C o n s i d e r i nves ti n g in the s t ock m a rke t $.$ An i nvestor has three choices: a high$-$

ri s k s t ock $,$ a l ow$-$ ri s k s t ock $,$ or a savings account t ha t would pay $$500$ f or

sure. If he invests in the stock, he must pay a $$200$ brokerage fee.

The stock market can either go up$,$ stay the same $,$ or go down. The

probability of each outcome is thought to be $\mathrm{.}5($Up$),\mathrm{.}3($Same$),$ and $\mathrm{.}2$

$($Down$).$ T he following table describes the earnings from the stocks in these

three events.

M ar ke t High R i s k S t o ck Low R i s k S to ck

Up $$1700$ $$1200$

Same $$300$ $$400$

Down $-$$$800$ $$100$

$($a$)$ U s i n g t h e e x p ecte d va l ue d eci si o n c ri te ri a $,$ w h a t i s t he o p t im a l de ci si o n$?$

$($b$)$ C o n s i d e r a ris k ave rse d e ci si o n ma ke r w i t h $$1000$ initial wealth and

u$($W$)=($W $)\mathrm{.}5.$ W ha t as t he e x p ecte d utility maximizing d eci si o n

now?

$($c $)$ W ha t i s t he ce rtai nty e q ui vale nt for both t he high risk low ri s k stocks?

$($d$)$ W ha t is t he ri s k premium for the high risk stock and the low risk stock?