PRMIA Exam I: Finance Theory, Financial Instruments, Financial Markets – 2015 Edition 8006 Exam Practice Test

Answer : A

A deep out of the money option will not react much to the change in the price of the underlying. In fact, the more out of the money it is, the more unresponsive it will be to changes in the prices of the underlying. Therefore, its delta will approach zero. Since delta is zero, gamma, which measures the rate of change in the delta, will also be zero as delta is unchanging. Therefore Choice 'a' is the correct answer.

Answer : B

Mortgage backed securities carry prepayment risk as borrowers tend to prepay mortgages when rates fall, and substitute it with newer cheaper mortgages. This creates the issue of 'negative convexity' for mortgages, ie, they lose value when rates rise, but do not gain in value when rates fall.

Prepayment risk can be offset by instruments that also carry negative convexity. A swaption is an option to borrow in the future at an agreed rate, which may be fixed or floating. An option to borrow in the future paying floating and receiving fixed guards against losses when rates fall, as the option can be exercised for a profit when rates are declining and the mortgage portfolio is being prepaid. A callable bond is very similar to an MBS in that the issuer can call it back when rates fall. Thus a long position in an MBS can be offset by a short position in a callable bond. Thus I and III are valid choices.

A cap allows exchanging fixed for floating when interest rates rise above an agreed rate. A long cap position allows borrowing at a fixed rate in exchange for floating, and a short cap implies receiving fixed and paying floating when rates go above the strike rate. Prepayment risk arises from falling interest rates, therefore a short cap will not protect against such a risk as falling interest rates would mean that no payments would be exchanged. Thus II does not help hedge against the risk in question.

A long position in a fixed for floating swap would require paying fixed and receiving floating when rates are falling. This would just make the problem from prepayments worse as the position would pay fixed and receive a falling rate. Thus IV is not an appropriate way to hedge prepayment risk.

Answer : C

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.

Answer : B

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.)

Answer : D

All the choices listed are valid assumptions underlying the BSM option valuation formula except that the BSM formula is based upon the option being exercisable only at expiry. The assumption is that early exercise is not permitted. In other words, BSM applies to European options and not American options. Therefore Choice 'd' represents the correct answer as it is not an assumption underlying Black Scholes.

Answer : A

The forward price for a commodity is nothing but the spot price plus carrying costs till the maturity date of the forward contract. Any increase in carrying costs therefore has the effect of increasing the forward price. Note that carrying costs include interest cost in respect of funding the position, costs of storage, less any convenience yield.

Increase in the carrying costs will not affect the spot prices.

Answer : D

T-bill futures 'discount' can be converted to a price for the bill using the formula Price = [1 - discount * number of days/360]. In this case, this works out to (1- 10% *90/360) * 100 = $97.50. Choice 'd' is the correct answer.