Question

Use the following information to calculate the expected return and standard deviation of a portfolio that is 30 percent invested in 3 Doors, Inc., and 70 percent invested in Down Co.

	3 Doors, Inc	Down Co
Expected Return, E(R)	18%	14%
Standard deviation	48	50

Correlation .33

Answer 1

	3 Doors	Down Co
Expected return	18%	14%
Standard deviation	48%	50%

Weight of 3 Doors = w₁ = 30% = 0.3, Expected return on 3 Doors = E[R₁] = 18%, Standard deviation of 3 Doors = σ₁ = 48%

Weight of 3 Down Co = w₂ = 70% = 0.7, Expected return on Down Co = E[R₂] = 14%, Standard deviation of Down Co = σ₂ = 50%

Expected Return of the portfolio

Expected return of the portfolio is calculated using the formula:

E[R_P] = w₁*E[R₁] + w₂*E[R₂] = 0.3*18% + 0.7*14% = 15.2%

Standard Deviation of the portfolio

Variance of the portfolio is calculated using the formula:

σ_P² = w₁²*σ₁² + w₂²*σ₂² + 2*w₁*w₂*ρ*σ₁*σ₂

ρ = Correlation between the stocks = 0.33

Variance of the portfolio = 0.3²*(48%)² + 0.7²*(50%)² + 2*0.3*0.7*0.33*48%*50% = 0.020736 + 0.1225 + 0.033264 = 0.1765

Standard deviation is square root of variance

Standard deviation of portfolio = 0.1765^1/2 = 0.420119030752

Answers

Expected Return = 15.2%

Standard Deviation = 42.0119030752%