PRMIA 8006 Exam Questions

To calculate the Modified Duration from Macaulay's duration, we use the relationship MD = D/(1+r), where MD is the modified duration and D the Macaulay Duration. Therefore Choice 'c' is the correct answer.

An m x n FRA is an agreement to borrow money for a period starting at time m and ending at time n at the contracted rate. Therefore, the buyer of the 3 x 6 FRA has committed to borrow $1m at the beginning of 3 months and return it at the end of 6 months, ie a total borrowing period of 3 months at a rate of 5%. Of course, the $1m is never actually exchanged, and at the beginning of the 3 month period when the next three months' interest rate is known (6%), the parties merely exchange the difference in the interest. SInce this interest was only due at the end of the 6 months and is being exchanged at the 3 month time point, it will have to be discounted to its present value.

The correct answer to this question is =(1,000,000 * (6% - 5%) * 3/12)/(1 + (6%*3/12))=$2463.05. Since interest rates rose, the borrower gained as he has the right to borrow at a lower rate, and therefore the seller will pay the borrower.

(Here:

- $1m is the notional

- 6% - 5% represents the difference between the contracted and the realized interest rates

- 3/12 is the 3 month period from month 3 to 6

- Finally, we divide by the current interest rate for 3 months to present value the payment from month 6 to month 3)

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 efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. For a given level of volatility, it identifies the portfolio with the maximum return. Therefore Choice 'b' is the correct answer.

If a reading is taken from the y-axis (ie returns) by dropping a perpendicular line on to the efficient frontier, we can get the minimum risk portfolio for the given level of returns. So the efficient frontier can be used to identify either the highest return per unit of volatility, or the lowest volatility given a desired level of returns. The efficient frontier does not describe the market portfolio, though the market portfolio may be one of the many points on the efficient frontier. Thus the other choices are incorrect.

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.