*The standard deviation of stock returns for stock A is 40%. The standard deviation of the market return is 20%. |
If the correlation between Stock A and the market is 0.70, what is Stock A's beta? |
*Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected |
return of 18% and a standard deviation of 60%. The correlation coefficient between stocks A and B |
is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A |
and 70% in Stock B. |
24-1 *The standard deviation of stock returns for stock A is 40%. The standard deviation of the market return is 20%. If the correlation between Stock A and the market is 0.70, what is Stock A's beta? 24-4 *Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between stocks A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B. 24-5 *The beta coefficient of an asset can be expressed as a function of the asset's correlation with the market as folows: bi=ῤiới/ớM a) Substitute this expression for beta into the SML, equation 24-9: [pg. 944, chapter 24, Brigham and Ehrardt, Financial Management, 13th edition]. This results in an alternative form of the SML. b) Compare your answer to part a with the CML, equation 24-6: [pg. 942, chapter 24, Brigham and Ehrhardt, Financial Management, 13th edition]. What similarities are observed? What conclusions can be drawn? 24-7 *The following data is given: yrNYSEStock X 13.0%4.0% 213.3%19.2% 318.0%10.1% 4-12.7%-5.0% 5-25.5%-14.3% 634.2%34.1% 722.8%7.1% 8-6.2%5.2% 95.6%15.8% 1020.5%25.1% 1129.6%20.0% Mean9.33%11.03% Stdeviat18.49%13.78% a) Use a spreadsheet to determine Stock X's beta coefficient. b) Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE. c) Assume that the situation during years 1 to 7 is expected to prevail in the future (ie: rhatx=rbarx, rhatM=rbarM, and both OX and bX in the future will equal their past values). Also assume that Stock X is in equilibrium-that is, it plots on the SML. What is the risk free rate? d) Plot the SML. e) Suppose you hold a large, well-diversified potfolio and are considering adding to that portfolio either Stock X or another stock, Stock Y, which has the same beta as Stock X but a higher standard deviation of returns. Stock X and Y have the same expected returns: rhatX=rhaty=10.6%. Which stock should you choose? 24-9 TEMPLATECHAPTER 25 BUILD MODEL TEMPLATE6/21/14 Chapter:25 Problem:7TEMPLATE Following is information for the required returns and standard deviations of returns for A, B, and C. Here are the expected returns and standard deviations for stocks A, B, and C: Stockrisi A8.0%35.11% B12.0%55.85% C24.0%92.44% Here is the correlation matrix: ABC A1.00000.15710.1891 B0.15711.00000.1661 C0.18910.16611.0000 a. Suppose a portfolio has 25 percent invested in A, 45 percent in B, and 30 percent in C. What are the expected return and standard deviation of the portfolio? wA =25% wB =45% wC =30% rp = Hint: for the portoflio standard deviation, start by creating a table like the one in Section 3.1 for the N-asset case. In fact, begin by creating a table with the products of the weights and standard deviations for each pair of stocks. If you are careful about how you construct the formulas, you can copy them. Then take the results from this intermediate table and multiply them by the correlations above. ABC wi = si = wi x si =Hint: put the products of weights and standard deviations for each stock in this row. wisiwi x si A25%35% Mike Ehrhardt: Hint: put the products of weights and standard deviations for each stock in this column.0.000000.000000.00000Hint: the values in this box should equal wi x si x wj x sj. B45%56%0.000000.000000.00000 C30%92%0.000000.000000.00000 Now multiply the products of wi x si x wj x sj by the correlations given above to create a table like the one in Section 3.1.A000Hint: the values in this box should equal wi x si x wj x sj x rij. B000 C000 Portfolio variance =0.0000Hint: portfolio variance is the sum of all the values in the table immediately above. sp =0.00% b. The partial model lists 66 different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. Hint: Use the formula to calculate the variance for each portfolio and then copy it down. This formula should have six values in it: 1 for Stock A, 1 for Stock B, 1 for Stock C, one for the cross-term of A and B, 1 for the cross-term of A and C, and 1 for the cross term of B and C. The results for portfolio #36 should match your results in part a. template Portoflio #wA wB wC Variancesp rp 10.00.01.00.854592.44%24.00% 20.00.10.90.710784.30%22.80% 30.00.20.80.586876.60%21.60% 40.00.30.70.482869.48%20.40% 50.00.40.60.398763.14%19.20% 60.00.50.50.334557.83%18.00% 70.00.60.40.290253.87%16.80% 80.00.70.30.265851.55%15.60% 90.00.80.20.261351.11%14.40% 100.00.90.10.276652.60%13.20% 110.01.00.00.311955.85%12.00% 120.10.00.90.704483.93%22.40% 130.10.10.80.575475.86%21.20% 140.10.20.70.466368.28%20.00% 150.10.30.60.377061.40%18.80% 160.10.40.50.307755.47%17.60% 170.10.50.40.258250.82%16.40% 