1. The S&P/ASX 200 index is currently at 4000. You manage a $4 million indexed e
ID: 2629222 • Letter: 1
Question
1. The S&P/ASX 200 index is currently at 4000. You manage a $4 million indexed equity portfolio. The S&P/ASX 200 futures contract has a multiplier of $25.
a) If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months? (1 mark)
b) If government pay 2% per six months and the semi-annual dividend yield is 1%, what is the parity value of the futures price? Show that if the contract is fairly priced, the total risk-free proceeds on the hedged strategy in part (a) provide a return equal to the government bond rate. (1 mark)
2. In early 2012, the spot exchange rate between the Swiss Franc and the U.S dollar was 1.0404($ per franc). Interest rates in the U.S. and Switzerland were 0.25% and the 0% per annum, respectably, with continuous compounding. The three-month forward exchange rate was 1.0300($ per franc). What arbitrage strategy was possible? How does your answer change if the exchange rate is 1.0500($ per franc).
Explanation / Answer
2)
If "$ per franc" means selling one SF gives you $1.0404, then
3 month Swiss rate...[e^(0.00025*(3/12)] - 1 = 0.00063
Note that at the current spot rate, if 1SF = $1.0404, then one SF costs 1/1.0404 = $0.96117
The three month forward gives you 1SF = $1.03, so one SF costs 1/1.03 = $0.97087
So you want to sell the SFs in the future and buy them now, in order to make a profit. Or, conversely, buy the dollar now, and sell it in the future.
So your arbitrage strategy is
(I'll use 1,000 nominal amount to show how this will work)
Borrow 1,000SF, in 3 months you'll owe 1,000(1.00063) = 1,000.63SF
Use (sell) the 1,000SF you borrowed to buy USD at spot = 1,000*1.0404 = $1,040.40
Enter into the forward contract to sell dollars/ buy SF
in three months, in order to pay off the SF loan, buy 1,000.63SF at the forward rate costing (selling dollars/buying SF) $0.97087*1000.63 = $971.48
Use the 1,000.63SF you bought in the forward to pay off the loan, and keep the USD difference.
Your profit is calculated: $1,040.40(received) - $971.48(paid) = $68.92
Part II:
"How does your answer change if the exchange rate is 1.0500($ per franc). "
If they mean the current spot rate is 1.05, that would mean you'd make even MORE money. They probably mean that, because with the Swiss rate > US rate, the Swiss franc would be depreciating against the dollar in 3 months, based on interest rate parity (e.g. the 1.0500 wouldn't be the forward rate, the forward rate should be less than the spot rate)
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