Exercise for Calculating Expected Return and Risk for an Individual Investment and a Portfolio Assume that you recently graduated and have taken a position working as a financial planner. Your first assignment is to advise a client who wishes to invest $100,000. The information below has been gathered by financial analysts and economists working for your corporation. Your supervisor has restricted you to the following investment alternatives: T-bills, High Tech, Collections, U.S. Rubber, and the Market Portfolio. An analyst working for your investment firm assigned the following probabilities for five possible states of the economy and expected returns for each investment for each of the five states. Using the information below make a recommendation. Estimated Rate of Return on Alternative Investments State of Economy Probability High of State Recession 0.1 T-Bills 8.0% U.S. Market 2-Stocks Tech Collections Rubber Portfolio HT&Coll -22.0% 28.0% 10.0% -13.0% Below Average 0.2 8.0% -2.0% 14.7% -10.0% 1.0% Average 0.4 8.0% 20.0% 0.0% Above Average 0.2 8.0% 35.0% -10.0% 7.0% 45.0% 29.0% 15.0% Boom 0.1 8.0% 50.0% -20.0% 30.0% 43.0% E(R) 8.0% 1.7% 13.8% 15.0% Standard Deviation 0.0% 13.4% 18.8% 15.3% I. Calculate the expected return E(R) for High Tech in the space below. E(R)= P(E(R)) T-bills High Tech Collections where: n = the number of states in the economy (5 in this example) P, is the probability of state i ocurring (i is recession, below avg, etc.) E(R) is the expected retum for the investment for state i. i=1 E(RHTbills) = .1(8%) + 2(8%) + .4(8%) + .2(8%) + .1(8%) = 8.0% U.S. Rubber E(Rcoll) = .1(28%) + .2(14.7%) + .4(0%) + 2(-10%) + .1(-20%) = 1.7% E(RUSR) = .1(10%) + 2(-10%) + .4(7%) + 2(45%) + .1(30%) = 13.8% Market Portfolio E(RMkt) = .1(-13%) + .2(1%) + .4(15%) + 2(29%) + .1(43%) = 15.0% II. Calculate the standard deviation for an individual security (High Tech). " = P(R-E(R)) where: n = the number of states in the economy (5 in this example) P, is the probability of state i ocurring (i is recession, below avg, etc.) E(R) is the expected retum for the investment calculated in step I above. Thill Coll = i=1 .1(8%8%) +.2(8%8%) +.4(8%8%) +.2(8%8%) +.1(8%8%) = 0%| .1(28%1.7%) +.2(14.7%-1.7%)+.4(0%-1.7%) +.2(-10%-1.7%)+.1(-20%-1.7%) =13.4% USR = .1(10%13.8%) +.2(-10%13.8%) +.4(7%13.8%) +.2(45%13.8%) +.1(3013.8%) = 188% .1(13%15%} +.2(1%15%) +.4(15%15%) +.2(29%15%) +. 1(43%-15%) -15.3% Mkt = HighTech III. Calculate the E(R) of a portfolio consisting of 50% in High Tech and 50% in Collections. IV. Calculate the standard deviation for the portfolio of High Tech and Collections. V. Why is the standard deviation of the potfolio of High Tech and Collections so small?