Start with asset A which has an expected return of 10% and a volatility of 30%.

Question

Start with asset A which has an expected return of 10% and a volatility of 30%.
1. Suppose that we introduce asset B with an expected return of 10% and a volatility
of 30%. The correlation between the two asset returns is 0.9. What is the optimal
combination of A and B? What is the volatility of this portfolio? [Hint: The expected
return of any combination is 10%, so you want to minimize the portfolio volatility.]
2. Now suppose that we introduce asset C with an expected return of 10% and a volatility
of 30%. The returns of asset C are uncorrelated with both the returns of asset A and
of asset B. What is the optimal combination of A, B, and C? What is the volatility of
this portfolio?
3. Did the introduction of B or C have a greater e ect in decreasing the portfolio volatility?
Why is this the case?

Explanation / Answer

Answer for the above question:

Portfolio variance = (weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight(2)*covariance(1,2)

Therefore 50% for A asset and 50% for B asset

put that in formula we get :

Portfolio variance = .5^(2*.3)+.5^(2*.3)+2*.5*.5*.9

Therefore for answer 1 the optimal combination is equal and portfolio variance is = 1.05

and for 2nd one once we introduce asset 3 with same amount of return and volatility the quivalent weights would be appropriate.

3.Since there is an asset added with an equal return and volatility the overall volatility would reduce because of deceease in weights.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.