In this problem you construct a minimum-variance frontier (i.e. the set of possible combinations of expected returns and standard deviation) for a case with two risky assets and analyze the role of return correlation.
A university endowment currently has a portfolio p of risky assets with expected return E (rp) = 0.07 (7%) and standard deviation σp = 0.11. The endowment is currently not investing in venture capital (VC) but would like to know how adding VC would expand the possible combinations of expected return and standard deviation. Suppose VC has an expected return of E (rV C ) = 0.12 and a standard deviation of σV C = 0.35.Consider investing in a mix of portfolio p and VC. Suppose the correlation between the return on portfolio p and the return on VC is 0.8.
(a) Calculate the expected return and standard deviation for each of the following 11 poten- tial portfolios: (xp, xV C ) = (1, 0), (0.9, 0.1), (0.8, 0.2), (0.7, 0.3), (0.6, 0.4), (0.5, 0.5), (0.4, 0.6), (0.3,0.7), (0.2,0.8), (0.1,0.9), (0,1). Graph your results: Plot the expected returns (vertical axis) against the standard deviations (horizontal axis).
(b) Repeat the exercise in (a), but now setting the correlation between the return on portfolio p and the return on VC to 0.1. Compare your graphs from (a) and (b) and explain in one sentence how the correlation changed the graph.