Financial Derivative Securities
1. The three year zero rate is 7% per annum and the four year zero rate is 7.5% pa (both continuously compounded). What is the one year (continuously compounded) forward rate starting in three years time?
2. The zero rate curve is flat at 6% pa with semi-annual compounding. What is the value of a FRA where the holder receives interest at the rate of 8% per annum with semi-annual compounding for a six month period on a principle of $1000 starting in 2 years?
3. The margin requirement on the S&P/ASX 200 futures contract is 10% and the stock index is currently 4400. Each contract has a multiplier of $25. How much margin must be put up for each contract sold? If the futures price falls by 1% to 4356, what will happen to the margin account of an investor who holds one contract? What will the investor’s percentage return based on the amount put up as margin be?
4. 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 $25.
a) If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months?
b) If government pay 2% per six months and the semi-annual dividend yield is 1%, what is the parity value of the futures price? Show that if the contract is fairly priced, the total risk-free proceeds on the hedged strategy in part (a) provide a return equal to the government bond rate.
5. In early 2012, the spot exchange rate between the Swiss Franc and the U.S dollar was 1.0404($ 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).
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