7. Suppose that you own a bar near the University of Nevada at Las Vegas. Every

Question

7. Suppose that you own a bar near the University of Nevada at Las Vegas. Every time the basketball team wins a home game, business is brisk and you clear $1000 for the day. When it loses, business is slow and on those days you clear only S200. Let be the probability that the basketball team wins. The problem is, you don't like risk;you would prefer a certain income to an uncertain one. Fortunately for you, gambling is legal in Nevada and there are many people who like to bet on sporting events. Thus you can "hedge" against low profit days by betting against the home team. a) Assuming that you can get fair odds (so that a bet is a fair bet) and that a bet pays off S1 when the home team loses then how much would the losses of the bet be in the case that the home team wins? Your answer will be a function of the probability . Using your answer to part a how much should you bet per game so that you will be perfectly "hedged" that is how much should you bet in order that you have a certain income? If is .7 then how much should you bet? b) c)

Explanation / Answer

a)Now you know that you will earn 1000$ when the home team wins and earn 200$ when the home team looses and so in the later case you want to maximize the profit and so you will be betting on the loose of home team in the gambling market where the payoff is 1$ when the home team looses and vice versa

Since this is a fair bet if you the home team wins you will end up loosing 1$

So considering the probability your payoff= (1-phi)*1-phi *1=1-2*phi

b)So suppose you are going to invest x in betting and phi is the probability of Home team winning as given then the equation will be

1000-x*phi=200+x*phi

2*x*phi=800

so., x=400/phi which is the amount which you will be investing in betting for the loss of home team

c)Now put phi=0.7 in the above equation to get the ans of you investing in the bet

x=400/0.7=571.4286$

So you should bet 571.4286$ on the loss of home team if you want to hedge considering the prob of home team winning (i.e. phi=0.7)

Hope this has helped you understanding the problem. Pls upvote the ans if it has really helped you. good Luck!!

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