An investment fund owns the following portfolio of three fixed-rate government bonds:

The total market value of the portfolio is EUR96,437,017. 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 are paid semiannually. The yields-to-maturity are stated on a semiannual bond basis, meaning an annual rate for a periodicity of 2. The Macaulay durations are annualized.

Calculate the average (annual) modified duration for the portfolio using the shares of market value as the weights.

Transcribed Image Text:

Par value Coupon rate Time-to-maturity Yield-to-maturity Market value Macaulay duration Bond A EUR25,000,000 9% 6 years 9.10% EUR24,886,343 4.761 Bond B EUR25,000,000 11% 8 years 9.38% EUR27,243,887 5.633 Bond C EUR50,000,000 8% 12 years 9.62% EUR44,306,787 7.652