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Question A trader comes in to work and finds the following prices 101 :
in relation to a stock: $ spot, $10 for a call expiring in one year with a strike price of $100, and $10 for a put
with the same expiry and strike. Interest rates are at 5% per year, and the stock does not pay any dividends. What should the trader do? (a)Buy the call, buy the put
and sell the stock (b)Buy the
put, sell the call and buy the
stock (c)Buy the call, sell the
put and sell the stock (d)Do
nothing
Your Answer is Correct
The correct answer is choice 'c'
The prices must satisfy the put-call parity, and if they do not, it means there is an arbitrage opportunity, The put-call parity is as follows. We plug in the values to check if the parity is maintainted.
Buying a call + Bank Deposit (PV of exercise price) = Buying the stock + Buying a put Thus the LHS = $10 + $100/(1 + 5%) = $105. and RHS = $100 + $10 = $110, ie the equality does not hold.
Since the trader can make a profit by buying low and selling high, and the set of positions on the left should be brought, and those on the RHS should be sold. Thus the trader should buy the call, sell the put and sell the stock to make a risk free profit. (There is no need to explicitly place a bank deposit at the risk-free rate).
￥ Question
What would be the most profitable strategy for an 102 :
investor who expects interest rates to rise:
(a)long floating rate notes
(b)short fixed rate bonds
(c)long inverse
floaters (d)long
inflation linked
bonds
Your Answer is Incorrect
The correct answer is choice 'b'
A rise in interest rates will cause fixed rate bond prices to fall. It will not affect the floating rate notes as their rates are going to float with the changes in interest rates. Inflation linked bonds will only be affected by changes in real interest rates, and even in a situation where the rise in interest rates is happening due to an increase in the real rates, a long position would hurt. As interest rates rise, the coupon payable on the inverse floater would fall, hurting a long position.
Of the given alternatives, the only position that would benefit from a rise in interest rates is the short position in fixed rate bonds. Hence Choice 'b' is the correct answer.
Question Which of the following statements is true: 103 :
A bullet bond refers to a bond: 104 : (a)that provides for fixed coupons and repayment of
principal at maturity (b)that is issued by a sovereign
(c)that carries no coupon payments during its lifetime
(d)that provides for floating rate interest payments during its lifetime
Your Answer is Correct
The correct answer is choice 'a'
Choice 'a' represents a correct description of a bullet bond. All other choices are incorrect.
￥ Question An investor holds $1m in face each of two bonds. Bond 1 105 :
has a price of 90 and a duration of 5 years. Bond 2 has
a price of 110 and a duration of 10 years. What is the combined duration of the portfolio in years? (a)7.
(b)7.
(c)7.
5 (d)
Your Answer is Correct
The correct answer is choice 'c'
The value of Bond 1 is $900,000 and the value of Bond 2 is $1,100,000, or their respective weights in the portfolio are 45% and 55% respectively. The combined duration is the weighted average of their individual durations, ie (45% x 5)
￥ Question What would be the total all in price payable on an 5% 107 :
annual coupon bond quoted at a
clean price of $98, where the settlement date is 60 days after the latest coupon payment. Use Act/360 day basis. (a)$98.
(b)$100.
(c)$98.
(d)$97.
Your Answer is Incorrect
The correct answer is choice 'a'
The all in price would be equal to the clean price plus accrued interest. The accrued interest for the 60 days that have passed since the last coupon payment is $5 x 60/360 = $0.83. Therefore the dirty price, or the all in price, will be $98.83. (Note that the $5 is the annual 5% coupon on the $100 face.)
Question Which of the following will have a higher reinvestment 108 : risk when compared to a 6% bond
issued at par? Assume all
bonds have identical yield to maturity.
Question What is the yield to maturity for a 5% annual coupon bond 109 : trading at par? The bond
matures in 10 years.
(a)Equal to 5%
(b)Less than 5%
(c)Greater than 5%
(d)Cannot be determined based on the given information
Your Answer is Correct
The correct answer is choice 'a'
The yield to maturity for a bond trading at par will be identical to its coupon. Therefore the yield to maturity for this bond will be 5%
Question What is the running yield on a 6% coupon bond selling at 110 :
a clean price
of $96? (a)6.25%
(b)5.70%
(c)6.30%
(d)6.00%
Your Answer is Correct
The correct answer is choice 'a'
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.
Question The price of a bond will approach its par as it approaches 111 :
maturity. This is called: (a)negative carry
(b)pull-to-par phenomenon
(c)duration
adjustment
(d)amortization
effect
Your Answer is Correct
The correct answer is choice 'b'
As a bond approaches maturity, its value will be driven less by the time value of money or its coupons, and more by its redemption value, ie the par. Therefore as maturity approaches, its value converges to its par value and this phenomenon is called pull to par.
Question Which of the following will have the effect of increasing 112 :
(d)Modified Duration x (1 + r) = Macaulay Duration
Your Answer is Correct
The correct answer is choice 'd'
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 'd' is the correct answer.
