All questions carry equal points.
1. (a) Suppose all distinct assets in the economy have a correlation of ρ = −.02 with every other asset. Let the variance of each asset be 0.25, and the investor holds an equally weighted portfolio of these assets. How many of such assets should an investor hold so that the variance of her portfolio is zero?
(b) If the correlation was 0.02 can the investor ever achieve a zero variance? (c) For the case that the correlation is 0.4, and the investor holds an equally weighted portfolio of 10 assets, calculate the amount of unsystematic and systematic risk in her portfolio. 2. (Diversiﬁcation over time). Suppose an investor invests $100 in a stock that in each period can either double or half with equal probability. The returns in each period are uncorrelated.
(a) Calculate the variance of the investors’ dollar position after one period. (b) Calculate the variance of the investor’s dollar position after holding the stock for two periods. Report the ratio of variance after two periods to the variance after one period (in (a)).
(c) Given your example for diversiﬁcation with uncorrelated stocks in your class notes comment on the ratio in (b) and why you might or might not have expected it to be 0.5.
(d) Suppose now in (b) that the investor only invested $36.8229 in the stock. Now calculate the variance after two periods and ratio of variance after two periods to the variance of investing $100 after one period (in (a)).
3. Suppose the CAPM holds, RF =4%, and the expected return on the market portfolio is 6%. Assume continuous compounding. Assume that oil β = 1.5. Let the spot price of oil be 100.
(a) Suppose the forward price of oil (F0 ) for a contract that matures in 2 years trades at $130. What is the quantity u − y implied by this forward price?
(b) Suppose there is no trading in 6-month and 1-year forward contracts. What would be the forward prices of oil at 6-month and 1-year maturities consistent with the...
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