Question

Use the following yearly rate of return valoes for Questions 1, 2, 3, and4. Market Risk-frre Year Stock A Stock B Stock C retura return 2008 9.0% 8.0% 11.0% 10.0% 1.0% 2009 10.0% 11.0% 3.0% 9.0% 10% 2010 -3.0% 6.0% -6.0% 8.0% 10% 2011 -3.0% -110% -11.0% -15.0% 1.0n% 2012 9.0 % 3.0% 6.% 6.0% 10% 2013 -8.0% -4.0% -2.0% 20% 10% 2014 11.0% 15.% 13.0% 6.0% 10% -2.0% 10% 2015 -9.0% -5.0% -5.0% 2016 3.0% 1.0% 10.0% 14.0% 14.0% 10.0% -30% 10% 2017 -6.0% -1.0% 5,0% 7% 20% 1.0% 2018 2.0% 1. Lamar wants to invest S1000 in a portfolio that invests in stocks A and B. Lamar does not want to short sell the historical returns shown above for (so portfolio weights cannot be negative). Lamar decides to computing expected portfolio return and variance of portfolio retum. (10 pts) (a) Find the expected return, standard deviation of return, and covariance of return for stocks A and B. (b) What is the highest expected portfolio return that Lamar can achieve? (c) Find the expected portfolio return and standard deviation of portfolio return for 4 possible portfolios. and plot the 4 portfolios on the mean-standard deviation plane S811 21

Answer 1

Stock A(in %) 00 os do w 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 TOTAL A-A' (A-A')^2 Stock B(in %) 7.27 52.8529 8.27 68.3929 -4.73 22.3729 -4.73 22.3729 1.27 1.6129 -9.7394.6729 -4 9.27 85.9329 15 -10.73 115.1329 8.27 68.3929 59.7529 .27 10.69292 602.1819 B-B 5.36 8.36 -8.64 -13.64 3.36 -6.64 12.36 -7.64 11.36 -3.64 -0.64 (B-B')^2 (A-A")(B-B") 28.7296 38.9672 69.8896 69.1372 74.6496 40.8672 186.0496 64.5172 11.2896 4.2672 44.0896 64.6072 152.7696 114.5772 58.3696 81.9772 129.0496 93.9472 13.2496 28.1372 0.4096 -2.0928 768.5456 598.9092 -7.73 wo 5 3 Expected return=mean total return / number of years number of years = 11 Expected return of A(A') = 19/11 =1.73(rounded of to two decimals) Expected return of B(B') = 29/11 = 2.64(rounded of to two decimals)

(a) Standard deviation (A-A')? n the above data E (A-A2 = 602-1819 from - 602.1819 I so standard deviation of A v on = 7.40% deviation of B2V (B-B') JB = 168.5456 Standard 8.3691 Covariance so = {(A-A) (B-B1) from the above data EA-A') (8-B') = 598.9092 COVAB = 598.9092 54.45 Co- relation = COVAB Say GB 54.45 7.48 8.36 0.88 =

(6) Expected return of A 1.13% B= 2.64% since Stock B gives highest return Investing 100% return in stock lamar achieve highest return on portfolio lan STOCK A = 0% Sto&B = 100 % portfolio return ox 1.73% + 1x2.64% 2.64% return (1) expected portfolio return = weighted average Standard deviation of portfolio = JCWAXTA) & (Wg X83) + Q Wax Wax TAXTg xcora let's Assume following weights A B 100 50 so 100 80

situation - L WA=0 WB = 100 post to lis return = 0x 1.73 + 1x264 - 2.64 % Standard deviation = V 012 + (1x8.36)+ 0 = 8.36 situation - 2 I WA = 50% Wp = 80% portfolio return = o.sx 1.73 + 0.5x2.64 0.865 +1:32 2185 JAB = √ (0.5x7.4)² + (0.5x8.36)² + 2x05x0.5 x 7.4 88.36X0.88 I 13.69 + 17.47 + 27.22 ✓ 58.38 = 7.64% situation-3 ou WA = 100 Wp = 0 portfolio referm = 1x 1.73 to 1.13.4. TAB = (1+7.42 + 0 to = 7.4%

Situation - y WA= 20 % - WB = 80% portfolio return = 0.24 1973 + 0 8x2 64. 0.346 + 2.112 2.458 / AB = V0-247:4)2+ (0888-36)+2x002X0-8X7.4%8:36X0:88 2.1904 +44 13+ 17.43 - 8.02% (164,2:165) X X Mean (return) Row *08-36, 2:64) (8.02, 2456) + X(74, 1:13) 6 6.5 7 Standard 7.5 deviation 8 8.5 graph can be used for better plot /