Reading 54: Term Structure and Volatility of Interest Rates change, extent, interest, direction, however

youzizhang

 

Q2. 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)   0.345.

B)   1.375.

C)   1.350.

youzizhang

 

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Correct answer is A)

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

cyyap1011

 thanks

parkers

a

shij

3x

liqingguo

a

yy21

好

harbuzi

f

dandinghe4748

3x

hkgee

thanks!