Free PRMIA 8006 Practice Exam with Questions & Answers | Set: 8

The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity . Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06

Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73

Therefore the total value of the bond today is $95.79

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.

Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the 'cheapest' to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond - (Futures Price x Conversion Factor).)

The bond with the lowest basis is generally the CTD. In the given question, the three basis calculations are:

1) 97 - (0.9 x 105) = 2.5

2) 101 - (1 x 105) = -4

3) 106 - (1.1 x 105) = -9.5

Since the third bond with a quote of 106 has the lowest basis, Choice 'b' is the correct answer.

For fixed income portfolios where standard cash flow discounting models are not available, duration calculations are based upon estimated price moves in response to a change in rates. Recall that we define duration as the percentage change in price expected for a 1% change in yield. In this case, we have three price points known to us:

Line | Price | Yield

a | $102 | r - 45bps

b | $100 | r

c | $ 97 | r + 45bps

(where r is the current yield)

The change in price from line a to line c is $102m - $97m = $5m. We use the middle point, ie $100m, to calculate the percentage change. Therefore the percentage change in price is $5m/$100m = 5%.

The change in yield between lines a and c is 90 basis points [=(r+45bps) - (r-45bps)]. In other words, the change in price is 5% for a 90 bps change in yield. So the duration can be calculated as 5/(90/100) = 5.56. The other answers are incorrect.

Since the equity portfolio has a beta of 1.5, we need to sell short enough number of futures contracts as to have $1 x 1.5 = $1.5m short in notional. The value of one S&P futures contract is 1000 x 250 = $250,000, and therefore in order to be short $1.5m, we need to sell 6 contracts.

There are two main theories that explain an upward sloping yield curve. The first is the market expectations hypothesis (called 'pure expectations'). According to this explanation, the yield curve represents investor expectations of future yields, and forward rates are predictors of future interest rates. The yield curve slopes upwards when investors expect interest rates to go up in the future. Thus, statement I is correct. By the same logic, statement II is incorrect.

The second explanation for an upward sloping yield curve is the liquidity preference theory - according to which investors value liquidity and are prepared to pay more for instruments that mature earlier. Having their money tied up in longer maturity instruments increases all kinds of risks, and therefore longer term instruments are priced lower than instruments maturing earlier. Since the price of instruments that mature earlier is higher, their yield is lower than that of longer dated securities, thereby leading to an upward sloping yield curve. Therefore statement III is correct.

Statement IV actually explains why an yield curve may be downward sloping - in fact an inverted yield curve is considered an indicator of an upcoming recession. Therefore statement IV does not explain an upward sloping yield curve, and is therefore not a correct choice for the answer.

Thus statements I and III correctly explain an upward sloping yield curve. Other choices are incorrect.

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.

In an interest rate swap, only the net payment is made. In this case,

- the customer pays the bank 4%*(3/12)*$100m

- the bank owes the customer (2% + 100bp))*(3/12)*$100m

Therefore the customer pays (4% - (2% + 100bp))*(3/12)*$100m. 3/12 represents the 3 month time interval. This is equal to a net payment of $250k from the customer to the bank. Therefore Choice 'c' is the correct answer and the rest are incorrect.

This question is based upon a weather derivative contract traded on the CME in the US. For each day, 'Heating-Degree-Days' (HDD) is calculated as equal to 65 degrees Fahrenheit minus the daily average temperature. The daily average temperature is based upon the temperature reported by the Earth Satellite Corporation using a specified automated weather station. Based upon daily values of HDD, an aggregated number called the 'CME degree days index' is calculated for each contract month. In other words, the index for a particular month is just the aggregation of the 'HDD' value for each of the days of that month. Each contract settles at the end of the month at a value equal to $20 x Degree Days Index. (In a similar way, 'Cooling Degree Days' are also calculated and a futures contract offered, except that CDD is equal to the average daily temperature minus 65 degrees). (Source: CME's website at CMEGroup.com)

In the given question, we are interested in hedging against the possibility of the temperature being too low. This means we should buy the HDD futures contract (the lower the temperature, the higher the difference of the average temperature from 65 degrees, and the higher the settlement). Therefore Choice 'b' is the correct answer. The lower the actual temperature turns out to be, the higher the payout to the grower. It would not be wise to wait till January to buy the contract as by then the prices of the contract would have already risen if the grower's fears of a colder January appear to be coming true. He can hedge his exposure by immediately locking in the January prices.

Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice 'b' is the correct answer.