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

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 value of the portfolio if only 3 rates change while the others remain constant?

• The 3-month rate increases by 20 basis points.
• The 5-year rate increases by 90 basis points.
• The 30-year rate decreases by 150 basis points.

A)   $1,009,469.00.

B)   $1,038,925.00.

C)   $961,075.00.

youzizhang

 

Correct answer is A)fficeffice" />

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

Change in Portfolio Value

Change from 3-month key rate increase:	(20 bp)(0.0265)	= 0.0053% decrease
Change from 5-year key rate increase:	(90 bp)(0.4195)	= 0.3776% decrease
Change from 30-year key rate decrease:	(150 bp)(0.8865)	= 1.3298% increase
Net change		0.9469% increase

This means that the portfolio value after the yield curve shift is:

1,000,000(1 + 0.009469) = $1,009,469.00

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