Suppose you have some money to invest-for simplicity $1 and are planning to put a fraction w into a stock market mutual fund and the rest,1-w, into a bond mutual fund. Suppose that a $1 invested in a stock fund yields Rs after one year and a $1 invested in a bond fund yields Rb. Rs and Rb are random variables with expected value of 8% and 7% respectively, and standard deviation of 7% and 4% respectively. The correlation between Rs and Rb is 0.25. If you place a fraction w of your money in the stock fund and the rest 1-w in the bond fund then the return on your investment will be R=wRs+(1-w)Rb

Question

Suppose you have some money to invest-for simplicity $1 and are planning to put a fraction w into a stock market mutual fund and the rest,1-w, into a bond mutual fund. Suppose that a $1 invested in a stock fund yields Rs after one year and a $1 invested in a bond fund yields Rb. Rs and Rb are random variables with expected value of 8% and 7% respectively, and standard deviation of 7% and 4% respectively. The correlation between Rs and Rb is 0.25. If you place a fraction w of your money in the stock fund and the rest 1-w  in the bond fund then the return on your investment will be R=wRs+(1-w)Rb

anonymous · Answer

a.   Compute the mean and standard deviation of R for w = .5 and w = .75 respectively.

      b.   What value of w makes the mean (or expected value) of R as large as possible? What is the standard deviation of R for this value of w?

      c.   What is the value of w that minimizes the standard deviation of R? (you can show this using algebra, or calculus).

anonymous · Answer

Can someone please get me started on this problem, haven't taken anything like this in a while ._.