2. Forward/Futures Contracts. Threemonths ago, a jeweler entered a one-year forward contract to buy 500 troyounces of gold for $1,850 per ounce. Today, the nine-month forward and futuresprice of gold closed at $1,670 per ounce. The interest rate is 2% per annum.

(a)   What is the value of thejeweler’s forward contract at the end of today?

(b)  If the jeweler had enteredfutures contracts on gold, what would have been his profit (loss)?

(c)   What would be the value of thegold futures contracts in part (b) at the end of today? Why?

Hedging with Index Futures.Jill manages a stock portfolio valued at $50 million on August 15. The beta ofher portfolio is 0.9. Jill wants to hedge her portfolio’s market risk for thenext three months, using S&P 500 index futures. The December index futureslevel is 1,150 on August 15 (each index point is worth $250). The Decemberfutures will expire in four months.  (a)    Tofully hedge her portfolio, how many of the December S&P 500 futurescontracts should Jill long or short?(b)   Ifthree months later, on November 15, Jill’s portfolio is valued at $45 millionwhile the December S&P 500 futures level is 1,020, what is the net profit(loss) of her hedged portfolio in part (a)?(c)    Assumingno index arbitrage and no transaction cost, what is the spot S&P 500 indexon August 15? The index’s dividend yield is 2.3% and the riskless interest rateis 0.8%, both per annum with continuous compounding.