4. (15 pts) You have observed the following returns over time Year Stock X Stock Y 13% -5 Market 1992 14% 199319 1994 -16 1995 3 1996 20 12% 10 -12 15 Assume that the risk-free rate is 6 percent and the market return is 11 percent. There is an equal probability for each observation to occur (.2 for cach) A. Calculate the betas of stock X and Y? Also calculate the bcta of the market? B. What are the required rates of return for stock X and Y? C. What is the required rate of return and beta for a portfolio consisting of 80 percent of Stock X and 20 percent of Stock Y? D. If Stock X-s expected return is 22 percent, is Stock X under- or overvalued? 5. Assume that you recently graduated with a major in finance, and you just landed a job as a financial planner with Merrill Finch inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds arc to be invested in a business at the end of one year, you have been instructed to plan for a one-ycar holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. RETURNS ON ALTERNATIVE INVESTMENTS RN ESTIMATED RATE OF STATE OF THE MARKET HIGH U.S RTF RECESSION 0.2 BELOW AVG 0.2 AVERAGE 0.2 ABOVE AVG 0.2 BOOM 8.0% -22.0% 2.0 20.0 35.0 50.0 28.0% 14.7 0.0 10.0 20.0 10.0%" 10.0 8.0 8.0 8.0 7.0 45.0 30.0 -13.0% 1.0 15.0 29.0 43.0 0.2 Merrill Finch's economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program which was used to estimate the rate of return on each alternative under cach state of the economy. High Tech Inc. is an electronics firm; Collections inc. collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund, and thus obtain average stock market results. Given the situation as described, answer the following questions (10 pts) What is the required rate of return for a portfolio consisting 80 percent of High Tech and 20 percent of U.S. Rubber? A (8 pts) The expected rates of return of the alternatives as supplied by Merrill Finch's computer program are as follows: B. Security Expected Return High Tech 17.4% U.S. Rubber13.8 T-bills 8.0 Collections 1.7 Is High Tech-s stock under-or overvalue? Why