Reading 21

An analyst has estimated the following: Correlation of Bahr Industries returns with market returns = 0.8 Variance of the market returns = 0.0441 Variance of Bahr returns = 0.0225 The beta of Bahr Industries stock is closest to: A) 0.57. B) 0.77. C) 0.67.

A) 0.57. Covariance of Bahr and the market = 0.8×√0.0225×√0.0441=0.02520.8×0.0225×0.0441=0.0252 Bahr beta = 0.0252/0.0441= 0.57

The expected rate of return is 1.5 times the 16% expected rate of return from the market. What is the beta if the risk free rate is 8%? A) 2. B) 3. C) 4.

A) 2. 24 = 8 + β (16 - 8) 24 = 8 + 8β 16 = 8β 16 / 8 = β β = 2

Which of the following is NOT an assumption of capital market theory? A) Investors can lend at the risk-free rate but borrow at a higher rate. B) The capital markets are in equilibrium. C) All assets are infinitely divisible.

A) Investors can lend at the risk-free rate but borrow at a higher rate. Capital market theory assumes that investors can borrow or lend at the risk-free rate. The other statements are basic assumptions of capital market theory.

An analyst collected the following data for three possible investments. Alpha Corporation has a beta of 1.6, Omega Company has a beta of 1.2, and Lambda, Inc. has a beta of 0.5. The expected return on the market is -3% and the risk-free rate is 4%. Assuming that capital markets are in equilibrium, which stock has the highest expected return? A) Lambda. B) Omega. C) Alpha.

A) Lambda. An expected decline in the overall market suggests the stock with the lowest beta (Lambda) and, therefore, the least sensitivity to the market should have the highest expected rate of return. RRStock = Rf + (RMarket - Rf) × BetaStock, where RR = required return, Rf = risk-free rate, and RMarket = market rate of return Alpha: 4% + 1.6(-3% - 4%) = -7.2% Omega: 4% + 1.2(-3% - 4%) = -4.4% Lambda: 4% + 0.5(-3% - 4%) = +0.5%

An analyst estimated the following for three possible investments. Security A: Current Price = 25.00, Forecast Price in One Year = 31.00, Annual Dividend = 2.00, Beta = 1.6 Security B: Current Price = 10.00, Forecast Price in One Year = 10.80, Annual Dividend = 0, Beta = 0.5 Security C: Current Price = 105.00, Forecast Price in One Year = 110.00, Annual Dividend = 1.00, Beta = 1.2 Given an expected return on the market of 12% and a risk-free rate of 4%, which of the three securities is correctly priced based on the analyst's estimates? A) Lambda. B) Alpha. C) Omega.

A) Lambda. In the context of the SML, a security is underpriced if its required return is less than its estimated holding period return, is overpriced if its required return is greater than its estimated holding period return, and is correctly priced if its required return is equal to its estimated holding period return. Here, estimated holding period return is calculated as: (ending price - beginning price + cash flows) / beginning price. The required return based on the CAPM is: risk free rate + Beta × (expected market rate − risk free rate). For Alpha: ER = (31 - 25 + 2) / 25 = 32%, RR = 4 + 1.6 × (12 - 4) = 16.8%. Stock is underpriced. For Omega: ER = (110 - 105 + 1) / 105 = 5.7%, RR = 4 + 1.2 × (12 - 4) = 13.6%. Stock is overpriced. For Lambda, ER = (10.8 - 10) / 10 = 8%, RR = 4 + 0.5 × (12 - 4) = 8%. Stock is correctly priced.

Which of the following is an assumption of the Capital Asset Pricing Model (CAPM)? A) No investor is large enough to influence market prices. B) Investors with shorter time horizons exhibit greater risk aversion. C) There are no margin transactions or short sales.

A) No investor is large enough to influence market prices. The CAPM assumes all investors are price takers and no single investor can influence prices. The CAPM also assumes markets are free of impediments to trading and that all investors are risk averse and have the same one-period time horizon.

Which of the following is the vertical axis intercept for the Capital Market Line (CML)? A) Risk-free rate. B) Expected return on the portfolio. C) Expected return on the market.

A) Risk-free rate. The CML originates on the vertical axis from the point of the risk-free rate.

