An investor has $1000 to invest in speculative stocks. He is considering investing m dollars in stock A and (1000- m) dollars in stock B. An investment in stock A has a 0.6 chance of doubling in value, and a 0.4 chance of being lost. An investment in stock B has a 0.7 chance of doubling in value, and a 0.3 chance of being lost. The investor's utility function for a change in fortune, x, is U(x)=log(0.0007x+1) for-1000 1000. x (a) What is R (for a fixed m)? (It consists of four elements. )
(b) what is the optimal value of m in terms of expected utility?
(Note: This perhaps indicates why most investors opt for a diversified portfolio of stocks.)