The effectiveness of the hedge is solely determined by the correlation between the position being hedged, and the position being used as the hedge. A hedge can be perfect when correlation is 1, and will be less than perfect when it is anything other than 1. The effectiveness of the optimal hedge is given by the formula  √(1-ρ 2 ) , where  ρ  is the correlation between the two. Therefore Choice 'c' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.

A covered call is an attempt to earn premium income by selling calls while protecting against the downside by holding long the underlying. In case prices rise, the holder of the covered call can give away the held underlying. In case prices fall or stay below the strike price of the sold call, the holder of the covered call gets to keep the premium.

The holder of the covered call will suffer a loss if the price of the underlying declines due to the long position held in the underlying. However, these losses will be partly offset by the premiums earned on the calls sold.

Choice 'd' does not represent a correct statement as in the event of a rise in the price of the underlying the holder of the covered call will lose any upside, but will not have unlimited losses. In the event of a decline in stock prices, his losses will be equal to the loss on the underlying, minus the premium earned.

Generally, it is not a good idea to exercise an option early as any more upside in the remaining period to expiry is being sacrificed. However, if an extraordinarily large dividend is coming due, and this dividend is larger than the interest foregone from holding the option, it may be a good idea to exercise the option early. In such cases, the exercise needs to happen before the ex-dividend date and not afterwards. Choice 'b' is therefore the correct answer.

Even if the option is deep in the money and delta is approaching 1, and exercise upon maturity is almost a certainty, it would still always be better to sell the option than exercise it . Therefore Choice 'a' is incorrect. Choice 'c' is correct in all cases except when a large dividend is coming in. Choice 'd' is not correct because an early exercise needs to happen prior to the ex-dividend date and not afterwards.

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.

An out of the money convertible security behaves just like a regular debt security as the option is near worthless. Therefore it is affected by changes in interest rates and the credit risk of the issuer, and unaffected by changes in the prices or volatility of the issuer's shares (the underlying).

The correct answer is Choice 'b', as this question is merely asking for the forward rate based on known spot rates. The forward rate applicable to the three month period commencing in 3 months time is given by [(1 + 6%*6/12)/(1 + 5%*3/12) - 1]*4 = 6.91%. Thus Choice 'b' is the correct answer.

Here is a step by step way to think about it: $1 invested now at 6% for 6 months grows to (1 + 6%*6/12)=1.03. At the same time, using the 3 month rate, $1 invested now at 5% for 3 months grows to (1 + 5%*3/12)=1.0125. Effectively, this means that the 1.0125 at the end of 3 months grow to 1.03 at the end of 6 months, implying the rate of interest during the 3 months from 3 to 6 months is (1.03/1.0125 - 1)*4 = 6.91%.

Fixed income instruments go through the 'pull-to-par' phenomenon as they get closer to maturity. In this case, since interest rates stay constant, the bond will rise in price over the year to get closer to its redemption value. Of course, you can apply the standard discounting logic as well to say that while one year's coupon payment drops off, the remaining years' cash flows get discounted for a year less and the value would go up. However it is just easier to remember that at maturity the bond will be close to its notional or face value, and therefore if it is selling at a discount now, it will rise in value over its remaining life to get to the face value.

Exactly the reverse logic would apply to bonds sold at a premium, they would decline in value over time as to get to the par value at maturity.

Contingent premium options are options where no premiums are due upfront, and are due only at expiry and only if the option finishes in the money. (If this sounds too good to be true, remember that at expiry it is possible that the premiums due exceed the payoffs from the option. So there is no free lunch.) For this reason they are also called pay-later options.

They are simple combinations of a vanilla option and the 'right' number of cash-or-nothing options. The buyer of a contingent premium option has effectively purchased a vanilla option and sold enough number of cash-or-nothing options so that the net premium due at inception is zero.

Therefore statement I, II and III are correct and Choice 'b' is the correct answer.

The most loss the fund manager can bear without facing a margin call is the loss that will make his margin balance account no lower than $4,000. This means he can have a loss of upto $1,000 before a margin call is triggered, implying that prices can fall by $10 per ounce (=$1,000/100 ounces per contract) without triggering a margin call. The margin call will be to top the margin up to the $5,000 initial margin.

A protective put is a put option purchased to protect against the fall in value of a long position. If the price of the underlying in respect of the long position goes down, the put options helps limit losses. If the price of the underlying goes up, the premium paid on the puts is lost but the investor gets to keep the entire upside from the rise in the price.

Therefore statements I, III and IV are correct. Statement II is not correct as any decline in the value of the underlying is offset by the gain from the put, which is the entire idea behind a protective put.