Which of the following statements about the security market line (SML) is least accurate? A) The independent variable in the SML equation is the standard deviation of the market portfolio. B) Securities plotting above the SML are undervalued. C) The SML measures risk using the standardized covariance of the stock with the market.

A) The independent variable in the SML equation is the standard deviation of the market portfolio. The SML uses either the covariance between assets and the market or beta as the measure of risk. Beta is the covariance of a stock with the market divided by the variance of the market. Securities that plot above the SML are undervalued and securities that plot below the SML are overvalued.

A stock that plots below the Security Market Line most likely: A) is overvalued. B) has a beta less than one. C) is below the efficient frontier.

A) is overvalued. Since the equation of the SML is the capital asset pricing model, you can determine if a stock is over- or underpriced graphically or mathematically. Your answers will always be the same. Graphically: If you plot a stock's expected return on the SML and it falls below the line, it indicates that the stock is currently overpriced, causing its expected return to be too low. If the plot is above the line, it indicates that the stock is underpriced. If the plot falls on the SML, it indicates the stock is properly priced. Mathematically: In the context of the SML, a security is underpriced if the required return is less than the holding period (or expected) return, is overpriced if the required return is greater the holding period (or expected) return, and is correctly priced if the required return equals the holding period (or expected) return.

The expected rate of return is twice the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%? A) 2. B) 3. C) 4.

B) 3. 24 = 6 + β (12 - 6) 18 = 6β β = 3

Which of the following statements about portfolio management is most accurate? A) As an investor diversifies away the unsystematic portion of risk, the correlation between his portfolio return and that of the market approaches negative one. B) Combining the capital market line (CML) (risk-free rate and efficient frontier) with an investor's indifference curve map separates out the decision to invest from the decision of what to invest in. C) The security market line (SML) measures systematic and unsystematic risk versus expected return; the CML measures total risk.

B) Combining the capital market line (CML) (risk-free rate and efficient frontier) with an investor's indifference curve map separates out the decision to invest from the decision of what to invest in. Combining the CML (risk-free rate and efficient frontier) with an investor's indifference curve map separates out the decision to invest from what to invest in and is called the separation theorem. The investment selection process is thus simplified from stock picking to efficient portfolio construction through diversification. The other statements are false. As an investor diversifies away the unsystematic portion of risk, the correlation between his portfolio return and that of the market approaches positive one. (Remember that the market portfolio has no unsystematic risk). The SML measures systematic risk, or beta risk.

Which is NOT an assumption of capital market theory? A) There are no taxes or transaction costs. B) Investments are not divisible. C) There is no inflation.

B) Investments are not divisible. Capital market theory assumes that all investments are infinitely divisible. The other statements are basic assumptions of capital market theory.

Which of the following statements regarding the Capital Asset Pricing Model is least accurate? A) It is useful for determining an appropriate discount rate. B) It is when the security market line (SML) and capital market line (CML) converge. C) Its accuracy depends upon the accuracy of the beta estimates.

B) It is when the security market line (SML) and capital market line (CML) converge. The CML plots expected return versus standard deviation risk. The SML plots expected return versus beta risk. Therefore, they are lines that are plotted in different two-dimensional spaces and will not converge.

Which of the following statements about the security market line (SML) and capital market line (CML) is most accurate? A) The SML involves the concept of a risk-free asset, but the CML does not. B) The SML uses beta, but the CML uses standard deviation as the risk measure. C) Both the SML and CML can be used to explain a stock's expected return.

B) The SML uses beta, but the CML uses standard deviation as the risk measure. The SML and CML both intersect the vertical axis at the risk-free rate. The SML describes the risk/return tradeoff for individual securities or portfolios, whereas the CML describes the risk/return tradeoff of various combinations of the market portfolio and a riskless asset.

Which of the following statements about risk is NOT correct? A) The market portfolio has only systematic risk. B) Total risk = systematic risk - unsystematic risk. C) Unsystematic risk is diversifiable risk.

B) Total risk = systematic risk - unsystematic risk. Total risk = systematic risk + unsystematic risk

Which of the following is the risk that disappears in the portfolio construction process? A) Interest rate risk. B) Unsystematic risk. C) Systematic risk.

