Question

2. What is the portfolio expected return and standard deviation? $4000 market value in stock A with E(RA) = 12% and $6000 market value in stock B with E(RB) = 9%. The standard deviations (σ) and correlation (ρ) are: σA = 25% σB = 20% ρAB = 0.5

For a 2 stock portfolio,

σ2port = wA2 σ2A + wB2 σ2B + 2 wA wB ρAB σA σB

σport = (wA2 σ2A + wB2 σ2B + 2 wA wB ρAB σA σB)^0.5

Answer 1

Amount invested in stock A = $4000

Amount invested in stock B = $6000

Total amount invested in the portfolio = $4000 +$6000 = $10000

Weight of stock A in the portfolio = WA = $4000/$10000 = 0.4

Weight of stock B in the portfolio = WB = 6000/10000 = 0.6

Expected return of stock A = E[RA] = 12%, Standard deviation of stock A = σA = 25%

Expected return of stock B = E[RB] = 9%, Standard deviation of stock B = σB = 20%

Correlation between stock A and stock B = ρAB = 0.5

Portfolio Expected Return

Expected return of the portfolio is calculated using the formula:

Expected return of the portfolio = E[RP] = WA*E[RA] + WB*E[RB] = 0.4*12% + 0.6*9% = 4.8%+5.4% = 10.2%

Portfolio Standard deviation

Variance of the portfolio is calculated using the formula:

Portfolio variance = σP2 = WA2*σA2 + WB2*σB2+2*ρAB*WA*WB*σA*σB = (0.4)2*(25%)2 + (0.6)2*(20%)2 + 2*0.5*0.4*0.6*25%*20% = 0.01 + 0.0144 + 0.012 = 0.0364

Standard deviation is the square root of variance

Standard deviation of the portfolio = σP = (0.0364)1/2 = 19.0787840283389% ~ 19.08% (Rounded to two decimals)

Answers

Portfolio Expected return = 10.2%

Portfolio standard deviation = 19.08%