Consider two assets. Suppose that the return on asset 1 has expected value 0.02 and standard...

Consider two assets. Suppose that the return on asset 1 has expected value 0.02 and standard deviation 0.05 and suppose that the return on asset 2 has expected value 0.04 and standard deviation 0.06.

Consider an equally weighted portfolio in which each asset receives weight 1/2 and let Rp denote the return on the portfolio.

Find the expected value of Rp and the variance of Rp as functions of ρ12, the correlation of the returns on the two assets.

Please use RStudio

Expert Solution

Stock	Return	SD	Weigh
A	0.02	5%	0.5
B	0.04	6%	0.5

Expected Return = w₁ x r₁ + w₂ x r₂

= 0.5 x 0.02 + 0.5 x 0.04

= 0.01 + 0.02

= 0.03 or 3%

Variance as a function of P₁₂

Variance = w₁² σ²_{1 +} w₂² σ₂² + 2 w₁ w₂ σ₁ σ₂ P₁₂

σ_p² = (0.5)²(5)² + (0.5)²(6)² + 2 x 0.5 x 0.5 x 6 x 5 x P₁₂

σ_p² = 6.25 + 9 + 15 P₁₂

σ_p² = 15.25 + 15 P₁₂ Variance as a function of P₁₂ (Required Equation)

jeff jeffy answered 2 years ago

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