# Suppose that investors can invest into three assets that earn the following expected returns

Suppose that investors can invest  into  three  assets  that  earn  the  following expected returns:

Asset 1: 0.09

Asset 2: 0.12

Asset 3: 0.14

and  have  the  following  standard  deviations  (on  the  diagonal,   in  bold)  and  cross-correlations (below the diagonal):

1. Using Solver in Excel, construct the (unconstrained) efficient frontier of the three assets.  In particular, construct the global minimum-variance portfolio and efficient portfolios  with  8%,  9%,  10%,  12%,  14%,  16%  and  18%  rate  of  expected  return.
2. Consider again a setting where short-selling is allowed and assume that investors, in addition to the three risky assets, can also invest in a risk-free asset that pays 2%. Construct the optimal risky portfolio (i.e., the tangency portfolio) and compute its Sharpe ratio.
3. Consider a mean-variance investor with risk aversion of 5.  What portfolio such an investor would choose to hold?
4. Reconsider part (e) and suppose that investing in Asset 2 is no longer possible â€”that is, suppose that investors have access to risky Assets 1 and 3, and the risk-free asset.  Construct the tangency portfolio in this case.  What is the Sharpe ratio of the constructed tangency portfolio?