B) Unsystematic risk. Unsystematic risk (diversifiable risk) is the risk that is eliminated when the investor builds a well-diversified portfolio.

In the context of the CML, the market portfolio includes: A) 12-18 stocks needed to provide maximum diversification. B) all existing risky assets. C) the risk-free asset.

B) all existing risky assets. The market portfolio has to contain all the stocks, bonds, and risky assets in existence. Because this portfolio has all risky assets in it, it represents the ultimate or completely diversified portfolio.

When the market is in equilibrium, all: A) assets plot on the CML. B) assets plot on the SML. C) investors hold the market portfolio.

B) assets plot on the SML. When the market is in equilibrium, expected returns equal required returns. Since this means that all assets are correctly priced, all assets plot on the SML. By definition, all stocks and portfolios other than the market portfolio fall below the CML. (Only the market portfolio is efficient.)

In equilibrium, an inefficient portfolio will plot: A) below the CML and below the SML. B) below the CML and on the SML. C) on the CML and below the SML.

B) below the CML and on the SML. An inefficient portfolio will plot below the CML. In equilibrium, all portfolios will plot on the SML.

In Fama and French's multifactor model, the expected return on a stock is explained by: A) excess return on the market portfolio, book-to-market ratio, and price momentum. B) firm size, book-to-market ratio, and excess return on the market portfolio. C) firm size, book-to-market ratio, and price momentum.

B) firm size, book-to-market ratio, and excess return on the market portfolio. In the Fama and French model, the three factors that explain individual stock returns are firm size, the firm's book value-to-market value ratio, and the excess return on the market portfolio. The Carhart model added price momentum as a fourth factor.

Portfolios that plot on the security market line in equilibrium: A) must be well diversified. B) may be concentrated in only a few stocks. C) have only systematic (beta) risk.

B) may be concentrated in only a few stocks. According to the capital asset pricing model, in equilibrium all securities and portfolios plot on the SML. A security or portfolio is not priced in equilibrium if it plots above the SML (i.e., is undervalued) or below the SML (i.e., is overvalued).

An analyst wants to determine whether Dover Holdings is overvalued or undervalued, and by how much (expressed as percentage return). The analyst gathers the following information on the stock: Market standard deviation = 0.70 Covariance of Dover with the market = 0.85 Dover's current stock price (P0) = $35.00 The expected price in one year (P1) is $39.00 Expected annual dividend = $1.50 3-month Treasury bill yield = 4.50%. Historical average S&P 500 return = 12.0%. Dover Holdings stock is: A) undervalued by approximately 2.1%. B) overvalued by approximately 1.8%. C) undervalued by approximately 1.8%.

B) overvalued by approximately 1.8%. To determine whether a stock is overvalued or undervalued, we need to compare the expected return (or holding period return) and the required return (from Capital Asset Pricing Model, or CAPM). Step 1: Calculate Expected Return (Holding period return) The formula for the (one-year) holding period return is: HPR = (D1 + S1 - S0) / S0, where D = dividend and S = stock price. Here, HPR = (1.50 + 39 - 35) / 35 = 15.71% Step 2: Calculate Required Return The formula for the required return is from the CAPM: RR = Rf + (ERM - Rf) × Beta Here, we are given the information we need except for Beta. Remember that Beta can be calculated with: Betastock = [covS,M] / [σ^2M]. Here we are given the numerator and the denominator, so the calculation is: 0.85 / 0.70^2 = 1.73. RR = 4.50% + (12.0 - 4.50%) × 1.73 = 17.48%. Step 3: Determine over/under valuation The required return is greater than the expected return, so the security is overvalued. The amount = 17.48% - 15.71% = 1.77%.

Based on Capital Market Theory, an investor should choose the: A) market portfolio on the Capital Market Line. B) portfolio that maximizes his utility on the Capital Market Line. C) portfolio with the highest return on the Capital Market Line.

B) portfolio that maximizes his utility on the Capital Market Line. Given the Capital Market Line, the investor chooses the portfolio that maximizes his utility. That portfolio may be exactly the market portfolio or it may be some combination of the risk-free asset and the market portfolio.

