You own a two-bond portfolio. Each has a par value of $1000. Bond A matures in 5 years, has a coupon rate of 8 percent, and has an annual yield to maturity of 9.20 percent. Bond B matures in 15 years, has a coupon rate of 8 percent and has an annual yield to maturity of 8.20 percent. Both bonds pay interest semiannually. (a) What is the value of your portfolio?(b) If each yield to maturity rises by one percentage point, then the value of your portfolio is $1,748.28. True or False?

True, The Value of the portfolio is $ 1748.28 , there is a reduction in value of portfolio due to increase in YTM rate.

Explanation:

Solution

Given that:

For Bond A

The Maturity period (n) = 5 years

The Coupon rate = 8% (coupon rate is paid semiannually)

Then,

The total semiannual period is 10.

YTM = R = 9.2%

Par value = $1000

So,

The Current price of the bond = Present value of all coupon cash flows + Present value of the bond at maturity

The Current price of the bond = 40*(1-1/(1+R/2)^10)/(R/2) + 1000/(1+R/2)^10

The Current price of the bond =40*(1-1/1.046^10)/.046 + 1000/1.046^10 = $952.756

For Bond B

The Maturity period (n) = 15 years

The Coupon rate = 8% (coupon rate is paid semiannually)

Then,

The total semiannual period is 30.

Thus,

YTM = R = 9.2%

Par value = $1000

So,

The Current price of the bond = Present value of all coupon cash flows + Present value of the bond at maturity

The Current price of the bond = 40*(1-1/(1+R/2)^30)/(R/2) + 1000/(1+R/2)^30

The Current price of the bond =40*(1-1/1.046^30)/.046 + 1000/1.046^30 = $903.406

Now,

The value of portfolio = $952.756+$903.406 = $1856.16 approx.

Thus,

If each yield to maturity increases by 1% point

Then,

YTM = 10.2%

The half yearly rate is 5.1%

The Current price of the bond A =40*(1-1/1.051^10)/.051 + 1000/1.051^10 = $915.48

The Current price of the bond B =40*(1-1/1.051^30)/.051 + 1000/1.051^30 = $832.82

This scenario changes to:

The Value of the portfolio = $915.48+ $832.82 = $ 1748.28

so, there is a reduction in value of portfolio due to increase in YTM rate.

The percentage decrease in value of portfolio = (1748.28 - 1856.16)/ 1856.16 = -5.81%

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