Pass the PRMIA PRM Certification 8013 Questions and answers with ExamsMirror

According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include

- bankruptcy,

- failure to pay,

- restructuring,

- obligation acceleration,

- obligation default and

- repudiation/moratorium.

Therefore all four events listed are credit events and Choice 'b' is the correct answer.

The dividend payment has a present value of $2.20*e^( -6%*6/12) = $2.14. Therefore the forward price for delivery 9 months hence should be ($102 - $2.14)*e^(7%*9/12) = $105.25

A quanto is any instrument in which one asset is a foreign currency. Examples include any option on a foreign currency asset with the strike price in foreign currency, and an option on a foreign currency asset with the foreign currency risk hedged.

Correlation products refer to credit products on a basket of credits. Options on options represent an option to buy or sell an option in the future, and they are not 'quantos'. Similarly, not every two asset instrument is a quanto unless one of the two assets is a foreign currency.

The buyer of a cap who is primarily interested in protecting against a rise in interest rates and does not mind losing some of the gains if interest rates were to fall can reduce her costs by selling a floor with a lower strike rate. Selling a cap would further expose her to the risk of rising rates, exactly what she is trying to protect herself against, and reducing the strike rate for the cap will actually increase the cost of the cap. Similarly, increasing the time period to which the cap applies will also increase the cost of the cap.

Since the 10 year rate has stayed the same, but the curve has gone from being flat to upward sloping, it means the shorter term interest rates have gone down. Recall that Macaulay duration is the PV of the payments received on a bond over its life weighted by the year each payment is received in. Also remember that a bond's current price is nothing but the summation of the different PVs of its various payments. It effectively gives the real average life of the bond - for example if a hypothetical (and impossible) bond derives half of its value from a payment today and the other half from a payment in 10 years, the investor can look at the average as being 5 years (0*50% + 10*50%). That is what is what we are calculating when deriving Macaulay duration.

In this case, a reduction in the near term interest rates increases the PV of the payments received prior to the payment at 10 years. This increases the value of the bond, and also increases the weightage of the earlier payments, decreasing the Macaulay duration (by shifting it closer to now and further behind from the maturity date).

This question touches upon a couple of issues that relate to hedging foreign exchange exposures using futures contracts. Firstly, many futures contracts on exchanges are available only at specific maturity dates, for example, the IMM dates. They may or may not coincide with actual liabilities for a running business. Also, futures contracts are standardized, ie their notional amounts are fixed rounded sums, and they can only be traded in whole numbers. This often means business using futures for hedging end up having a close enough, but not perfect hedge.

For our importer in the question, clearly he has to buy USDs so he can make his payment. Since each contract gives him USD 100k, he should buy 11 contracts that will get him very close to the amount he finally needs. Also, the contract expires a month later than his liability is due. This means he should offset the contract by closing it out in August soon as he has made his payment. This will allow him to stay hedged till August. If he does not sell out of the contracts, he will become exposed to a long position for one month till the contract settles, a risk which is unnecessary for him.

Therefore Choice 'b' is the best answer.

The London Interbank Offered Rate (LIBOR) is published by the British Bankers' Association (BBA). The BBA polls the rates offered by at least eight banks drops the top and bottom quartile, and averages the middle two quartiles of the rates to arrive at the LIBOR.

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.]

The weighted average cost of capital (WACC) is given by the average cost of debt and equity, weighted by their proportions in the capital structure. The cost of debt should be considered after taxes, as interest is a tax deductible expense. Therefore the WACC in this case can be calculated as = [10% x (1-25%) x 0.5] + [14% x 0.5] = 10.75%

Kappa indices, which include the Sortino ratio and the Omega statistic, consider semi-variance, ie variance calculated only in respect of the downside risk instead of variance (which includes both upside and downside). This is because one criticism of other risk adjusted performance measures is that they take both upside and downside risk into account, even though a portfolio manager or investor is only concerned with managing the downside. The Kappa indices consider returns that are below a threshold to measure performance by. Therefore statement I is correct.

The Treynor ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta]. It therefore calculates the excess return per unit of systematic risk and not specific risk. Therefore statement II is not correct.

Increasing portfolio leverage, ie borrowing to invest more in the portfolio, will increase the excess return of the portfolio in a linear fashion. However, it will also increase the volatility of such a portfolio in an identical linear way. Since Sharpe ratio is the ratio of 'excess returns' to standard deviation, the Sharpe ratio will stay constant. In other words, leverage does not impact Sharpe ratio, which is an attribute of this measure that allows us to compare performance across managers and funds regardless of leverage used. Statement III is not correct.

Jensen's alpha results from security selection, ie from specific risk the manager has taken. In a market portfolio, all specific risk is diversified away and only systematic risk remains. Therefore, statement IV is correct.