Question

1.how to Calculate the expected rate of return and volatility for a portfolio of investments and describe how diversification affects the returns to a portfolio of investments ?

2.Understand the concept of systematic risk for an individual investment and calculate portfolio systematic risk (beta).

3.Estimate an investor’s required rate of return using the Capital Asset Pricing Model.

Answer 1

1]

Expected 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

Expected variance for a two-asset portfolio σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2

where σ_p² = variance of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁² = variance of Asset 1

σ₂² = variance 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

Expected return of three-asset portfolio R_p = w₁R₁ + w₂R₂ + w₃R₃

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

w₃ = weight of Asset 3

R₃ = expected return of Asset 3

Expected variance for a three-asset portfolio σ_p² = w₁²σ₁² + w₂²σ₂² + w₃²σ₃²+ 2w₁w₂Cov_1,2 + 2w₂w₃Cov_2,3 + 2w₁w₃Cov_1,3

where σ_p² = variance of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

w₃ = weight of Asset 3

σ₁² = variance of Asset 1

σ₂² = variance of Asset 2

σ₂² = variance of Asset 2

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

Cov_2,3 = covariance of returns between Asset 2 and Asset 3

Cov_1,3 = covariance of returns between Asset 1 and Asset 3

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

Cov_2,3 = ρ_2,3 * σ₂ * σ_3, where ρ_2,3 = correlation of returns between Asset 2 and Asset 3

Cov_1,3 = ρ_1,3 * σ₁ * σ_3, where ρ_1,3 = correlation of returns between Asset 1 and Asset 3

This model can be extended to "n" number of assets, and the expected return and standard deviation can be calculated.

Diversification does not affect the expected returns on investments. However, it decreases the overall risk (standard deviation of the portfolio). This is because when uncorrelated assets are added to a portfolio, there is less volatility, since the asset prices are less likely to move together in the same direction at the same time.