The following data are available for three bonds A, B and C. These bonds are used by a bond portfolio manager to fund an outflow scheduled in 6…

(i) Calculation of Bond Duration Bond A Year Cash flow P.V. @ 9% Proportion of bond value Proportion of bond value x time (years) 1 10 0.917 9.17 0.086 0.086 2 10 0.842 8.42 0.079 0.158 3 10 0.772 7.72 0.073 0.219 4 10 0.708 7.08 0.067 0.268 5 10 0.650 6.50 0.061 0.305 6 10 0.596 5.96 0.056 0.336 7 10 0.547 5.47 0.051 0.357 8 10 0.502 5.02 0.047 0.376 9 10 0.460 4.60 0.043 0.387 10 110 0.4224 46.46 0.437 4.370 106.40 1.000 6.862 Duration of the bond is 6.862 years or 6.86 year. Bond B Year Cash flow P.V. @ 9% Proportion of bond value Proportion of bond value x time (years) 1 11 0.917 10.087 0.091 0.091 2 11 0.842 9.262 0.083 0.166 3 11 0.772 8.492 0.076 0.228 4 11 0.708 7.788 0.070 0.280 5 11 0.650 7.150 0.064 0.320 6 11 0.596 6.556 0.059 0.354 7 11 0.547 6.017 0.054 0.378 8 111 0.502 55.772 0.502 4.016 111.224 1.000 5.833 Duration of the bond B is 5.833 years or 5.84 years. Bond C Year Cash flow P.V. @ 9% Proportion of bond value Proportion of bond value x time (years) 1 9 0.917 8.253 0.082 0.082 2 9 0.842 7.578 0.076 0.152 3 9 0.772 6.948 0.069 0.207 4 9 0.708 6.372 0.064 0.256 5 109 0.650 70.850 0.709 3.545 100.00 1.000 4.242 Duration of the bond C is 4.242 years or 4.24 years. (ii) Amount of Investment required in Bond B and C Period required to be immunized = 6.000 Year Less: Period covered from Bond A = 3.087 Year To be immunized from B and C = 2.913 Year Let proportion of investment in Bond B and C is b and c respectively then b + c = 0.55 (1) 5.883b + 4.242c = 2.913 (2) On solving these equations, the value of b and c comes 0.3534 or 0.3621 and 0.1966 or 0.1879 respectively and accordingly, the % of investment of B and C is 35.34% or 36.21% and 19.66 % or 18.79% respectively. (iii) With revised yield the Revised Duration of Bond stands 0.45 x 7.15 + 0.36 x 6.03 + 0.19 x 4.27 = 6.20 year No portfolio is not immunized as the duration of the portfolio has been increased from 6 years to 6.20 years. (iv) New percentage of B and C bonds that are needed to immunize the portfolio. Period required to be immunized = 6.0000 Year Less: Period covered from Bond A = 3.2175 Year To be immunized from B and C = 2.7825 Year Let proportion of investment in Bond B and C is b and c respectively, then b + c = 0.55 6.03b + 4.27c = 2.7825 b = 0.2466 On solving these equations, the value of b and c comes 0.2466 and 0.3034 respectively and accordingly, the % of investment of B and C is 24.66% or 25% and 30.34 % or 30.00% respectively.