You just won $$500$ million dollars in the lottery. You are considering buying a racehorse for $$1$

million. There is a small $(10\%)$ chance that the horse is very successful an earns a return of $1000\%.$

However, there is a $90\%$ chance that the horse is a "lemon", and you lose your entire investment

$($return of $-100\%).$ You may assume that the horse's performance is uncorrelated with the market,

that the market return is $15\%,$ the Sharpe ratio of the market is $0\mathrm{.}25,$ and the market risk premium

is $5\%.$ Should you buy the horse? Why or why not?