Question A 'consol' is a perpetual bond issued by the UK 114 : government. Its running yield is 5%. What is its duration? (a)20 years
(b)5 years
(c)Infinity
(d)25 years
Your Answer is Incorrect The correct answer is choice 'a'
The duration of a perpetuity is 1/running yield. Therefore the correct answer is 1/.05 = 20 years
Question A bond has a Macaulay duration of 6 years. The yield to 115 :
maturity for this bond is currently 5%. If interest rates rise across the curve by 10
basis points, what is the impact on the price of the bond? (a)Decrease of 57 basis points
(b)Increase of 10 basis points
(c)Increase of 57 basis points
(d)Decrease of 10 basis points
Your Answer is Correct
The correct answer is choice 'a'
Since Macaulay duration is 6 years, the modified duration is 6/(1+5%) = 5.71. This means that if interest rates were to rise by 1%, the bond price would decrease by 5.71%. Since interest rates have risen by 10 bps, (100bps = 1%), the bond's price would fall by roughly 0.571%, or 57 basis points
Question When hedging one fixed income security with another, the 116 :
hedge ratio is determined by: (a)The yield beta
(b)The volatility of the hedge
(c)The yield beta and the basis point values of the hedge instrument and the security being hedged. (d)Basis point value or PV01 of the two instruments
Your Answer is Correct The correct answer is choice 'c'
When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we
therefore produce a 0.05% change in the value of the bond. Since the bond is currently valued at $102, the change works out to $102 x 0.05% = $0.051.
Question An investor holds $1m in a 10 year bond that has a basis 118 :
point value (or PV01) of 5 cents. She seeks to hedge it
using a 30 year bond that has a BPV of 8 cents. How much of the 30 year bond should she buy or sell to hedge against parallel shifts in the yield curve? (a)Buy $1,600,
(b)Sell $1,600,
(c)Sell $625,
(d)Buy $1,000,
Your Answer is Incorrect
The correct answer is choice 'c'
When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond. Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in
yield for primary position/change in yield for the hedge security.
The hedge ratio is determined both by the yield beta and the BPVs of the two securities. In this case, the yield beta is 1 (as the question speaks of a parallel shift in the yield curve, ie all rates rise or fall together), and the ratio of the BPVs is 5/8. Therefore she should sell 5/8 x 1,000,000 = $625,000 of the 30 year bond.
Choice 'c' is the correct answer.
￥ Question For an investor short a bond, which of the following is 119 :
true: I. Higher convexity is
preferable to lower convexity II. An increase in yields is preferable to a decrease in yield III. Negative convexity is preferable to positive convexity (a)I and II
(b)I and III
(c)I, II and III
(d)II and III
Your Answer is Incorrect
The correct answer is choice 'd'
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
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. Question Which of the following is NOT true about a fixed rate 121 :
bond: I. The higher the coupon, the
lower the duration II. The higher the coupon, the lower the convexity III. If the bond is callable, it has negative modified duration IV. If the bond is callable, the bond has negative convexity (a)III
(b)IV
(c)I
(d)II
Your Answer is Correct
The correct answer is choice 'a'
A higher coupon brings forward the cash flows of a bond,
thereby lowering duration. Therefore statement I is true. The lower the duration the lower the convexity. Therefore a higher coupon leads to lower duration and therefore lower convexity. Thus statement II is true.
Bonds do not have negative modified duration, therefore statement III is false.
If the bond is callable, it leads to negative convexity as a fall in interest rates is likely to induce the issuer to call the bond and re-issue at the new lower interest rates (much like refinancing mortgages when interest rates fall), therefore the upside from a fall in rates is limited. This creates 'negative convexity'. Thus statement IV is correct.
Question Which of the following statements is a correct 122 : description of the phrase
present value of a basis point? (a)It refers to the discounted present value of 1/100th of 1% of a future cash flow (b)It is another name for duration
(c)It is the principal component representation of the
duration of a bond (d)It refers to the present value impact of 1 basis point move in an interest rate on a fixed income security
Your Answer is Correct
The correct answer is choice 'd'
This is a trick question, no great science to it. Remember that the 'present value of a basis point' refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called 'DV01' (dollar value of a basis point). Remember these other terms too.
interest rates by 10 bps causes
its price to decline to $94.50. A decrease in interest rates by 10 bps causes its price to increase to $95.60. Estimate the modified duration of the bond. (a)5.
(b)-
(c)5.
(d)
Your Answer is Incorrect
The correct answer is choice 'c'
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 $5.5/$ = 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.
Question A bond with a 5% coupon trades at 95. An increase in 125 :
interest rates by 10 bps causes
its price to decline to $94.50. A decrease in interest rates by 10 bps causes its price to increase to $95.60. Estimate the convexity of the bond. (a)-
(b)5.
(c)
(d)1.
Your Answer is Correct
The correct answer is choice 'c'
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. In this case, for the up move, the modified duration = ($0.60/10 bps)
- 100 / $95 = 6.32% or 6.32 years. For the down move in price, the modified duration is ($0.50/10 bps) * 100 / $95 = 5.26% or 5.26 in terms of modified duration. 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 10basis points and not 20. Therefore convexity
