Two-Fund Theorem and One-Fund Theorem.

Question 1
Part (a)
(i) State the Two-Fund Theorem, then state the One-Fund Theorem. (2 point)
(ii) If all investors are mean-variance optimizers, what does the one-fund theorem imply about the
portfolio-weights that different investors put on different risky assets? [Assume that short-selling is allowed, that there is a risk-free asset, that no investors are infinitely risk-averse, and that all investors
have the same estimates of means, variances, and covariances.] (1 point)
(iii) Explain how the result from (ii) enables us to determine what the “one fund” must be. Will this
“one fund” always place a positive weight on every risky asset? Explain why or why not. (3 points)
2
Part (b)
(i) We spent a lot of time in lecture showing why it is reasonable to assume that risky assets’ long-horizon
(log-)returns follow a Gaussian distribution. Explain why this distributional result helps to justify an
exclusive focus on the mean and variance of a portfolio’s returns.
(2 points)