Pass the PRMIA PRM Certification 8006 Questions and answers with CertsForce

The optimal hedge ratio answers the question of how much of the hedge to buy to hedge a given position. If 103.11.e1 is the standard deviation of the asset to be hedged, and 103.11.e2 is the standard deviation the asset being used to hedge against price movements in x, then the minimum variance hedge ratio is given by the expression 103.11.e3. In this question, correlation = 0.00378/(6%*7%) = 0.9. The minimum variance hedge ratio is given by (6%/7%)*0.9 = 0.77

He should therefore hold 0.77 x $10m /$100k = 77 contracts.

[We can also do a direct covar based calculation for the min variance hedge ratio as follows:

103.11.a3

= 0.00378 / (0.07 * 0.07) = 0.7714]

Choice 'b' is the correct answer. The other relationships are not correct.

The 'running yield' refers to the coupon rate divided by the current price. In this case, it is 6/96 = 6.25%. Remember that the running yield is also called the current yield.

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.

Choice 'd' is the correct answer. Continuously compounded returns are given by the log of S2/S1. The expression (S2 - S1)/S1 gives discrete returns, not continuously compounded returns.

Note that the question is only asking for the return over the given time period, not annualized returns. So t is not relevant here. If we had to find annualized returns, and t were expressed in years, then the annualized return would have been (1/t)*ln(S2/S1).

Also refer to the tutorial on interest rates and compounding for more information on continuously compounded rates.

Investors in CDOs bear credit risk. The SPV is merely a conduit that owns the underlying assets on which the sponsoring institution has bought protection. The investors have sold them this protection, and are on the hook for defaults or other credit events. The reference entity is relevant only to CDSs, not CDOs. Choice 'b' is the correct answer.

Given covered interest parity, the currency with a lower interest rate will trade at a forward premium. Choice 'b' is the correct answer.

For an intuitive reasoning, consider a currency forward contract that matures in 3 months. The seller has agreed to sell, say JPY 1,000,000 in exchange for USD 10,000 in the future. In order to cover himself, he borrows the USD right now and converts it to JPY at spot which he puts in a JPY deposit. Assuming JPY interest rates are less than USD interest rates, he pays more on his USD borrowing than he receives on his JPY deposit. Therefore he has to price the forward contract at a premium to spot to cover the interest rate differential.

The dates on which the interest rates applicable to the floating rate leg of an IRS are determined are called 'reset dates'. Choice 'c' is the correct answer, the other choices are incorrect. Settlement date is the date a transaction settles, normally a few days after the trade is done depending upon the market. Trade date is the date the terms of the transaction are agreed. (Settlement normally happens on T+n, where T is the trade date, and n the number of days to settlement as decided by agreement or market convention.)

The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond - such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.

An increase in yields makes bond prices decrease, something that would benefit the short. Therefore statement II is true for an investor short a bond.

Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor.

Choice 'b' is the correct answer.

This question highlights the difference between zero rates, yield-to-maturity and forward rates. Forward rates are from one point in time to another, for example say from year 4 to 5 in the future. A zero rate is from time 0, or now, to a point in time in the future. The zero rate is dependent on the forward rates for all the different periods from now to the future. The yield curve represents the various zero rates at different points in time, and if it is upward sloping it means forward rates for years further out are greater than the years prior. That is what causes the zero rate yields to increase over time and the curve to slope upwards. So the forward rate from year 9 to 10 will certainly be higher than the 10 year zero rate.

The yield-to-maturity for a bond is the rate at which the payments on the bond discount to be equal to the current bond price. It is therefore the average rate that applies to the bond. This average is based upon the different zero rates for the years in which bond holders receive payments. Since coupons are smaller than the payment at maturity, the zero rate that applies to the payment at maturity will have the most impact on the numerical value of the bond's yield-to-maturity. Also affecting the yield-to-maturity will be the values of the coupon payments, which will be discounted at lower rates when the yield curve is upward sloping. So the yield-to-maturity will be an average lower than the 10 year zero. Since the 10 year zero will be lower than the forward rate from t=9-10, the yield-to-maturity will be the lowest rate of the three.