GENERALIZED BOND EQUATION

GENERALIZED BOND EQUATION Initial question: What will be the most profitable: To buy fewer high coupon bonds, or more low coupon bonds, assuming their yield, risk etc. is the aame at the time of purchase. In other words; how does an investor chose between different bonds of the same maturity,risk etc. when the yield is the same for all? Initial assumption: Buy x high coupon bonds (label I) or buy y low coupon bonds (label 2). Initially therefore the value of one holdings Is exactly equal to the value of the other holding. x.vi = y.v2 (y>x) Diestiort After n years, during which the average interest rate was equal to kav , what Is the relationship that determines the value of one holding relative to the other? The equation i/x2 AI ( 1* kav f rt X vi yix .v2 - t -h appears to describe this relationship. Here vi = Value of high couponbond after n years v2 = Value of low couponbond after n gears x = Number of high couponbonds y = Number of low couponbonds = Difference in arrual coupon income between the 2 bonds kav= Average interest rates that could have been earned on the couponpayments during the n years.(Approximation) h answer to the question therefore depends on the interest rates that Prevail on the date of sale of the holdings, and also on the interest rates axing the years the bonds were held. It is therefore not possible to select a high couponbond versus a low couponbond, unless a forecast of interest rates is also 'tact EFTA01088806 VALUE OF INVESTMENT WHEN 2000000-, INTEREST RATE IS 20% ••• 1750000 1500000 4 1250000 0 1000000 750000 500000 86 90 92 94 96 98 2... YEAR 0 10% COUPON, 1000 BONDS 0 15%COUPON 728 BONDS EFTA01088807 VALUE OF INVESTMENT WHEN 2000000 INTEREST RATE IS 10% 1750000 1500000 1250000 1000000 750000 500000 88 90 92 94 96 98 2. YEAR 0 15% COUPON 728 BONDS 10%COUPON 1000 BONDS EFTA01088808