Financial Institutions - Chapter 9: Interest Rate Risk PT 2

Briefly explain the principles of interest rate risk

• Interest rates and prices of fixed-income assets and liabilities are inversely related. As interest rates go up, bond prices fall.

• The longer the maturity of a security, the greater the it’s sensitivity to interest rates.

• The increase in sensitivity decreases with increasing maturity.

Practice quiz question: How does an increase in interest rates affect a banks market values of assets and liabilities?

An increase in interest rates DECREASES the market value of the FI’s financial assets and liabilities

Practice quiz question: How does an increase in interest rates affect the banks market value of liabilities?

An interest rate increase benefits the bank by DECREASING the market value of their liabilities.

Why does a bond with a lower coupon rate have a higher interest rate risk?

A lower coupon bond pays smaller cash flows, so, you are waiting longer to receive most of your money back and the longer the maturity, the greater the sensitivity to changes in interest rates as stated previously.

How do you determine which bond has greater interest rate risk if the coupon rate and time to maturity isn’t a sufficient indicator?

Through measuring duration (effective maturity). The bond with the higher duration has the greater interest rate risk.

What is duration?

The time to maturity that measures the interest rate risk?

Assume you have a 6 year, 8% coupon bond with a face value of 1000 and yield to maturity of 8%. How would you determine the duration?

1. Determine the cashflows until maturity: 1000 × 0.10 = 100

2. Analyze each cashflow in isolation as a series of zero coupon bonds, through determining the present value of each.

3. Sum the PV of all cash payments

4. Multiply the year by the PV

5. Sum t*PV

6. Divide the sum by the sum of the PV of all cash payments to determine the annual duration.

Why is the duration of a coupon bond usually lower than the time-to-maturity?

This is because of the intermediary payments, as you don’t have to wait until maturity to receive cash payments as you would with a zero-coupon bond.

What does it mean if a bond has a time to maturity of 6 years but a duration of 4.99 years?

This means that it takes 4.99 years to recover the initial investment and everything after that until the 6 year mark is the interest on the bond.

What is a Consol bond?

A bond that is a perpetuity, and pays coupon payments forever. This illustrates the difference between maturity and duration. The maturity of a Consol bond is infinite but, the duration is equal to 1 + 1/R (yield to maturity).

What is a floating rate note and how is the duration determined?

A bond for which the interest is reset periodically. In this case, the duration is the time to wait until the next reset period at which time the FRN is at par.

Why is the duration for discretionary interest rate securities usually zero (demand deposits, saving deposits and notice deposits)?

Their rates can be reset immediately at the institutions discretion, so their value changes very little when markets move. In practice, their duration may be slightly above zero since repricing is not always instantaneous.

Briefly explain the properties of duration

• The longer the maturity of a bond, the longer it’s duration, all else being equal

• When interest rates increase, the duration of a coupon bond falls, all else being equal.

• The higher the coupon the shorter the duration, all else being equal

• Duration is additive. The duration of a portfolio is the weighted average of the duration of the individual securities with the weights reflecting the proportion of the portfolio invested in each

What is the economic explanation for duration?

Interest elasticity of the securities price to small interest rate changes. The formula used to demonstrate this is:

• Change in price = -D (change R/1+R)

When the maturity of a coupon bond increases, its duration increases

What is the leverage adjusted duration gap?

The duration of assets - k duration of liabilities. K is the leverage factor.

How do you ensure there is no change in equity following a change in interest rates?

By putting the duration gap equal to 0, the change in equity will be 0 regardless of the change in interest rates.

What is immunization?

A strategy used to protect a portfolio from interest rate risk by matching the duration of assets and liabilities. To do so, invest in a bond equal to the investment horizon.

How do you solve for immunization?

• Determine the cash flows for each year

• Determine the FV of each cashflow

• Determine the PV of the CF after 5 years by discounting the PV of year 6 CF.

• Sum the price and the total FV of all cash payments to get the total future cash flows

How does a change in interest rates affect PV and FV’s

As interest rates increase PV falls because cash flows are discounted more heavily so money received in the future is less worthy today. FV increases because money grows faster overtime through compounding.

Briefly explain the weakness of duration

• Cost: It may be costly to restructure the balance sheet of the whole bank, to equate DA and kDL

• Dynamics: Duration changes as the time changes. Immunization requires a continuous re-balance of the portfolio to ensure the duration matches the investment horizon

• Large interest rate changes: Duration assumes a linear relationship between bond prices and interest rates, while the true relationship is curved. For large changes convexity must be considered

• Parallel shifts in the yield curve: With using the duration model, we assume the yield curve is flat as we have the same change on assets and liabilities

• Default risk: We assume no delay or default in payment of cashflows

• Embedded options: Duration doesn’t account for prepayment options