Question

statistics

4. An investor holds a portfolio consisting of two stocks. She puts 25% of her money in Stock A and 75% into Stock B. Stock A has an expected return of Ri=8% and a standard deviation of 0,=12%. Stock B has an expected return of Rg=15% with a standard deviation of o,=22%. The portfolio return is P=0.25RA +0.75R, (a) Compute the expected return on the portfolio. (b) Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are perfectly positively correlated. (c) Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns have a correlation of 0.5. (d) Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are uncorrelated.

Answer 1

Quun data WA = 25% WIB = 75 %. Expected retuen RA = 8% RB = 15% standard deviation - SA= 12%. Po = 2a). Expected return on portfolia = WARATUR RB = 0.25 0.08 +0.75 0.15 = 0.1325 Rp - 13-25% | When two stock returns are perfectly positively Correlated. Correlation = til Standerd deviation of retums of portfolio - Op = WA AT WB B = 0.25 ×0.12 + oors X0.2 20.115 Top = 19.5%

@ WA = 954. Ap=15). Corelation an = 0.5 A = 1/ 2"). COVIA TA. J A 12 1. x 22.4x0.5 COVIA,B) = 0.0132 op - ſwa. A) + (WB ) + 2. WA WB on FB "As) (or) op - Waa) 7(10.7) 4 %. Waibe COV(A,B) Op = 16.25 X012) 7 (0.45 x0,20+ 240-25X0-15 X 0.0132 op = 0.0009 + 0.027225 + 0.00495 op- Jo.033075 up = 0. 1819 (or) 18.19%)

When two stuck returs are uncorelated means NAB) = 0 portfolio Standard desiation of op - Jawat BWe"+ 2.Wr. We Th Fr Pren. Op = 5 (0.25X012)+(0.15X021) + a op = 50.0009 + 0.027225 Op = 0.1677 op - 16517%