Question

Suppose a financial institution currently has a positive duration gap. How would its net worth be expected to vary with changes in interest rates? Explain. Explain how a financial institution could “immunize” its net worth from changes in interest rates.

Answer 1

Let's firs understand the duration gap before getting into this question:

Duration gap = Duration of assets - market value of liabilities / market value of assets x Duration of liabilities

If a financial institution has a positive duration gap, that means duration of assets > duration of liabilities. This further means (rate sensitive) assets are more sensitive to changes in interest rate than liabilities are.

Thus if interest rate rises:

• Market value of assets will fall more sharply than that of liabilities
• Hence, equity value will decline

If interest rate decreases

• Market value of assets will increase more sharply than that of liabilities
• Hence, equity value will increase

Immunization of net worth:

• Adjust the asset and liabilities such that Duration gap is zero.
• Increase the duration of the liabilities to match with that of the assets