Question

4. Your investment horizon is IH = 6 years, invest the amount of 3 000 000 CZK to be hedeed against interest rate risk having 2 zero-coupon-bonds (c=0%) A, B with the following parameters: A. FV = 1000 CZK, y = 3 %, n = 1 year; B... FV = 1000 CZK, y = 3 %, n = 7 years. One day after the relevant portfolio was built, interest rates fell by 1%: a) Build a portfolio immunized against interest rate risk - how much CZK do you investn bonds A, B? b) Calculate the future value Ve of the portfolio for the investment horizon at changed rates c) Calculate the yield Y, (p. a.) to the investment horizon under the above conditions. IH = lyears. invrest the ammnt y= % y: 3% n=7. A- Fu= 1ow cale (2/k 121 B. Fv= 1mo

. Your investment horizon is IH = 6 years, Invest the amount of 3 000 000 CZK to be hedged against interest rate risk having 2 zero-coupon-bonds (c=0%) A, B with the parameters:

A... FV = 1000 CZK, y = 3 %, n = 1 year;

B... FV = 1000 CZK, y = 3 %, n = 7 years.

One day after the relevant portfolio was built, interest rates fell by 1%:

a) Build a portfolio immunized against interest rate risk - how much CZK do you bonds A, B?

b) Calculate the future value of the portfolio for the investment horizon at changed rates

c) Calculate the yield Y. (p. a.) to the investment horizon under the above conditions .

help please.
All explanation please.
thank you.

Answer 1

Since its a zero coupon bond so there is no use of calculation of Macaulay duration.

(a) Simply we will create an immunized portfolio by allocating different percentage of amount to both the available bonds with following formula,

[X1*D1]+[X2*D2]=6(investment horizon)

X1= % of bond 1, D1 = duration of bond 1, X2 =% of bond 2, D2 = duration of bond 2

[X1*1]+[X2*7]=6

Since X1+X2=1[ we invest only in these two bonds]

X1=1-X2

[(1-X2)*1]+[X2*7]=6

by solving

X2= 0.8333

X1=0.1667

So we will allocate 83.33% fund in 2nd bond which has a duration of 7 years

and 16.67% fund in 1st bond which has a duration of 1 year.

(b) At changed rate with 1% drop in interest rates yield of bonds will also drop by 1% giving them an effective yield of 2%.

We will calculate 2% return on 16.67% fund of 3 million for 1 year[bond 1]

3000000*[16.67/100]*[2/100]*1=10002

and 2% return on 83.33% fund of 3 million for 6 years [bond 2]

3000000*[83.33/100]*[2/100]*6= 299988

Future value of fund(portfolio)= 10002+299988+3000000= 3309990

(c) Yield per annum to the investment horizon

[[309990/3000000]*100]/6=1.7221