An investment fund contains the following 3 fixed-rate government bonds:

Bond A Bond B Bond C

Par value $20,000,000 $20,000,000 $40,000,000

Coupon rate 7.0% 9.0% 6.0%

Time-to-maturity 3 years 5 years 7 years

Yield-to-maturity 7.21% 7.45% 7.71%

Market value (USD) 19,888,485 21,274,578 36,352,583

Macaulay duration 2.757 4.165 5.748

Each bond is on a coupon date so that there is no accrued interest.

The market values are the full prices given the par value.

Coupons on all 3 bonds are paid semiannually.

The yields-to-maturity are stated on a semiannual bond basis.

The Macaulay durations are annualized.

a) Calculate the portfolio's (annual) modified duration using shares of market values as weights.

b) Estimate the percentage loss in the portfolio's market value if the (annual) yield-to-maturity on each bond goes up by 30 bps.