Question

10

Tou have access to the following 3 $1000 par bonds: Dond I costs $1000 and has an 8% coupon rate until maturity in 2 years. Bond 2 costs $980 and pays a 7% coupon rate until it matures i Bond 3 costs $1020 and pays a 10% coupon rate until it matures in 2 years. Assume annual coupon payments. Find a portfolio combination of bond 1 and bond 2 that produces the same cash flows as that of bond 3. (You do not have to use Gauss Newton.) Which is cheaper: bond 3 or the portfolio?

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Answer 1

Current Price of bond =

Bond 1=Cost $1000 with Yield of $160(8%) for 2 year at ROI of 8%.

Bond 2=Cost $980 with Face Value of $1000 with Yield of $70(7%) for 1 year at ROI of 9.184%.

Bond 3=Cost $1020 with Face Value of $1000 with Yield of $200(10%) for 2 year at ROI of 8.865 %

$\dpi{100} \small ROI=\frac{Yield}{Cost of Bond}$

Portfolio Combination of Bond 1 & 2

Return on Respective Bonds if Investment Ratio 20:80.

$ 200 Bond 1 at 7% will yeild $14/Year +$800 Bond 1 at 9.184% will yield $73.472 Year.T

Total Yield per year=87.472.

Cost of Combined Bond=$984.

Combined ROI=8.95%

There fore Portfolio combination of Bond 1 & 2 will be the cheaper buy over the Bond 3.