B. * Consider prospect theory (which you implicitly used in part A) a little more closely. Suppose that an investor bases her decision on a one-year investment horizon and evaluates risky gambles relative to a reference point that is equal to the amount she invests. Suppose she invests $1,000, which then becomes her reference point. If invested in risk-free bonds, the $1,000 will be worth $1,022.54, one year from now. If she invests the same amount in stocks, her investment will be worth $900 with probability 0.12 and $1,100 with probability 0.88. The utility of any amount x is evaluated using the function u1x, r2 5 1001x 2 r2 2 0.51x 2 r2 2 if x $ r and 5 4001x 2 r2 1 21x 2 r2 2

if x , r,

(29.21)

where r is the reference point, and the utility of a gamble that results in x1 with probability d and x2 with probability 11 2 d2 is given by U 5 du1x1

, r2 1 11 2 d2u1x2

, r2.