You own a two-bond portfolio. Each has a par value of $1,000. Bond A matures in

Question

You own a two-bond portfolio. Each has a par value of $1,000. Bond A matures in five years, has a coupon rate of 8 percent, and has an annual yield to maturity of 9.20 percent. Bond B matures in fifteen years, has a coupon rate of 8 percent and has an annual yield to maturity of 9.20 percent. Both bonds pay interest semi-annually.

What is the value of your portfolio? What happens to the value of your portfolio if each yield to maturity rises by one percentage point?

B.

Rather than own a five-year bond and a fifteen-year bond, suppose you sell both of them and invest in two ten-year bonds. Each has a coupon rate of 8 percent

(semi-annual coupons) and has a yield to maturity of 9.20 percent. What is the value of your portfolio? What happens to the value of your portfolio if the yield to

maturity on the bonds rises by one percentage point?

Explanation / Answer

Part A)

To calculate the total value of the portfolio, we need to arrive at the present value of each type of bond. The present value can be calculated with the use of PV function/formula of EXCEL/Financial Calculator. The formula/function for PV is PV(Rate,Nper,PMT,FV) where Rate = Yield to Maturity, Nper = Period, PMT = 8% and FV = Face Value of Bonds

____________

Bond A:

Here, Rate = 9.20%/2, Nper = 5*2 = 10, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond A = PV(9.20%/2,10,40,1000) = $952.76

____________

Bond B:

Here, Rate = 9.20%/2, Nper = 15*2 = 30, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond B = PV(9.20%/2,30,40,1000) = $903.41

____________

Total Portfolio Value = 952.76 + 903.41 = $1,856.17

____________

When yield to maturity rises by one percentage point

Bond A:

Here, Rate = 10.20%/2, Nper = 5*2 = 10, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond A = PV(10.20%/2,10,40,1000) = $915.47

____________

Bond B:

Here, Rate = 10.20%/2, Nper = 15*2 = 30, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond B = PV(10.20%/2,30,40,1000) = $832.81

____________

Total Portfolio Value = 915.47 + 832.81 = $1,748.28

__________________________

Part B)

Here, both the bonds are of equal nature, therefore, we will perform calculation for a single bond and mutiply it by 2.

Here, Rate = 9.20%/2, Nper = 10*2 = 20, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond A and B = PV(9.20%/2,20,40,1000) = $922.62

____________

Total Portfolio Value = 922.62*2 = $1,845.24

____________

When yield to maturity rises by one percentage point

Here, Rate = 10.20%/2, Nper = 10*2 = 20, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function for PV, we get,

Value of Bond A and Bond B = PV(10.20%/2,20,40,1000) = $864.07

____________

Total Portfolio Value = 864.07*2 = $1,728.14

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