Question

Problem 1

Consider the following two potential investments Nexit and Rexit. You plan to invest 8,000 KD in investment Nexit and 12,000 KD in investment Rexit.

Date	Return Nexit	Return Rexit
2016	0.03	-0.04
2017	-0.05	0.08
2018	0.08	0.07
2019	0.12	0.13

a. Build a portfolio consisting of Nexit and Rexit based on the information above.

b. Calculate the average return of the portfolio.

c. Calculate the risk of the portfolio.

Answer 1

a]

Weight of Nexit = 8,000 / (8,000 + 12,000) = 0.4

Weight of Rexit = 12,000 / (8,000 + 12,000) = 0.6

b] and c]

Average return and standard deviation of each investment is calculated using AVERAGE and STDEV.S functions in Excel.

Covariance is calculated using COVARIANCE.S function.

Return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2

Return of two-asset portfolio = (0.4 * 0.0450) + (0.6 * 0.06) = 0.054, or 5.4%

standard deviation for a two-asset portfolio σ_p = (w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2)^1/2

where σ_p = standard deviation of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁ = standard deviation of Asset 1

σ₂ = standard deviation of Asset 2

Cov_1,2 = covariance of returns between Asset 1 and Asset 2

Cov_1,2 = ρ_1,2 * σ₁ * σ_2, where ρ_1,2 = correlation of returns between Asset 1 and Asset 2

standard deviation = ((0.4² * 0.0733²) + (0.6² * 0.0716²) + (2 * 0.6 * 0.4 * 0.001733))^1/2

standard deviation = 0.0595, or 5.95%

Return =  = 0.054, or 5.4%

standard deviation = 0.0595, or 5.95%