As you know, the risk of two assets is calculated by getting the square root of...

As you know, the risk of two assets is calculated by getting the square root of the equation:

s_P²= w₁²s₁²+ w₂²s₂²+ 2w₁w₂r₁₂s₁s₂

Explain what would happen if one of the two assets was a risk-free asset. In other words, what would be the risk of the combination of the two assets? You have to explain that in accordance with the above equation.

Solutions

Expert Solution

Given equation:

S_p² =w₁²s₁² + w₂²s₂² + 2w₁w₂r₁₂s₁s₂

_{So, here we have two assets - asset 1 and asset
2.}

If one of the two assets was a risk-free asset, then it means that the standard deviation of risk-free asset is zero.

Let us assume that asset 2 is risk-free. So, it's risk =Standard deviation =s₂ =0

So, the entire last term of the above equation, i.e., 2w₁w₂r₁₂s₁s₂ becomes 0. Also the term, w₂²s₂² becomes 0. The only term that remains is w₁²s₁². It means the risk of the combination of the two assets would become the risk of one asset only. The portfolio risk is same as the risk of that asset which has the risk.

s_p² = w₁²s₁² + w₂²s₂² + 2w₁w₂r₁₂s₁s₂

s_p² =w₁²s₁² + w₂²(0)² + 2w₁w₂r₁₂s₁(0)

(since, the risk-free asset's risk, i.e., standard deviation is s₂ =0)

s_p² =w₁²s₁² + 0 + 0 =w₁²s₁²

s_p =

Thus, the portfolio risk is only the risk of the asset which is not risk-free (here, asset 1).

orchestra answered 1 year ago

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