Question

Sandra Kapple presents Maria Van Husen with a description, given in the following exhibit, of the bond portfolio held by the Star Hospital Pension Plan. All securities in the bond portfolio are non-callable U.S. Treasury securities.

STAR HOSPITAL PENSION PLAN BOND PORTFOLIO

Par value (in US \()	Treasury security	Market value (in US \))	Current Price	Up 100 basis points	Down 100 basis points	Effective duration
\(48,000,000	2.375% due 2010	\)48,667,680	$101.391	99.245	103.595	2.15
50,000,000	4.75% due 2035	50,000,000	100.000	86.372	116.887
98,000,000	Total bond portfolio	98,667,680	-------	--------	-------	--------

a. Calculate the effective duration of each of the following:

i. The 4.75% Treasury security due 2035

ii. The total bond portfolio

b. Van Husen remarks to Kapple, “If you changed the maturity structure of the bond portfolio to result in a portfolio duration of 5.25, the price sensitivity of that portfolio would be identical to the price sensitivity of a single, non-callable Treasury security that has a duration of 5.25.” In what circumstance would Van Husen’s remark be correct?

Short answer

a. (i) 15.26 (ii) 8.79

b. In case of zero-coupon bond

Step-by-step solution

Given information

Formula = ∆P/P = −D x ∆y

∆P = −D x ∆y x P

∆P / ∆y x P = - D

Calculation of duration of the bond in ‘a’

(i) Duration = (116.87 – 100.00) / (2 x 100 x 0.01)

= 15.26 Years

(ii) Portfolio duration can be calculated using the weighted average of time to receipt of the cash flow.

= (50/98.667) x 15.26 + (48.667/ 98.667) x 2.15

= 8.79

Evaluation of circumstances

Van Heusen's remark would have been correct if the portfolio consisted of zero-coupon bonds.