Respuesta :
Answer:
From the below calculations, the change in value of both portfolios is 0.60%
I first of all, determine the present value of both portfolios,incorporate increase of 10 basis points,then compared the change in values.
Explanation:
The applicable formula in this scenario is given FV=PV*e^(r*N)
FV is the future value is the bonds' face value repayable on redemption
PV is our unknown
e has a constant value of 2.7182818
r is the yield given as 10%
N is the number of years the investment will last
Using the formula above the present value of each portfolio can be determined.
The formula can be rewritten as PV=FV*e^-(r*N)
PV of portfolio A=20*e^-(10%*1)+60*e^-(10%*10)
=(20*2.7182818^-10%)+(60*2.7182818^-100%)
=$40.17 million
A 10 basis points increase which is 0.1% ,in yield will give the below present value of portfolio A:
PV of portfolio A=20*2.7182818^-(10.1%*1)+60*2.7182818^-(10.1%*10)
=(20*2.7182818^-10.1%)+(60*2.7172818^-101%)
=$39.93 million
Hence percentage change in the value of portfolio A is given below:
percentage change=(40.17 -39.93)/40.17
=0.60%
The present value of portfolio using yield of 10% and 10.1% van also be determined in the same manner
PV of portfolio B=50*2.7182818^-(10%*5.95)
=50*2.712818^-59.5%
=$27.58 million
With a yield of 10.1%
PV of portfolio B=50*2.7182818^-(10.1%*5.95)
=50*2.7182818^-60.095 %
=$27.41 million
percentage change in portfolio B=(27.58-27.41)/27.58
=0.60%
