# A financial institution has the following liabilities which it is trying to immunize against a change in interest rates (all are priced to yield 8%): 5-year (annual payments) 8% coupon bonds with a total par value of $38 million. Three payments of $24 million, each one due at the end of the next three years. 12-year (annual payments) 12% coupon bonds with a total par value of $20 million.

**QUESTION**

Discusion

A financial institution has the following liabilities which it is trying to immunize against a change in interest rates (all are priced to yield 8%):

- 5-year (annual payments) 8% coupon bonds with a total par value of $38 million.
- Three payments of $24 million, each one due at the end of the next three years.
- 12-year (annual payments) 12% coupon bonds with a total par value of $20 million.

Available for the purpose of immunization each year are a 1-year zero coupon bond (a rolling issue, new ones each year) and consol (perpetual) bonds with a 11% coupon, both yielding 10% to maturity. Assuming that you re-balance the portfolio each year immediately after any payments are made, what is the dollar amount of each hedging instrument you will hold at t=0 and t=1 to completely neutralize the institution’s exposure to interest rate changes over the coming year?

**ANSWER**

** Interest Rate Immunization Strategy for a Financial Institution: A Comprehensive Analysis**

**Introduction**

In the realm of finance, managing interest rate risk is of utmost importance for financial institutions. The concept of immunization provides a mechanism to neutralize the impact of interest rate changes on a portfolio. In this essay, we will explore the immunization strategy for a financial institution facing interest rate risk and seeking to hedge its liabilities effectively.

**Understanding the Liabilities**

The financial institution in question has three main liabilities that it aims to immunize against interest rate fluctuations. These liabilities include:

5-year (annual payments) 8% coupon bonds with a total par value of $38 million.

Three payments of $24 million, each due at the end of the next three years.

12-year (annual payments) 12% coupon bonds with a total par value of $20 million.

To achieve interest rate neutrality, the institution must ensure that its assets’ value matches its liabilities’ present value.

**Hedging Instruments**

The financial institution has two hedging instruments available for immunization purposes:

1-year zero coupon bonds (a rolling issue, new ones each year).

Consol (perpetual) bonds with an 11% coupon, yielding 10% to maturity.

**Immunization Strategy**

To completely neutralize the institution’s exposure to interest rate changes over the coming year, we need to construct a portfolio that aligns the duration of the assets with the duration of the liabilities.

At t=0:

At the beginning of the strategy, the financial institution should analyze the present value of its liabilities and determine the required hedging instruments. Let’s break down the calculation:

a) 5-year 8% coupon bonds:

The present value of the liability can be calculated using the following formula:

PV = Coupon Payment × [1 – (1 + r)^(-n)] / r + Face Value / (1 + r)^n

where r is the discount rate and n is the number of years.

Using this formula, the present value of the 5-year 8% coupon bonds is calculated as follows:

PV = $38,000,000 × [1 – (1 + 0.08)^(-5)] / 0.08 + $38,000,000 / (1 + 0.08)^5

b) Three payments of $24 million due at the end of the next three years:

These payments need to be discounted to their present value using the appropriate discount rate for each year.

c) 12-year 12% coupon bonds:

Similarly, we calculate the present value of the 12-year 12% coupon bonds using the discount rate.

Once the present value of the liabilities is determined, the financial institution can decide on the allocation of hedging instruments.

At t=1:

After one year has passed, the financial institution must re-balance its portfolio to maintain interest rate neutrality. This involves recalculating the present value of the liabilities and adjusting the allocation of hedging instruments accordingly.

**Conclusion**

Interest rate immunization is a crucial risk management strategy for financial institutions. By constructing a portfolio that aligns the duration of assets with liabilities, institutions can minimize their exposure to interest rate fluctuations. In this essay, we discussed the liabilities of a financial institution and the available hedging instruments to neutralize interest rate risk. However, for a comprehensive analysis and accurate results, detailed calculations and continuous monitoring are essential.

By implementing an effective immunization strategy, financial institutions can protect themselves against adverse interest rate movements and enhance their overall financial stability.

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