dkishore1

Which kind of risk remains if the option-adjusted spread is deducted from the nominal spread?

A) credit risk.

B) option risk.

C) liquidity risk.

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The OAS captures the amount of credit risk and liquidity risk.

dkishore1

An analyst has constructed an interest rate tree for an on-the-run Treasury security. Given equal maturity and coupon, which of the following would have the highest option-adjusted spread?

A) A putable corporate bond with a AAA rating.

B) A putable corporate bond with a Aaa rating.

C) A callable corporate bond with a Baa rating.

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The bond with the lowest price will have the highest option-adjusted spread. All other things equal, the callable bond with the lowest rating will have the lowest price.

dkishore1

Which of the following correctly explains how the effective duration is computed using the binomial model. In order to compute the effective duration the:

A) binomial tree has to be shifted upward and downward by the same amount for all nodes.

B) yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.

C) the nodal probabilities are shifted upward and downward and the binomial tree recalculated each time.

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Apply parallel shifts to the yield curve and use these curves to compute new forward rates in the interest rate tree. The resulting bond values are then used to compute the effective duration.

dkishore1

Which of the following most accurately explains how the effective convexity is computed using the binomial model. In order to compute the effective convexity the:

A) yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.

B) binomial tree has to be shifted upward and downward by the same amount for all nodes.

C) volatility has to be shifted upward and downward and the binomial tree recalculated each time.

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Apply parallel shifts to the yield curve and use these curves to compute new forward rates in the interest rate tree. The resulting bond values are then used to compute the effective convexity.

dkishore1

An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the duration of the Treasury security. The usual way to do this is to estimate the changes in the bond’s price associated with a:

A) parallel shift up and down of the forward rates implied by the binomial model.

B) parallel shift up and down of the yield curve.

C) shift up and down in the current one-year spot rate all else held constant.

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The usual method is to apply parallel shifts to the yield curve, use those curves to compute new sets of forward rates, and then enter each set of rates into the interest rate tree. The resulting volatility of the present value of the bond is the measure of effective duration.

dkishore1

An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the convexity of a callable corporate bond with maturity and coupon equal to that of the Treasury security. The usual way to do this is to calculate the option-adjusted spread (OAS):

A) compute the convexity of the Treasury security, and divide by (1+OAS).

B) compute the convexity of the Treasury security, and add the OAS.

C) shift the Treasury yield curve, compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula.

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The analyst uses the usual convexity formula, where the upper and lower values of the bonds are determined using the tree.

dkishore1

Steve Jacobs, CFA, is analyzing the price volatility of Bond Q. Q’s effective duration is 7.3, and its effective convexity is 91.2. What is the estimated price change for Bond Q if interest rates fall/rise by 125 basis points?

Fall

Rise

A) +7.70% −10.55%

B) +10.55% −7.70%

C) −10.55% +7.70%

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Estimated change if rates fall by 125 basis points:

(-7.3 × -0.0125) + (91.2)(0.0125)2 = 0.1055 or 10.55%


Estimated change if rates rise by 125 basis points:

(-7.3 × 0.0125) + (91.2)(0.0125)2 = -0.0770 or -7.70%

dkishore1

A CFA charter holder observes a 12-year 7 ¾ percent semiannual coupon bond trading at 102.9525. If interest rates rise immediately by 50 basis points the bond will sell for 99.0409. If interest rates fall immediately by 50 basis points the bond will sell for 107.0719. What are the bond's effective duration (ED) and effective convexity (EC).

A) ED = 8.031, EC = 2445.120.

B) ED = 40.368, EC = 7.801.

C) ED = 7.801, EC = 40.368.

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ED = (V- − V+) / (2V0(∆y))
= (107.0719 − 99.0409) / (2 × 102.9525 × 0.005) = 7.801
EC = (V- + V+ − 2V0) / (2V0(∆y)2)
= (107.0719 + 99.0409 − (2 × 102.9525)) / [(2 × 102.9525 × (0.005)2)] = 40.368

dkishore1

A putable bond with a 6.4% annual coupon will mature in two years at par value. The current one-year spot rate is 7.6%. For the second year, the yield volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The bond is putable in one year at 99. Using a binomial interest rate tree, what is the current price?

A) 98.246.

B) 98.885.

C) 98.190.

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The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value at all nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
Vi,U = [(100 + 6.4) / 1.076 + (100+6.4) / 1.076] / 2 = 98.885
Vi,L = [(100 + 6.4) / 1.068 + (100 + 6.4) / 1.068] / 2 = 99.625.
Since 98.885 is less than the put price, Vi,U = 99
V0 = [(99 + 6.4) / 1.076) + (99.625 + 6.4) / 1.076)] / 2 = 98.246.

dkishore1

Using the following tree of semiannual interest rates what is the value of a putable bond that has one year remaining to maturity, a put price of 99, coupons paid semiannually with payments based on a 5% annual rate of interest?

         7.59%
6.35%
         5.33%

A) 99.00.

B) 98.75.

C) 97.92.

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The putable bond price tree is as follows:

		100.00
A → 99.00
99.00		100.00
	99.84
		100.00

As an example, the price at node A is obtained as follows:
PriceA = max[(prob × (Pup + coupon / 2) + prob × (Pdown + (coupon / 2)) / (1 + (rate / 2)), put price] = max[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0759 / 2)) ,99] = 99.00. The bond values at the other nodes are obtained in the same way.
The calculated price at node 0 =
[0.5(99.00 + 2.5) + 0.5(99.84 + 2.5)] / (1 + (0.0635 / 2)) = $98.78 but since the put price is $99 the price of the bond will not go below $99.