Answer:
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%
