(b) (2 points) If you buy the asset, how much have you effectively paid for it in each outcome?

(c) (4 points) Would you expect the forward price to be above or below $100?

3. Futures vs. Forward Contracts (Easy, 10 points total) Our discussion of futures vs. for- ward contracts may seem a bit abstract. Hopefully by working through an example it will be- come more concrete. You go long one hypothetical one-year futures contract that is marked-to-market to hedge having to buy the underlying asset. For simplicity, suppose that instead of marking to market daily, it is only done every six months. (This saves us having to compute 252 settlements.) The futures price today is $100. Six months from now, you get F1 - $100 deposited in your margin account, where Fi is the futures price six months from now. (This value could be negative, in which case we interpret that as a withdrawal.) When you close out in a year, you get another F2 Fi deposited in your margin account, where F2 is the futures price when you close out. For simplicity, suppose that F2 = S2, the spot price of the underlying asset, so that there is no basis risk at the end of the year. Of course, in total that means that we get Fi $100 + S2 Fi = S2 $100 added to our margin account. The total balance perfectly hedges the price movements: no matter what the spot price S2 end up being, you get S2 $100, and therefore you will always effectively pay $100. That was the point of hedging in the first place. This argument ignores interest rates. If the six-month zero rate expressed annually with continuous compounding at this intermediate date (six months from now) is r, then you end up adding e0.5" (F1 - $100) + S2 - F1 to your margin account. The gain accrues interest, and the loss occurs the additional loss from not getting interest. Suppose there are two possible outcomes six months from now: Fi r Outcome 1 Outcome 2 110 90 0.0% 10.0% Suppose the two outcomes are equally likely. (a) (4 points) How much money is in your margin account in each outcome? Leave swer in terms of S2. your an