You are considering the following two strategies for investing in zero-coupon Treasuries with a target (modified) duration of 15 years:

a. Strategy 1: investing $10M in a 15-year ZCB with a modified duration of 14.55.

b. Strategy II: investing $5M in a 5-year ZCB with a modified duration of 4.93 and another $5M in a 25-year ZCB with a modified duration of 23.81.

What will be the percentage change in the market value of your portfolio under each strategy if interest rates shift as follows immediately following your investment? (for strategy II, take a weighted average of the percentage changes at both ends)

Maturity Change

5 -75bps

15 +25bps

25 +50bps

Solutions

Expert Solution

For strategy 1 , % change in market value of portfolio

= -( 0.25% *14.55)

= -3.6375%

For strategy 2 ,

% change in 5 year ZCB

= -( -0.75% *4.93)

= 3.6975%

and

% change in 25 year ZCB

= -( 0.50% *23.81)

= -11.905%

So, Weighted Average % change in portfolio = (3.6975%-11.905%)/2

= -4.10375%

So, Weighted Average % change in portfolio is-4.10375%

Junaid answered 1 year ago

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