Ch. 9 Risk Management Review

What is a consol bond?

A consol bond is a bond that pays a fixed coupon each year forever. The formula for a Consol Bond's duration is D = 1 + 1/R

Why is it critical for an FI manager who has a portfolio immunized to match a desired investment horizon to rebalance the porfolio periodically.

Assets approach maturity at different rates of speed than the duration of the same assets approaches zero. After a period of time, a portfolio of assets that was immunized against interest rate risk will no longer be immunized. Portfolio duration will exceed the remaining time in the investment or target horizon, and changes in interest rates could prove costly to the institution.

What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the two methods? What is marking to market?

Book value accounting reports assets and liabilities at their original issue value. Market value accounting reports assets and liabilities at their current market values. If assets and liabilities are held to maturity, interest rate changes do not affect the valuation of the FI. If deposits or loans have to be refinanced, then market value accounting presents a better picture of the condition of the FI. Marking to market is the process by which changes in economic value of assets and liabilities are accounted.

What is convexity? Why is it a desirable feature to capture in portfolio of assets?

Convexity is a property of fixed-rate assets that reflects non-linearity in the reflection of price-yield relationships. The more convex is a given asset, the more insurance against interest rate changes is purchased.

What is dollar duration? How is dollar duration different from duration?

Dollar duration is the duration times the price of the asset and can tell you the dollar change in value for a 100 basis point shift. Dollar duration is the modified duration times price

How is duration related to the interest elasticity of a fixed-income security? What is the relationship between duration and the price of the fixed-income security?

Duration is related to the interest elasticity in that it is the first derivative of the price function with respect to rate changes (change in price for a given change in R/(1+R)). The higher the duration, the more rate sensitive an asset tends to be. The relationship between duration and price is through interest. If interest rates are high, price is low, and duration is shorter.

In general, what changes have occurred in the financial markets that would allow financial institutions to restructure their balance sheets more rapidly and efficiently to meet desired goals?

Growth of purchased funds markets, asset securitization, and loan sales markets have considerable increased the speed of major balance sheet restructurings. As these markets develop, cost of transactions has also decreased. Growth and development of derivative securities markets provides significant alternatives to managing risk.

What will happen to the realized return if interest rates decrease? Explain.

If interest rates decrease, the realized yield on the bond will be less than the expected yield because the decrease in reinvestment earnings will be greater than the gain in bond value.

Assume that a goal of the regulatory agencies of financial institutions is to immunize the ratio of equity to total assets (change in equity/assets = 0). Explain how this goal changes the desired duration gap for the institution. Why does this differ from the duration gap necessary to immunize the total equity?

In this case, the duration of the assets and liabilities should be equal. If change in equity = change in assets, then the leveraged adjusted duration gap is positive, since change in equity would exceed k change in assets by the amount (1-k).

What are the principles of interest rate-price relationships for fixed-rate financial assets?

Rule 1: Interest rates and price of fixed-rate assets move inversely Rule 2: The longer the maturity of a fixed-income financial asset, the greater is the change in price for a given change in interest rates Rule 3. The change in value of longer-term fixed-rate financial assets increases at a decreasing rate Rule 4. For a given percentage change in interest rates, the increase in price for a decrease in rates is greater than the decrease in value for an increase in rates.

What are the two different general interpretations of the concept of duration and what is the technical definition of this term? How does duration differ from maturity?

Since Duration measures the weighted-average life of an asset/liability in economic it has economic meaning as the interest rate sensitivity (interest elasticity) of an asset's value to change in the interest rate. Duration takes into account the time of arrival and the rate of reinvestment of all cash flows during the assets life. Technically, Duration can be considered the weighted average time to maturity using the relative present values of cash flows as weights.

Consider the case in which an investor holds a bond for a period of time longer than the duration of the bond, that is, longer than the original investment horizon. If interest rates rise, will the return that is earned exceed or fall short of the original required rate of return? Explain.

The actual return earned will exceed the yield expected at the time of purchase since the benefits from higher reinvestment rates would exceed the price reduction effect if the investor holds the bond for a sufficient length of time.

If an FI uses only duration to immunize its portfolio, what three factors affect changes in the net worth of the FI when interest rates change?

The three factors are: 1. The leverage adjusted duration gap [D(A)-D(L)k] (greater the gap, the more exposed the FI is to changes in interest rates) 2. A or the size of the FI, the larger A is, the larger is the shock, the larger is the interest rate risk exposure 3. Interest rate shock - the larger the shock, the larger the interest rate exposure

Identify and discuss three criticisms of using the duration gap model to immunize the portfolio of a financial institution.

Three Criticisms are: 1. Immunization is a dynamic problem because duration changes over time. It is therefore necessary to rebalance the portfolio as the duration of the assets and liabilities changes over time. 2. Duration matching can be costly because it is not easy to restructure the balance sheet periodically, especially for large FIs 3. Duration is not an appropriate tool for immunizing portfolios when the expected interest rate changes are large because of the existence of convexity. Convexity exists because the relationship between security price changes and interest rate changes is not linear.