Explanation
The fair price for the futures contract should be [1000 x ( 1 + (2%-1%)/2)] = 1005. This means the futures contract is 'rich' at 1020. The trader should therefore short the futures contract, and buy the index spot. To buy the spot index, he will incur a borrowing cost of 2%, which will be partly offset by the dividend yield of 1%, and at the end of six months he will owe a net amount of 1005 and hold the index. At the same time the futures contract would expire too, and he would be able to sell at the agreed price of 1020, making a risk free profit of
15.

Explanation
We can calculate the duration of the bond as follows:
PV of 1st coupon payment: $5/(1 + 5%/2) = $4.878
PV of final payment: $105/(1 + 5%) = $100
Weighted average of the two = (0.5*$4.878 + 1*$100)/($4.878 + $100) = 0.9767, ie this is the Macaulay duration.
Thus the modified duration is 0.9767/(1 + 5%/2) = 0.9529
(Note that Modified Duration = Macaulay Duration/(1 + y/n), where n is the compounding frequency) In addition to this calculation, in this particular question we can intuitively arrive at the correct answer by eliminating the incorrect choices. Since the bond matures in a year, its modified duration will be less than a year. Therefore Choice 'a' and Choice 'b' cannot be correct. Similarly, 0.700 appears too low as the coupons are not so heavily weighted towards earlier in the year. Therefore only Choice 'c' can be the correct answer.

Explanation
As the compounding frequency increases, the nominal rate needs to decrease to produce the same amount of dollars at the end of a given time period. A continuously compounded rate of return has an infinite number of discrete compounding periods, and therefore the nominal rate expressed as a continuously compounded rate will always be nominally lower than any other rate.
Refer to the tutorial on interest rates for more details on continuously compounded rates work.

Explanation
T-bill futures and fed futures are very short term futures contracts, and unlikely to provide much of a hedge against a rise in interest rates. FRAs however are customized and would be the right instrument for the borrower to hedge his interest rate risk. A long FRA position gives him the right to borrow at an agreed rate in the future. This rate will not change regardless of the changes in interest rates, and therefore Choice 'b' is the correct answer.

Explanation
Bootstrapping is not one of the various approaches to try to value a convertible security. The rest of them are, and therefore Choice 'b' is the correct answer.