Pass the PRMIA PRM Certification 8006 Questions and answers with ExamsMirror

When using a futures contract to hedge a position, the correct way to determine the number of futures contracts to use is to use the following formula. This adjusts for the 'tailing the hedge' adjustment required as a result of the daily settlement feature of futures contracts.

Minimum Variance Hedge Ratio x Dollar Value of Position / Dollar Value of Single Futures Contract

When using forward contracts to hedge a position, no adjustment to tail the hedge is required (as settlement happens only at the end), and the number of units of the exposure when compared to the number of units per contract should be used. The formula in the case of forward contracts is:

Minimum Variance Hedge Ratio x Units in Position Held / Units in Single Futures Contract

In practice however, the difference between the above two formulae is de-minimis; and for the exam you should be okay to use either of the above two to determine the number of contracts - unless the question is directed to testing your knowledge of the 'tailing the hedge' adjustment.

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate and this discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increase in dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)

When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond.

Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.

The hedge ratio is determined both by the yield beta and the BPVs of the two securities. Choice 'd' is the correct answer.

Implied volatilities are the same for calls and puts with similar exercise and strike prices. If not, it would offer an arbitrage opportunity. Therefore Choice 'b' is the correct answer.

The duration of a perpetuity is 1/running yield. Therefore the correct answer is 1/.05 = 20 years