# Investments

For Kim WoodsWeek 3 Problems (Need each tab in Excel)Chapter 6 Question 23Tom Max, TMP’s quantitative analyst, has developed a portfolio construction modelabout which he is excited. To create the model, Max made a list of the stocks currentlyin the S&P 500 Stock Index and obtained annual operating cash flow, price, and totalreturn data for each issue for the past five years. As of each year-end, this universe wasdivided into five equal-weighted portfolios of 100 issues each, with selection based solelyon the price/cash flow rankings of the individual stocks. Each portfolio’s average annualreturn was then calculated.During this five-year period, the linked returns from the portfolios with the lowestprice/cash flow ratio generated an annualized total return of 19.0 percent, or 3.1 percentagepoints better than the 15.9 percent return on the S&P 500 Stock Index. Max alsonoted that the lowest price-cash-flow portfolio had a below-market beta of 0.91 overthis same time span.a. Briefly comment on Max’s use of the beta measure as an indicator of portfolio risk inlight of recent academic tests of its explanatory power with respect to stock returns.b. You are familiar with the literature on market anomalies and inefficiencies. Againstthis background, discuss Max’s use of a single-factor model (price–cash flow) in hisresearch.Chapter 6 Problem 1Compute the abnormal rates of return for the following stocks during period t (ignore differentialsystematic risk):Stock Ri t RmtB 11.5% 4.0%F 10.0 8.5T 14.0 9.6C 12.0 15.3E 15.9 12.4Rit = return for stock i during period tRmt = return for the aggregate market during period tChapter 6 Problem 2Compute the abnormal rates of return for the five stocks in Problem 1 assuming the followingsystematic risk measures (betas):Stock βiB 0.95F 1.25T 1.45C 0.70E −0.30Chapter 6 Problem 3Compare the abnormal returns in Problems 1 and 2 and discuss the reason for the differencein each case.Chapter 7 Question 12Stocks K, L, and M each has the same expected return and standard deviation. The correlationcoefficients between each pair of these stocks are:K and L correlation coefficient = +0.8K and M correlation coefficient = +0.2L and M correlation coefficient = −0.4Given these correlations, a portfolio constructed of which pair of stocks will have thelowest standard deviation? Explain.Chapter 7 Question 13A three-asset portfolio has the following characteristics.AssetExpectedReturnExpectedStandardDeviation WeightX 0.15 0.22 0.50Y 0.10 0.08 0.40Z 0.06 0.03 0.10The expected return on this three-asset portfolio isa. 10.3%b. 11.0%c. 12.1%d. 14.8%Chapter 7 Problem 3The following are the monthly rates of return for Madison Cookies and for Sophie Electricduring a six-month period.Month Madison Cookies Sophie Electric1 −0.04 0.072 0.06 −0.023 −0.07 −0.104 0.12 0.155 −0.02 −0.066 0.05 0.02Compute the following.a. Average monthly rate of return_Ri for each stockb. Standard deviation of returns for each stockc. Covariance between the rates of returnd. The correlation coefficient between the rates of returnWhat level of correlation did you expect? How did your expectations compare with thecomputed correlation? Would these two stocks be good choices for diversification? Whyor why not?Chapter 7 Problem 7Month DJIA S&P 500 Russell 2000 Nikkei1 0.03 0.02 0.04 0.042 0.07 0.06 0.10 −0.023 −0.02 −0.01 −0.04 0.074 0.01 0.03 0.03 0.025 0.05 0.04 0.11 0.026 −0.06 −0.04 −0.08 0.06Compute the following.a. Average monthly rate of return for each indexb. Standard deviation for each indexc. Covariance between the rates of return for the following indexes:DJIA–S&P 500S&P 500–Russell 2000S&P 500–NikkeiRussell 2000–Nikkeid. The correlation coefficients for the same four combinationse. Using the answers from parts (a), (b), and (d), calculate the expected return and standarddeviation of a portfolio consisting of equal parts of (1) the S&P and the Russell2000 and (2) the S&P and the Nikkei. Discuss the two portfolios.