Reading 56: LOS f ～ Q1- 6 class, following, black, describes

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

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

B)   shifting the whole yield curve linearly.

C)   changing the yield of a specific maturity.

D)   changing the curvature of the entire yield curve.

2.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 times 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.

D)   simple average of the key rate durations.

3.Carol Stephens, CFA, manages a relatively small portfolio for one of her clients. Stephens feels that interest rates will change over the next year but is uncertain about the extent and direction. She is confident, however, that the yield curve will change in a nonparallel manner and that modified duration will not accurately measure her portfolio's yield-curve risk exposure. To help her evaluate the risk of her clients' portfolio, she has assembled the table of rate durations shown below.

Issue	Value ($1,000's)	3 mo	2 yr	5 yr	10 yr	15 yr	20 yr	25 yr	30 yr
Bond 1	100	0.03	0.14	0.49	1.35	1.71	1.59	1.47	4.62
Bond 2	200	0.02	0.13	1.47	0.00	0.00	0.00	0.00	0.00
Bond 3	150	0.03	0.14	0.51	1.40	1.78	1.64	2.34	2.83
Bond 4	250	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Bond 5	300	0.00	0.88	0.00	0.00	1.83	0.00	0.00	0.00

What is the 10-year key rate duration for the portfolio?

A)   1.350.

B)   1.375.

C)   1.400.

D)   0.345.

4.What is the effective duration for Bond 2?

A)   0.023.

B)   0.130.

C)   1.470.

D)   1.620.

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

A)   1.61.

B)   1.64.

C)   3.23.

D)   1.59.

6.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 the key rates at the short end of the yield curve.

B)   Increase all key rates by the same amount.

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

D)   Decrease all key rates by the same amount.

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

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

B)   shifting the whole yield curve linearly.

C)   changing the yield of a specific maturity.

D)   changing the curvature of the entire yield curve.

The correct answer was C)

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.

2.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 times 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.

D)   simple average of the key rate durations.

The correct answer was B)

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.

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3.Carol Stephens, CFA, manages a relatively small portfolio for one of her clients. Stephens feels that interest rates will change over the next year but is uncertain about the extent and direction. She is confident, however, that the yield curve will change in a nonparallel manner and that modified duration will not accurately measure her portfolio's yield-curve risk exposure. To help her evaluate the risk of her clients' portfolio, she has assembled the table of rate durations shown below.

Issue	Value ($1,000's)	3 mo	2 yr	5 yr	10 yr	15 yr	20 yr	25 yr	30 yr
Bond 1	100	0.03	0.14	0.49	1.35	1.71	1.59	1.47	4.62
Bond 2	200	0.02	0.13	1.47	0.00	0.00	0.00	0.00	0.00
Bond 3	150	0.03	0.14	0.51	1.40	1.78	1.64	2.34	2.83
Bond 4	250	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Bond 5	300	0.00	0.88	0.00	0.00	1.83	0.00	0.00	0.00

What is the 10-year key rate duration for the portfolio?

A)   1.350.

B)   1.375.

C)   1.400.

D)   0.345.

The correct answer was D)

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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4.What is the effective duration for Bond 2?

A)   0.023.

B)   0.130.

C)   1.470.

D)   1.620.

The correct answer was D)

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

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

A)   1.61.

B)   1.64.

C)   3.23.

D)   1.59.

The correct answer was B)

The 20-year rate duration for Bond 3 is 1.64 and can be taken directly from the table.

6.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 the key rates at the short end of the yield curve.

B)   Increase all key rates by the same amount.

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

D)   Decrease all key rates by the same amount.

The correct answer was C)

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.