Q1) The 12-month, 15-month, 18-month zero rates are 7.4%, 7.5%, 7.6% with continuous compounding. What is the value of an FRA that enables the holder to earn 8.6% (with semiannual compounding) for a 6-month period starting in one year on a principal of $1,000,000?
Q2) A quoted price of a 6% semiannual T-bond that matures on 7/15/2015 is 95-3. Today is 3/15/2010. What is the cash price? Round the number to the nearest 2 decimal points.
Q3) The price of a stock is $36 and the price of a three-month call option on the stock with a $36 strike is $3.60. Suppose a trader has $3,600 to invest and is trying to choose between buying 1,000 options (10 contracts) or 100 shares of stock. How high does the stock price have to rise for an investment in options to be as profitable as an investment in the stock?
Q4) A company enters into a long futures contract to buy 1,000 barrels of oil for $62 per barrel. The initial margin is $10,000 and the maintenance margin is $4,000. What oil futures price will trigger a margin call?
Q5) An interest rate is 18% per annum when expressed with semiannual compounding. What is the equivalent rate with continuous compounding? Report the answer in % and round the number to the nearest 2 decimal percentage points such as 5.75%.
Q6) An interest rate is 12.5% per annum expressed with continuous compounding. What is the equivalent rate with semiannual compounding?
Q7) A trader sells 100 European put options (1 contract) with a strike price of $48 and a time to maturity of six months. The price received for each option is $3. The price of the underlying asset is $40 in six months. What is the trader's gain or loss? If loss, report a negative number.
Q8) On 3/5/2012, you entered into a semiannual interest rate swap contract, where you pay a fixed rate of 4% per annum and receive LIBOR on a principal amount of $1,000,000. Suppose the 6-m LIBOR rates were 5.00% on 3/5/2012 and 5.50% on 9/5/2012. What is the net cash flow of the swap contract on 9/5/2012?
Q9) A company has a $33 million stock portfolio with a beta of 1.2. The S&P index futures price is currently standing at 1000. Futures contracts on $250 times the index can be traded. How many contracts is needed to reduce the beta to 0.8? If a short position is needed, report a negative number.
Q10) The three year zero rate is 5.5% and the four year zero rate is 6.7% (both continuously compounded). What is the forward rate (continuously compounded) for the fourth year? Report in % and round the number to the nearest 2 decimal percentage points such as 5.78%. Q11) The spot price of an investment asset is $33 and the risk-free rate for all maturities (with continuous compounding) is 8%. The asset provides $3.4 income at the end of the second year. What is the three-year forward price? Required minimum-2 page