Question

Returns and Standard Deviations Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Stock C Boom Bust 1.75 .25 06 14 .16 .02 .33 -06 a. What is the expected return on an equally weighted portfolio of these three stocks? b. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C?

Answer 1

Solution: are (9) Calculation of Expected Retum on an equally weighted posttouo weighted posttouo f these three (stock A, Stock B and stock c) Stocks. (I) weight of Stock A „Stock B and stock c As per question, there are three stocks and they equally weighted portfolo. so (Wa) weight of Stock A = 5 x100 = 33.07 (WB) Weight of Stoce B = 5x100 (WC) height of stock C = 4x100 = 33.33% I Now, we will calculate Expected Return portfolio in Boom and Bust state OR 0.3333 3x100 2 33,33% ORO 3333 Boom Stale stodia in Boom stale + Expected Retum Of weight of x Expected Ret. + Weight of x 5x bected Ret + Weight x Expo Re of stocka portfolio in Boomstate (WA) WBS in spomstale qwe) in Using the value Expected Relüm of 0.3333 X 6 +0.3333x16 +0.3333x33 portfolio in Boomstale Expected Relum of bortfolio in Boom stale 1.9998+ 5.3320 + 10.9989 -) 18.3315 Expected Retum of bratfolio in Bbom stale = 18.3315 %

→ Expected Relumf zwerything the best shortcut the light that we are + weight x 5x Ret Stock Xfstovec burtfolio in Bust stale (WA) WB) (We). in Bust Stale in Bust Stale in Bust Stale Using the the values, Exp. Ret. of portfolio in Bust staré 0.3333x14 +0.3333x2 +0.3333x66) Exp. Ret. of. Portfolio in Bust state 4.6662 + 0.6666 + (-1.9998) Exp Ret. of Portfolia 3.3330% in Bust stale of Portfolio in Boom stale Expected Relumit Pootfolio Expected Retum Probability x Exp. Ret. Of probability Exp. Reti Of Portfolio (ERP) Of Boom of Bust! Portfolio in Buststal Using the values, Expected Retum = 0.75 X 18.3315 + 0.25 X 3.3330 Of bortfolio (ERP) Expected Retum of 13.7486 + 0.8333 Portfolo (ERP) Expected Relam of Portfolio (ERP)= 14.5819 So, Expected Relumonan equally weighted boot foue_14.58% an these three Stocks

(b) Calculation of variance of 4 variance of a portfoco invested 20% each in A and B and 60% inc. Stock A, Stock Band stocks 20% OR 0.20 stock B (WB) Weight of (I) weight of (Wa) weight of Stock A = 20% OR 0.20 (Ne) Weight of stock c 60% OR 0.60 (D) Calculation of Expected Relum Perottolo in Boom and Bust" state of economy 0120 X6 + 0.207.16 + 0160 x 33 → Expected Retum of Portfolio in Boom state Expected Reti Pootfolio_ 1.2 + 3,2 + 19.0 in Boom stale Exbeeted Ret Portfou'o = 24,2% in. Boom State → Exb. Ret. Of Portfolio 0.20x14 + 0.20%2+ 0.60X66) in Bust State Exp Ret. of Portfolio = 28+0.40 +(3.6) in Bust state Exp: Ret. of Portfolio -0.4 in Bust stale

X II) Calculation 7 Expected Retem of portfolio (ERP) Expected Rethm of Prob. of Exp. Ret of Prob. Of Exp. Ret. of Boom x Portfolio Portfolio (ERP) Bust Portfolio in Boomstate in Buststalē Using the values, Expected Retum of Post folo (ERP) = 0.75 x 24.2 +0.25 *(-0.4) Expected Retom of Portfolo (ERP) = 18.15+40.1) Expected Relum 4 portfolo (ERP) = 18.05 (12) Calculation of variance Portfolio of Variance f = scom ÉRP) , stale Prob. o fy (Exb. Reti Exp. Ret. It Prob.of / ExpRet - ExpRet Portfolio of Portfolio of portfolio Bust * ( Of Portfolio of protfolio in Boom (ERP) in Bust Stare Using the ralues, ) Vanime of = 0.75(242 = 10-05) 2 0.75(24.2 - 10.05 +0.25*(-0.4-18.05) Portfolio Variante of Portfolio 2 0.75(6:15)*+ 0.25*(-10.45) Variance of Portfolio = 0.75 X 37:0225 +0.25 x 340.4025 Vanance of Pertfolio = 28.366875 +85.100625 Van'ance of Puot folio = 113.4675