The risk-free rate is 5% and the expected market return is 15%. A portfolio manager is estimating a return of 20% on a stock with a beta of 1.5. Based on the SML and the analyst's estimate, this stock is: A) overvalued. B) properly valued. C) undervalued.

B) properly valued. Based on the CAPM, the portfolio should earn: E(R) = 0.05 + 1.5(0.15 − 0.05) = 0.20 or 20%. On a risk-adjusted basis, this portfolio lies on the SML and is, thus, properly valued.

The beta of stock D is -0.5. If the expected return of Stock D is 8%, and the risk-free rate of return is 5%, what is the expected return of the market? A) +3.5%. B) +3.0%. C) -1.0%.

C) -1.0%. RRStock = Rf + (RMarket - Rf) × BetaStock, where RR = required return, R = return, and Rf = risk-free rate A bit of algebraic manipulation results in: RMarket = [RRStock - Rf + (BetaStock × Rf)] / BetaStock = [8 - 5 + (-0.5 × 5)] / -0.5 = 0.5 / -0.5 = -1%

A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio? A) 0.568. B) 0.147. C) 0.725.

C) 0.725. Sharpe ratio = (22% - 7.50%) / 20% = 0.725.

A stock has a beta of 1.55 and an expected return of 17.3%. If the risk-free rate is 8%, the expected market risk premium is: A) 12.0%. B) 14.0%. C) 6.0%.

C) 6.0%. 17.3 = 8 + 1.55(MRP) 9.3 = 1.55(MRP) MRP = 9.3 / 1.55 = 6

The stock of Mia Shoes is currently trading at $15 per share, and the stock of Video Systems is currently trading at $18 per share. An analyst expects the prices of both stocks to increase by $2 over the next year and neither company pays dividends. Mia Shoes has a beta of 0.9 and Video Systems has a beta of (-0.3). If the expected market return is 15% and the risk-free rate is 8%, which trading strategy does the CAPM indicate for these two stocks? Mia Shoes;Video Systems A) Buy;Buy B) Buy;Sell C) Sell;Buy

C) Sell;Buy The required return for Mia Shoes is 0.08 + 0.9 × (0.15-0.08) = 14.3%. The forecast return is $2/$15 = 13.3%. The stock is overvalued and the investor should sell it. The required return for Video Systems is 0.08 - 0.3 × (0.15-0.08) = 5.9%. The forecast return is $2/$18 = 11.1%. The stock is undervalued and the investor should buy it.

An analyst determines that three stocks have the following characteristics: Stock X: Beta = 1.0, Estimated Return = 10% Stock X: Beta = 1.6, Estimated Return = 16% Stock X: Beta = 2.0, Estimated Return = 16% If the risk-free rate is 4% and the expected return on the market is 10%, which of the following statements is most accurate? A) Stock X is undervalued. B) Stock Y is overvalued. C) Stock Z is properly valued.

C) Stock Z is properly valued. Using the CAPM, the required rate of return for each stock is: E(RX) = 4% + 1.0(10% − 4%) = 10.0%. 10.0% − 10.0% = 0.0%, properly valued. E(RY) = 4% + 1.6(10% − 4%) = 13.6%. 16.0% − 13.6% = 2.4% undervalued. E(RZ) = 4% + 2.0(10% − 4%) = 16.0%. 16.0% − 16.0% = 0.0%, properly valued.

When a risk-free asset is combined with a portfolio of risky assets, which of the following is least accurate? A) The standard deviation of the return for the newly created portfolio is the standard deviation of the returns of the risky asset portfolio multiplied by its portfolio weight. B) The expected return for the newly created portfolio is the weighted average of the return on the risk-free asset and the expected return on the risky asset portfolio. C) The variance of the resulting portfolio is a weighted average of the returns variances of the risk-free asset and of the portfolio of risky assets.

C) The variance of the resulting portfolio is a weighted average of the returns variances of the risk-free asset and of the portfolio of risky assets. This statement is not correct; the standard deviation of returns for the resulting portfolio is a weighted average of the returns standard deviation of the risk-free asset (zero) and the returns standard deviation of the risky-asset portfolio.

Which of the following terms refer to the same type of risk? A) Undiversifiable risk and unsystematic risk. B) Systematic risk and firm-specific risk. C) Total risk and the variance of returns.

