Explanation
For fixed income portfolios where standard cash flow discounting models are not available, duration calculations are based upon estimated price moves in response to a change in rates. Recall that we define duration as the percentage change in price expected for a 1% change in yield. In this case, we have three price points known to us:
Line | Price | Yield
a | $102 | r - 45bps
b | $100 | r
c | $ 97 | r + 45bps
(where r is the current yield)
The change in price from line a to line c is $102m - $97m = $5m. We use the middle point, ie $100m, to calculate the percentage change. Therefore the percentage change in price is $5m/$100m = 5%.
The change in yield between lines a and c is 90 basis points [=(r+45bps) - (r-45bps)]. In other words, the change in price is 5% for a 90 bps change in yield. So the duration can be calculated as 5/(90/100) = 5.56. The other answers are incorrect.

In an American option, early exercise of the option is permitted. In a European option, early exercise is not permitted. Therefore Choice 'b' is the correct answer.

Explanation
An easy way to analyze the impact on convexity is to think about the impact on duration. If the change causes duration to increase, it would cause the convexity to increase too, and if it causes the duration to decrease, it would reduce convexity as well.An increase in yields reduces duration, and therefore reduces convexity.
An increase in maturity increases duration, and therefore increases convexity.
An increase in the coupon rate reduces duration, and therefore reduces convexity.
An increase in duration increases convexity.
Therefore statements II and IV represent situations where convexity increases.

Explanation
This question addresses the key differences between futures and forward contracts. Forward contracts are over the counter (OTC) instruments, while futures are exchange traded. Therefore Choice 'b' is not a true statement.
Futures contracts require an initial margin to be paid to the exchange, and gains and losses to be settled daily, while forward contracts generally settle only at the maturity of the contract. Therefore Choice 'a' is a true statement.
The exchange is the counterparty in a futures contract, and through its system of initial and variation margins guarantees the performance of the contract. Futures therefore have very little credit risk when compared to forwards. Therefore Choice 'c' is a true statement.
Because futures gains and losses give rise to daily cash flows, while the P&L on forward contracts is settled only at the end of the contract, the timing differences create small pricing differences between the two.
Therefore Choice 'd' is a true statement.

Explanation
A portfolio is considered dominated when it is not on the efficient frontier, which is another way of saying that there exists another portfolio with a better risk reward payoff. Therefore Choice 'a' is the correct answer.If the portfolio has a higher mean and the same or lower standard deviation than any other portfolio, this means it is already on the efficient frontier and is not dominated. The other choices do not make any sense in the context of the question.