Suppose all distinct assets in the economy have a correlation of = .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.

a. 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 un- systematic and systematic risk in her portfolio.