Question

In: Statistics and Probability

A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with term...

  1. A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with term of 1 year and 4 years are available for investment. The effective rate of interest is 7.5%.

    1. (a) How much of each bond should the company buy in order to achieve full immunization?

    2. (b) Show empirically that immunization has been achieved even for large changes in the interest rate. Take as an example a decrease in the interest rate to 0% and an increase to 100%.

Solutions

Expert Solution

Solution:

A)

To immunize against interest rate fluctuation risk, company has to invest in bond or bond portfolio, so that duration of bond or bond portfolio is equal to the investment horizon i.e. 2 years in this case.

A zero coupon bond always has a duration equal to its maturity.

Hence the duration of one year term zero coupon bond would be 1 year and the duration of four year term zero coupon bond would be 4 years.

But the company investment horizon is 2 years. So, we have to invest in 1 year and 4 year term zero coupon bonds in such a proportion that the total duration of the bond portfolio would be 2 years.

Let us assume that to maintain portfolio duration of 2 years, the proportion of total fund to be invested in one year term bond be p and in four year term bond be 1-p.

So, we can write the following:

(p*1)+[(1-p)*4]=2

Therefore p=0.67

It means, to maintain the portfolio duration of 2 years, 67% sould be invested in 1 year term bond and 33% sould be invested in 4 year term bond.

Total amount to be invested= $1,000/1.075*1/1.075= $865

Investment to be made in 1 year term bond = $865*67%= $579.55

Investment to be made in 4 year term bond = $865*33%= $285.45

It means to immunize the company should buy $579.55 of 1 year term bond and $285.45 of 4 year yerm bond.

I am giving answer to only fist part .

Please post b) as new question ..


Related Solutions

A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with term...
A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with term of 1 year and 4 years are available for investment. The effective rate of interest is 7.5%. (b) Show empirically that immunization has been achieved even for large changes in the interest rate. Take as an example a decrease in the interest rate to 0% and an increase to 100%.
A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with terms...
A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with terms of 1 year and 4 years are available for investment. The effective rate of interest is 7.5%. How much of each bond should the company buy in order to achieve full immunization?
Consider a zero-coupon bond maturing in 2 years with a face value of $1,000 and a...
Consider a zero-coupon bond maturing in 2 years with a face value of $1,000 and a yield to maturity of 2%. Assume the recovery rate is 40%, and that default can only happen exactly at the end of the 2-year period. There is a credit default swap (CDS) available for this bond, and the premium is 0.8%. For both a bondholder and a CDS buyer (with notional value $1,000), compute the cash flows two years from today in the case...
ABC's bonds will be maturing in 8 ​years, pay 8 percent coupon rate on the $1,000...
ABC's bonds will be maturing in 8 ​years, pay 8 percent coupon rate on the $1,000 par value. a. The value of the bond is ​$________​, if the coupon is paid semiannually.  ​(Round to the nearest​ cent.) b. The value of the bond is ​$________​, if the coupon is paid​ annually.
(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for...
(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for $527.82. What is its yield to maturity? Assume annual compounding. Record your answer to the nearest 0.01% (no % symbol). E.g., if your answer is 3.455%, record it as 3.46.
Your company has a $125,000 liability it must pay 4 years from today. The company is...
Your company has a $125,000 liability it must pay 4 years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $13,000 a year for the next 4 years, starting one year from today. The savings account pays a return of 8.00% compounded monthly. solve for the value Question 8 options: $43,284...
At maturity, each of the following zero coupon bonds (pure discount bonds) will be worth $1,000....
At maturity, each of the following zero coupon bonds (pure discount bonds) will be worth $1,000. For each bond, fill in the missing quantity in the following table. Assume semi-annual compounding. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answers to 2 decimal places, e.g. 15.25 or 15.25%.) Price Maturity (years) Yield to maturity A $445 8 ??? % B $405 ??? 7 % C ??? 15 11 %
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A 1 7.25 % B 2 8.25 C 3 8.75 D 4 9.25 a. According to the expectations hypothesis, what is the market’s expectation of the one-year interest rate three years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What are the expected values of next year’s yields on bonds with maturities of (a) 1 year; (b) 2...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A 1 8.50 % B 2 9.50 C 3 10.00 D 4 10.50 a. According to the expectations hypothesis, what is the market’s expectation of the one-year interest rate three years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What are the expected values of next year’s yields on bonds with maturities of (a) 1 year; (b) 2...
Blackwell, Inc. has a $72,000 liability it must pay three years from today. The company is...
Blackwell, Inc. has a $72,000 liability it must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $16,000 each year for the next three years, starting one year from today. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT