There are three risky assets:

Asset Asset 1 Asset 2 Asset 3

i i 10% 10% 5% 20% 10% 10%

The correlation between asset 1 and 2 is 50%. Asset 3 is uncorrelated to asset 1 and 2.

1. Suppose you can only invest in risky asset 1 and 2 (asset 3 is not available). Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio?

2. Suppose now you invest in all three risky assets. Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio?

3. Suppose you can invest in all three risky assets and the risk-free rate is 2%. Calculate the portfolio weights of the tangency portfolio.

Problem 5 There are three risky assets: Asset Hi Oi Asset 1 10% 10% Asset 2 5% 20% Asset 3 10% 10% The correlation between asset 1 and 2 is 50%. Asset 3 is uncorrelated to asset 1 and 2. 1. Suppose you can only invest in risky asset 1 and 2 (asset 3 is not available). Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio? 2. Suppose now you invest in all three risky assets. Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio? 3. Suppose you can invest in all three risky assets and the risk-free rate is 2%. Calculate the portfolio weights of the tangency portfolio. Problem 5 There are three risky assets: Asset Hi Oi Asset 1 10% 10% Asset 2 5% 20% Asset 3 10% 10% The correlation between asset 1 and 2 is 50%. Asset 3 is uncorrelated to asset 1 and 2. 1. Suppose you can only invest in risky asset 1 and 2 (asset 3 is not available). Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio? 2. Suppose now you invest in all three risky assets. Calculate the portfolio weights of the minimum-variance portfolio with an expected return of 10%. What is the volatility of the portfolio? 3. Suppose you can invest in all three risky assets and the risk-free rate is 2%. Calculate the portfolio weights of the tangency portfolio