Reading 59: Valuing Mortgage-Backed and Asset-Backed Securiti

points

LOS g: Analyze the interest rate risk of a security given the security's effective duration and effective convexity.

Q1. Given the following information, which bond has the greater interest rate risk and what is the change in price if rates increase by 50 basis points?

	Par	Market Price	PVBP per $1,000 par value
Bond A	2,000,000	1,987,500	0.885
Bond B	7,000,000	8,588,250	1.025

A) Bond B, change in price = - $88,500.

B) Bond A, change in price = - $358,750.

C) Bond B, change in price = - $358,750.

Q2. The option adjusted spread (OAS) is used to analyze risk by adjusting for the embedded options. Which of the following risks does the OAS reflect?

A) Credit risk.

B) Prepayment risk.

C) Maturity risk.

Q3. Given the following information, which bond has the greater interest rate risk and what is the change in price if rates increase by 50 basis points?

	Duration	Convexity
Bond A	4.5	45.8
Bond B	7.8	125.0

A) Bond B, change in price = -3.59%.

B) Bond B, change in price = -27.4%.

C) Bond A, change in price = -2.14%.

Q4. The Calgary Institute Pension Fund includes a $65 million fixed-income portfolio managed by Cara Karstein, CFA, of Noble Investors. Karstein is asked by Calgary to provide an analysis of the interest rate risk of the bond portfolio. Karstein uses a binomial interest rate model to determine the effect on the portfolio of a 100 basis point (bp) increase and a 100 basis point decrease in yields. The results of her analysis are shown in the following figure.

Par Value	Security	Market Value	Current Price	Price If Yield Change
Par Value	Security	Market Value	Current Price	Down 100 bp	Up 100 bp
$25,000,000	4.75% due 2010	$25,857,300	$105.96	$110.65	$101.11
$40,000,000	5.85% due 2025	$39,450,000	$98.38	$102.76	$93.53
$65,000,000	Bond portfolio	$65,307,300

At a subsequent meeting with the trustees of the fund, Karstein is asked to explain what a binomial interest rate model is, and how it was used to estimate effective duration and effective convexity. Karstein is uncertain of the exact methodology because the actual calculations were done by a junior analyst, but she tries to provide the trustees with a reasonably accurate step-by-step description of the process:

Step 1:	Given the bond’s current market price, the Treasury yield curve, and an assumption about rate volatility, create a binomial interest rate tree and calculate the bond’s option-adjusted spread (OAS) using the model.
Step 2:	Impose a parallel upward shift in the on-the-run Treasury yield curve of 100 basis points.
Step 3:	Build a new binomial interest rate tree using the new Treasury yield curve and the original rate volatility assumption.
Step 4:	Add the OAS from Step 1 to each of the 1-year rates on the tree to derive a “modified” tree.
Step 5:	Compute the price of the bond using this new tree.
Step 6:	Repeat Steps 1 through 5 to determine the bond price that results from a 100 basis point decrease in rates.
Step 7:	Use these two price estimates, along with the original market price, to calculate effective duration and effective convexity.

Julio Corona, a trustee and university finance professor, immediately speaks up to disagree with Karstein. He claims that a more accurate description of the process is as follows:

Step 1:	Given the bond’s current market price, the on-the-run Treasury yield curve, and an assumption about rate volatility, create a binomial interest rate tree.
Step 2:	Add 100 basis points to each of the 1-year rates in the interest rate tree to derive a “modified” tree.
Step 3:	Compute the price of the bond if yield increases by 100 basis points using this new tree.
Step 4:	Repeat Steps 1 through 3 to determine the bond price that results from a 100 basis point decrease in rates.
Step 5:	Use these two price estimates, along with the original market price, to calculate effective duration and effective convexity.

Corona is also concerned about the assumption of a 100 basis point change in yield for estimating effective duration and effective convexity. He asks Karstein the following question: “If we were to use a 50 basis point change in yield instead of a 100 basis point change, how would the duration and convexity estimates change for each of the two bonds?”

Karstein responds by saying, “Estimates of effective duration and effective convexity derived from binomial models are very robust to the size of the rate shock, so I would not expect the estimates to change significantly.”

Which of the following statements is most accurate?

A) The two methodologies will result in the same effective duration and convexity estimates only if the same rate volatility assumption is used in each and the bond’s OAS is equal to zero.

B) Corona’s description is a more accurate depiction of the appropriate methodology than Karstein’s.

C) Karstein’s description is a more accurate depiction of the appropriate methodology than Corona’s.

Q5. Assume that the effective convexity of the 4.75% 2010 bond is 3.45. The effective duration of the 4.75% 2010 bond and the percentage change in the price of the bond for an 80 basis point decrease in the yield are closest to:

Effective Duration % Change in Bond Price

A) 4.21 +2.09%

B) 4.58 +1.79%

C) 4.50 +3.62%

Q6. The convexity of the 5.85% 2025 bond for a 100 basis point change in rates is closest to:

A) ?23.88.

B) ?12.18.

C) 3.57.

Q7. Assume that the duration of the 5.85% 2025 bond is 2.88. The duration of the portfolio is closest to:

A) 3.01.

B) 3.12.

C) 3.52.