C) Total risk and the variance of returns. Variance is a measure of total risk.

Which of the following statements about systematic and unsystematic risk is most accurate? A) As an investor increases the number of stocks in a portfolio, the systematic risk will remain constant. B) The unsystematic risk for a specific firm is similar to the unsystematic risk for other firms. C) Total risk equals market risk plus firm-specific risk.

C) Total risk equals market risk plus firm-specific risk. Total risk equals systematic (market) plus unsystematic (firm-specific) risk. The unsystematic risk for a specific firm is not similar to the unsystematic risk for other firms in the same industry. Unsystematic risk is firm-specific or unique risk. Systematic risk of a portfolio can be changed by adding high-beta or low-beta stocks.

An investor believes Stock M will rise from a current price of $20 per share to a price of $26 per share over the next year. The company is not expected to pay a dividend. The following information pertains: RF = 8% ERM = 16% Beta = 1.7 Should the investor purchase the stock? A) No, because it is overvalued. B) No, because it is undervalued. C) Yes, because it is undervalued.

C) Yes, because it is undervalued. In the context of the SML, a security is underpriced if the required return is less than the holding period (or expected) return, is overpriced if the required return is greater the holding period (or expected) return, and is correctly priced if the required return equals the holding period (or expected) return. Here, the holding period (or expected) return is calculated as: (ending price - beginning price + any cash flows/dividends) / beginning price. The required return uses the equation of the SML: risk free rate + Beta × (expected market rate − risk free rate). ER = (26 - 20) / 20 = 0.30 or 30%, RR = 8 + (16 - 8) × 1.7 = 21.6%. The stock is underpriced therefore purchase.

For an investor to move further up the Capital Market Line than the market portfolio, the investor must: A) diversify the portfolio even more. B) reduce the portfolio's risk below that of the market. C) borrow and invest in the market portfolio.

C) borrow and invest in the market portfolio. Portfolios that lie to the right of the market portfolio on the capital market line ("up" the capital market line) are created by borrowing funds to own more than 100% of the market portfolio (M). The statement, "diversify the portfolio even more" is incorrect because the market portfolio is fully diversified.

All portfolios that lie on the capital market line: A) have some unsystematic risk unless only the risk-free asset is held. B) contain at least some positive allocation to the risk-free asset. C) contain the same mix of risky assets unless only the risk-free asset is held.

C) contain the same mix of risky assets unless only the risk-free asset is held. All portfolios on the CML include the same tangency portfolio of risky assets, except the intercept (all invested in risk-free asset). The tangency portfolio contains none of the risk-free asset and "borrowing portfolios" can be constructed with a negative allocation to the risk-free asset. Portfolios on the CML are efficient (well-diversified) and have no unsystematic risk.

Which of the following is the most accurate description of the market portfolio in Capital Market Theory? The market portfolio consists of all: A) equity securities in existence. B) risky and risk-free assets in existence. C) risky assets in existence.

C) risky assets in existence. The market portfolio, in theory, contains all risky assets in existence. It does not contain any risk-free assets.

James Franklin, CFA, has high risk tolerance and seeks high returns. Based on capital market theory, Franklin would most appropriately hold: A) a high-beta portfolio of risky assets financed in part by borrowing at the risk-free rate. B) a high risk biotech stock, as it will have high expected returns in equilibrium. C) the market portfolio as his only risky asset.

C) the market portfolio as his only risky asset. According to capital market theory, all investors will choose a combination of the market portfolio and borrowing or lending at the risk-free rate; that is, a portfolio on the CML.

One of the assumptions underlying the capital asset pricing model is that: A) only whole shares or whole bonds are available. B) each investor has a unique time horizon. C) there are no transactions costs or taxes.

C) there are no transactions costs or taxes. The CAPM assumes frictionless markets, i.e., no taxes or transactions costs. Among the other assumptions of the CAPM are that all investors have the same one-period time horizon and that all investments are infinitely divisible.

The correlation of returns on the risk-free asset with returns on a portfolio of risky assets is: A) negative. B) positive. C) zero.

C) zero. The risk-free asset has zero correlation of returns with any portfolio of risky assets.