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Unformatted text preview: portfolio that has a Beta of 3.14159 (Hint: recall that the beta of a portfolio is a weighted average of the component betas). If CAPM holds, then optimal portfolio are a combination of the market and the risk free asset, which have betas of 1 and 0, respectively. Thus for the optimal portfolio to have a beta of 3.14159 it must be that: wm = 3.14159 wf = ‐2.14159 Page 4 of 10 /10 4) An investor with a dislike of variance and a particular dislike of extreme events has the following Utility function: U = E(rp) – p2 – (Ap2)2 where A is some constant. Suppose you are considering only portfolios that are on the Capital Market Line. Write down one equation that relates the optimal weight in the market portfolio to the following parameters: A, the risk free rate, the expected return on the market, and the standard deviation of the market. You do not need to isolate for wm, and indeed, wm might appear more than once in your equation. U = wmE(rm) + (1‐wm)rf – wm2m2 – (Awm2m2)2 U = wmE(rm) + (1‐wm)rf – wm2m2 –A2wm4m4 Set the derivative equal to 0: 0 = E(rm) – rf – 2wmm2 – 4A2wm3m4 Page 5 of 10 /15 5) Consider an average investor, often called a representative investor, who has certain utility function that implies the following optimal allocation to the market portfolio: 2% The representative investor can never borrow or lend. We assume here that the risk free asset is in zero net supply. For every borrower there is a lender. Thus, at the aggregate level, the representative investor neither borrows nor lends. Instead, market conditions change such that when there is a shock to market standard deviation there is also a shock to expected excess returns, such that the optimal allocation to the market portfolio is always 100%. Suppose that at t = 0: the value of the market is $100, the expected return on the market is 10%, and the risk free rate is 4%. a) At t = 0, what must the standard deviation of the market equal? %
% → % An instant later, there is a shock to market volatility, which goes to 30% (but the risk free rate is unchanged). Assume...
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This note was uploaded on 02/11/2014 for the course FINE 441 taught by Professor Ruslangoyenko during the Fall '08 term at McGill.
- Fall '08