Explanation
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity . Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79

Explanation
The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).
Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53

Explanation
The buyer of an FRA is considered 'long', and a 3 x 6 FRA allows him or her to borrow funds at the agreed rate starting at the end of month 3 till the end of month 6. (ie, 3 x 6 indicates that the borrowing period commences at 3 months, and ends at 6 months, for a period of 6 - 3 = 3 months). The seller has exactly the opposite position, ie he or she is committed to lend funds at the agreed rate for 3 months starting at the end of
3 months from today (for a 3 x 6 FRA). [Note that the obligation to borrow or lend in and FRA does not mean that either parties will actually do that, instead they will just exchange cash flows to get to get to an identical economic situation.] Since the seller, or the short, is committed to lending in the future starting 3 months from now, it is akin to borrowing now for 3 months, and investing the borrowed amount for 6 months. During the first 3 months, the amounts borrowed and lent 'cancel' out (conceptually) and after the 3 months the short returns the amount borrowed, and is left with just the net amount lent, ie the FRA.
Thus the correct answer is Choice 'd'. Choice 'b' describes the position of the FRA buyer. Choice 'a' and Choice 'c' are nonsensical.

Explanation
Convexity is nothing but the second derivative with respect to price - or in other words, it is the first derivative of the modified duration. If we could determine two data points for modified duration, we can determine convexity too.
The modified duration is the percentage change in bond price from a 1% change in yield.
In this case, for the up move, the modified duration can be calculated as follows:
Change in price for 10 bps change in yield = $0.60/$95 =0.006316
Change in price for a 1% change in yield = 0.006316 * 10 = 0.06316
Therefore modified duration = 0.06316 * 100 = 6.316
For the down move in price, the modified duration is similarly $0.50/$95 * 10 * 100 = 5.263.
The convexity therefore is the difference between these two modified durations divided by the change in interest rates - note that these two points are separated by 10 basis points and not 20. Therefore convexity is (6.32 - 5.26)/0.1% = 1052.6.
[Note on how duration was calculated: In this case, we can estimate the duration of the bond as follows: we know that a 10 bps increase in rates causes the price to move to $94.50, and a 10 bps decrease causes the price to increase to $95.60. Thus, over the range of the 20 bps, the average change in price per basis point is ($95.60
- $94.50)/20 bps = $1.10/20 = $0.055/basis point, or $0.055* 100 = $5.5 for 100 basis points (ie 1%). We know that modified duration is equivalent to the percentage change in the bond price as a result of a 1% change in interest rates. A 1% change in the interest rates leading to a $5.5 change in a bond priced at $95 equates to $5.5/$95 = 5.79%, in other words the modified duration is roughly equal to 5.79 years.
In fact if we know the price of a bond at any two different interest rates, we can make an estimate of modified duration. Modified duration is just the first derivative with respect to price, and given two prices and the associated yields, we can easily calculate modified duration to be the ratio of the change in price to the change in interest rates. In this question, we are given both an up move and a down move. Using this estimation, only one data point (ie, either the up price or the down price) in addition to the starting point ($95) would have been enough to come to a rough estimate of modified duration. You will notice that the modified duration would be slightly different if we were to use the high point and the starting point (ie $95.60 and $95), and the starting point and the lower point ($95 and $94.50). The difference is due to convexity. The decrease in price is lower than the increase in price - and this is due to the convexity of the bond.]

Explanation
The investor would benefit from the risk reversal and the bull spread as both these strategies have a payoff profile that benefit from rising prices of the underlying. The collar is the opposite of risk reversal, and benefits during a bear market, and the butterfly spread benefits when prices remain range bound. Therefore Choice 'c' is the correct answer.