Reading 53: Term Structure and Volatility of Interest Rates- center, security, interpret, div, class

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Session 14: Fixed Income: Valuation Concepts
Reading 53: Term Structure and Volatility of Interest Rates

LOS f: Compute and interpret the yield curve risk of a security or a portfolio by using key rate duration.

 

 

 

What adjustment must be made to the key rate durations to measure the risk of a steepening of an already upward sloping yield curve?

A) Increase all key rates by the same amount.

B) Increase the key rates at the short end of the yield curve.

C) Decrease the key rates at the short end of the yield curve.

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Decreasing the key rates at the short end of the yield curve makes an upward sloping yield curve steeper. Performing the corresponding change in portfolio value will determine the risk of a steepening yield curve.

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Which of the following best describes key rate duration? Key rate duration is determined by:

A) changing the curvature of the entire yield curve.

B) changing the yield of a specific maturity.

C) shifting the whole yield curve in a parallel manner.

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Key rate duration can be defined as the approximate percentage change in the value of a bond or bond portfolio in response to a 100 basis point change in a key rate, holding all other rates constant, where every security or portfolio has a set of key rate durations, one for each key rate maturity point.

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Key Rate Durations
Issue	Value ($1,000's)	weight	3 mo	2 yr	5 yr	10 yr	15 yr	20 yr	25 yr	30 yr	Effective Duration
Bond 1	100	0.10	0.03	0.14	0.49	1.35	1.71	1.59	1.47	4.62	11.4
Bond 2	200	0.20	0.02	0.13	1.47	0.00	0.00	0.00	0.00	0.00	1.62
Bond 3	150	0.15	0.03	0.14	0.51	1.40	1.78	1.64	2.34	2.83	10.67
Bond 4	250	0.25	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.06
Bond 5	300	0.30	0.00	0.88	0.00	0.00	1.83	0.00	0.00	0.00	2.71
Total Portfolio		1.00	0.0265	0.325	0.4195	0.345	0.987	0.405	0.498	0.8865	3.8925

The portfolio key rate duration for a specific maturity is the weighted value of the key rate durations of the individual issues for that maturity. In this case, the 10-year key rate duration for the portfolio is:

(0.10)(1.35) + (0.20)(0.00) + (0.15)(1.40) + (0.25)(0.00) + (0.30)(0.00) = 0.345

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What is the effective duration for Bond 2?

A) 0.023.

B) 1.620.

C) 1.470.

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Key Rate Durations
Issue	Value ($1,000's)	weight	3 mo	2 yr	5 yr	10 yr	15 yr	20 yr	25 yr	30 yr	Effective Duration
Bond 1	100	0.10	0.03	0.14	0.49	1.35	1.71	1.59	1.47	4.62	11.4
Bond 2	200	0.20	0.02	0.13	1.47	0.00	0.00	0.00	0.00	0.00	1.62
Bond 3	150	0.15	0.03	0.14	0.51	1.40	1.78	1.64	2.34	2.83	10.67
Bond 4	250	0.25	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.06
Bond 5	300	0.30	0.00	0.88	0.00	0.00	1.83	0.00	0.00	0.00	2.71
Total Portfolio		1.00	0.0265	0.325	0.4195	0.345	0.987	0.405	0.498	0.8865	3.8925

The effective duration for any individual issue is the sum of the individual key rate durations for that issue. For Bond 2, the effective duration is:

0.02 + 0.13 + 1.47 = 1.62

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What is the 20-year rate duration for Bond 3?

A) 1.64.

B) 1.61.

C) 3.23.

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The 20-year rate duration for Bond 3 can be taken directly from the table (= 1.64).

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An analyst has a list of key rate durations for a portfolio of bonds. If only one interest rate on the yield curve changes, the effect on the value of the bond portfolio will be the change of that rate multiplied by the:

A) median of the key rate durations.

B) key rate duration associated with the maturity of the rate that changed.

C) weighted average of the key rate durations.

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This is how an analyst uses key rate durations: For a given change in the yield curve, each rate change is multiplied by the associated key rate duration. The sum of those products gives the change in the value of the portfolio. If only the five-year interest rate changes, for example, then the effect on the portfolio will be the product of that change times the five-year key rate duration.