180.10.60.30.228747.82%15.20% 190.10.70.20.219046.80%14.00% 200.10.80.10.229347.88%12.80% 210.10.90.00.259450.93%11.60% 220.20.00.80.571575.60%20.80% 230.20.10.70.457267.62%19.60% 240.20.20.60.362860.23%18.40% 250.20.30.50.288353.70%17.20% 260.20.40.40.233748.35%16.00% 270.20.50.30.199144.62%14.80% 280.20.60.20.184342.93%13.60% 290.20.70.10.189443.52%12.40% 300.20.80.00.214446.31%11.20% 310.30.00.70.455667.50%19.20% 320.30.10.60.356159.67%18.00% 330.30.20.50.276552.58%16.80% 340.30.30.40.216746.56%15.60% 350.30.40.30.176942.06%14.40% 360.30.50.20.157039.62%13.20% 370.30.60.10.157039.62%12.00% 380.30.70.00.176942.06%10.80% 390.40.00.60.356859.73%17.60% 400.40.10.50.272152.16%16.40% 410.40.20.40.207245.52%15.20% 420.40.30.30.162340.28%14.00% 430.40.40.20.137237.04%12.80% 440.40.50.10.132136.34%11.60% 450.40.60.00.146838.31%10.40% 460.50.00.50.275152.45%16.00% 470.50.10.40.205245.29%14.80% 480.50.20.30.155139.38%13.60% 490.50.30.20.124935.34%12.40% 500.50.40.10.114633.85%11.20% 510.50.50.00.124235.24%10.00% 520.60.00.40.210645.89%14.40% 530.60.10.30.155339.41%13.20% 540.60.20.20.120034.64%12.00% 550.60.30.10.104632.34%10.80% 560.60.40.00.109133.03%9.60% 570.70.00.30.163140.38%12.80% 580.70.10.20.122635.02%11.60% 590.70.20.10.102131.95%10.40% 600.70.30.00.101431.85%9.20% 610.80.00.20.132736.43%11.20% 620.80.10.10.107032.71%10.00% 630.80.20.00.101231.82%8.80% 640.90.00.10.119434.56%9.60% 650.90.10.00.108532.94%8.40% 661.00.00.00.123335.11%8.00% c. The partial model provides a scatter diagram (shown below) showing the required returns and standard deviations calculated above. This provides a visual indicator of the feasible set. If you would like a return of 10.50 percent, what is the smallest standard deviation that you must accept?Hint: you could sort the date above by rp and sp. For rp = 10.50%, the smallest (and the only) standard deviation is 33.87%; see portfolio #49. 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000Portfolio Standard Deviation Portfolio Required Return mini case a) Suppose Asset A has an expected return of 10% and a standard deviation of 20%. Asset B has an expected return of 16% and a astandard deviation of 40%. If the correlation between A and B is 0.35, what are the expected return and standard deviation of a portfolio eighted 30% in A and 70% in B? c) Suppose a risk free asset has an expected return of 5%. By definition, its standard deviation is 0, and its correlation with any other asset is also 0. Using only asset A and the risk-free asset, plot the attainable portfolios. f) What is the CAPM? Hat are the assumptions that underlie the model? g) Now add the risk free asset. What impact does this have on the efficient frontier? h) Write out the eqution for the CML and draw it on a graph. Interpret the plotted CML. Now add a set of indiference curves and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk free asset. What is the composition of the risky portfolio? i) What is a characteristic line? Ho is this line used to estimate a stock's beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk. j) What are the two potential tests that can be conducted to verify the CAPM? What are the results of such tests? What is Roll's critique of CAPM tests? k) Briefly explain the difference between the CAPM and the Arbitrage Pricing Theory (APT). 9781111444389.pdf FREQUENTLY USED SYMBOLS ACP Average collection period ADR American Depository Receipt APR Annual percentage rate AR Accounts receivable b Beta coefficient, a measure of an asset’s market risk bL Levered beta bU Unlevered beta BEP Basic earning power BVPS Book value per share CAPM Capital Asset Pricing Model CCC Cash conversion cycle CF Cash flow; CFt is the cash flow in Period t CFPS Cash flow per share CR Conversion ratio CV Coefficient of variation Δ Difference, or change (uppercase delta) Dps Dividend of preferred stock Dt Dividend in Period t DCF Discounted cash flow D/E Debt-to-equity ratio DPS Dividends per share DRIP Dividend reinvestment plan DRP Default risk premium DSO Days sales outstanding EAR Effective annual rate, EFF% EBIT Earnings before interest and taxes; net operating income EBITDA Earnings before interest, taxes, depreciation, and amortization EPS Earnings per share EVA Economic Value Added F (1) Fixed operating costs (2) Flotation cost FCF Free cash flow FVN Future value for Year N FVAN Future value of an annuity for N years g Growth rate in earnings, dividends, and stock prices I Interest rate; also denoted by r I/YR Interest rate key on some calculators INT Interest payment in dollars IP Inflation premium IPO Initial public offering IRR Internal rate of return LP Liquidity premium M (1) Maturity value of a bond (2) Margin (profit margin) M/B Market-to-book ratio MIRR Modified Internal Rate of Return MRP Maturity risk premium MVA Market Value Added n Number of shares outstanding N Calculator key denoting number of periods N(di) Represents area under a standard normal distribution function