Market participants frequently use the concept of duration to immunized portfolios. Since many institutional investors have liabilities that must be met on schedule with the proceeds of a bond portfolio, immunization attempts to ensure that regardless of what happens to interest rate levels between the present and the due date of one’s liabilities, enough cash will be available to meet them.
Duration allows investment managers to construct a portfolio that immunizes a fixed-income portfolio against liability streams. Bond immunization, using duration as a tool, is a financial technique employed to protect a series of future cash flow requirements funded by a fixed-income portfolio from interest rate changes.
For example, a fund manager may have a liability at a known future date for which he wants to have sufficient funds. He wants to buy a bond today to cover this future liability without having to worry about inevitable changes in interest rates. That is, he wants to make immune his future liability from interest rates. By buying a bond with a duration equal to his investment horizon, the future liability will be covered mostly by the bond for a range of interest rate environments.
To understand how duration works, one must first understand market risk and reinvestment risk.
Market Risk
Market risk, also called price risk, measures the price sensitivity of a bond with respect to changes in interest rates. When interest rates rise, the price of the bond falls; when interest rates fall, the price of the bond rises. The change in price due to a change in interest rate levels is called market risk. Market risk has an immediate impact on the price of the bond when interest rates change.
Reinvestment Risk
A bondholder receives periodic coupon payments from his investments. These coupon payments can be reinvested to earn additional income. Assuming the bondholder keeps the bond until he sells it at his investment horizon, he would receive the following cash flows: (1) the price plus accrued interest from the buyer of the bond at the horizon date, (2) all the coupon payments he received since he purchased the bond, and (3) the interest on interest he received from reinvesting his coupon payments.
The first cash flow component is market risk. Interest rate changes directly affect the price of the bond. The second cash flow component, the coupon payments, is fixed. That is why bonds are called fixed-income securities. The coupon payment is known; and therefore, its cash flow is not affected by changes in interest rates. The last cash flow component, interest on interest, is reinvestment risk. It is affected by changes in interest rates.
When interest rates rise, the reinvestment income is higher. When interest rates fall, the reinvestment income is lower. Therefore, when general levels of interest rates change, they affect both market risk, the price of the bond, and reinvestment risk, the future income derived from reinvesting coupon payments. Reinvestment risk affects investments in the long term.
The interesting thing about market risk and reinvestment risk is that they tend to offset each other. When interest rates rise, bond prices fall but reinvestment income increases. When interest rates fall, bond prices rise but reinvestment income falls.
From the previous section we know that market risk and reinvestment risk tend to offset each other when interest rate levels change. If the investment horizon is equal to the duration of the bond, the market risk is equal to the reinvestment risk.
This is the special property of duration. With an investment horizon equal to the duration, the return on the investment to the horizon date will remain relatively constant for various interest rate scenarios. The change in the price of the bond is offset by the change in the reinvestment income. Therefore, the total return to the horizon date is the same. Duration is a powerful tool for an investment manager to buy a bond to protect a future liability with a fair degree of immunization from interest rate movements.
Risk Profile
Value Date Duration Maturity
| Increasing | Increasing |
| <-- Market Risk | Reinvestment Risk --> |
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Market risk is greatest if the investment horizon is close to the current valuation date. If you are planning to sell the bond tomorrow, you are not concerned about reinvestment income; however, you are concerned if rates rise considerably between today and tomorrow as your bond will tank (drop rapidly in price). Traders that are in and out of the markets for short periods of time are much more concerned about market risk.
Reinvestment risk is greatest if the investment horizon is at maturity. The compounding effect of reinvested coupons is very significant. If the bond is being held to maturity, there is no market risk. The bond at maturity will return a 100% face value. If interest rates rise or fall, the bond will still return face value at maturity - no more, no less.
At an investment horizon equal to duration, the market risk is equal to the reinvestment risk. They cancel each other out. By using duration, portfolios can be structured to fully defend a future series of cash flows, which is called bond immunization.
Rebalancing a Portfolio
Investment managers must periodically reevaluate the duration of their portfolios for several reasons. First, as time passes, a bond’s duration decreases. Secondly, duration is also affected by large price changes. Thus, even though a dedicated bond portfolio may have immunized cash flow liabilities, the investment manager must reevaluate it regularly. Changes in assumptions or liability streams will also affect the portfolio. Adjustments may be necessary to actively manage the portfolio. That is, the portfolio must be rebalanced to match the investment objectives.