Actual

Assumed

$Duration of

$Convexity of

maturity date

maturity

Treasury

Implied zero

Implied

Duration

$Duration of

$100 par of

Duration of

Convexity

$Convexity of

$100 par of

Convexity of

Zero rates - 20 bp

Zero rates + 20 bp

(do not use)

Coupon

(use this)

bond price

price per $1 par

zero rate

of zero

$1 par of zero

Treasury bond

Treasury bond

of zero

$1 par of zero

Treasury bond

Treasury bond

New zero prices

New bond prices

New zero prices

New bond prices

8/15/2051

2.000%

30.0

100.81318

0.5490

2.009%

29.7017

16.3077

2265.81

22.4753

896.89

492.44

61647.78

611.51

0.5827

106.0196

0.5174

96.9515

Suppose your liability is $100,000,000 par of the 10-year 3%-coupon bond above.

Liab. par value

100,000,000

Construct an asset portfolio consisting of the 2-year 4.75%-coupon bond and the 30-year 0%-coupon bond with the same market value and

the same duration/dollar duration as your liability.

That is, what are the par amounts, N2 and N30, of those bonds in the asset portfolio?

N2

N30