Pass the PRMIA PRM Certification 8006 Questions and answers with ExamsMirror

Choice 'a' correctly describes a holder extendible option. Choice 'd' describes a writer extendible option. The other choices are meaningless.

Repos are collateralized borrowing arrangements. They are used for providing short term funding. They are not used for managing credit risk exposures. They are also used by central banks as part of their money market operations. They are also useful for facilitating short positions, for example, in corporate bonds where the party desirous of shorting the bond may 'borrow' the bond on repo in order to be able to sell it short.

The highest possible transformation line, ie the transformation line with the maximum slope, is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier. This line is called the 'capital markets line'. Investors can pick any point on this line according to their risk appetite, and doing so would maximize the return they can obtain for their desired level of risk. The capital markets line is tangential to the efficient frontier. The Sharpe ratio stays constant throughout the CML. Therefore statement IV is not true, while the rest are.

Explanation:

The BSM formula assumes that prices are lognormally distributed. Therefore Choice 'b' does not represent a valid assumption underlying Black Scholes. All other choices represent valid assumptions.

Explanation:

The correct answer is the index value times the contract size, in this case 1500 x 50.

One way to think about index futures is this: Consider equity index trading as trading in the shares of a company whose share price is equal to a number of dollars which is the same as the index. If the 'contract multiplier' for a index futures contract is 50, that means the futures contract is for 50 shares of such a fictitious company. Therefore the notional value of the contract will be 15000 x 50, and Choice 'a' is the correct answer.

A 'hard call protection' means the bond cannot be called until a certain date, regardless of what the share price is. Therefore statement I is false. Also note that a 'soft call protection' means that a bond can be called only if the share price reaches a certain threshold.

It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price - because these shares can instead be sold in the market at the higher share price than the lower conversion price. Statement II is true.

When the issuer's share price is very high, the convertible bond trades at a discount to the share price because it is almost certain to be called by the issuer and be redeemed at par. Therefore statement III is right. Statement IV is incorrect because convertible bonds need to pay less coupon than equivalent non-convertible bonds because of the value of the option embedded in them.

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.]

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.

Callable corporate bonds need to be priced lower and therefore yield more to investors as they are likely to be called by the issuer when interest rates fall and the issuer finds it attractive to refinance the debt using new cheaper debt.

They are most unlikely to be called when their prices have fallen because falling prices indicate higher rates, which means the issuer is able to fund himself at a cheaper rate.

Because of their callable feature, they are less convex and may actually carry negative convexity.

Therefore Choice 'b' is the only correct statement and the right answer.

As the compounding frequency increases, the nominal rate needs to decrease to produce the same amount of dollars at the end of a given time period. A continuously compounded rate of return has an infinite number of discrete compounding periods, and therefore the nominal rate expressed as a continuously compounded rate will always be nominally lower than any other rate.

Refer to the tutorial on interest rates for more details on continuously compounded rates work.