s unsystematic risk.Diversification makes the portfolio’s systematic risk more stable
Capital Asset Pricing Model CAPM is the easiest of many techniques used to estimate the risk-adjusted required return on an asset.The CAPM specifies the required return for each level of systematic risk.The CAPM uses beta as the measure of risk
CAPM Required Return = rf + (rm – rf)βAccording to CAPM, an asset’s risk-adjusted required return depends uponThe rate of return on a risk-free security (risk-free rate), rf (Usually the t-bill rate)The risk premium on the market (rm – rf) (The anticipated return on the market (rm) minus the risk-free rate (rf).)The asset’s systematic risk (the asset’s beta) (β)
Some Observations from the CAPM Graph According to CAPM, the relationship between an asset’s risk-adjusted required return and its beta is a straight line.The larger an asset’s beta, the larger its required return.When an asset’s beta is zero, its required return is equal to the risk-free rate.When an asset’s beta is one, its required return is equal to the return on the market portfolio.When an asset’s beta is negative, its required return is less than the risk-free rate.
Changes in Risk-Adjusted Required Return Every thing else equal, what happens to the risk-adjusted required return on an asset whenThe asset’s beta increases (decreases)? (How could that happen?)The risk-free rate increases (decreases)?The risk premium on the market increases (decreases)?
CAPM Example Suppose the t-bill rate is 4%, the expected return on the market is 10% and a stock has a beta of 1.2. What is the required return on the stock?Required Return = rf + (rm – rf)β= .04 +(.10 – .04)1.2= .04 +(.06)1.2= .04 + .072 = .112 or 11.2%
CAPM Example (Continued) A beta of 1.2 implies The stock is riskier than the marketThe stock’s risk premium (7.2%) is 1.2 times the risk premium on the market (6%)Why is the required return on the stock (11.2%) NOT 1.2 time the return on the market (1.2 × 10% = 12%)?
Risk Management An investor may reduce risk bySelecting low beta stocks (reduces systematic risk)Constructing a diversified portfolio (reduces unsystematic risk)An investor may reduce unsystematic risk by selecting stocks with poorly correlated returns.For a security to help diversify a portfolio, the correlation between the return on the security and the return on other securities in the portfolio should be low, but it doesn’t have to be negative.

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