The Risk Point Method

Ravi E. Dattatreya, senior vice president at Sumitomo Bank Capital Markets, explains a new method for assessing and managing yield curve risk.

Duration is a popular tool employed by sophisticated users for interest rate risk measurement. By effectively using it, an institution can all but eliminate basic market risk. Among the other types of interest rate risk, we focus on yield curve risk, which has attained importance recently. To model yield curve risk, we use a form of price sensitivity relative to a specific hedge instrument. This number, called the risk point, helps us use a variety of hedge instruments to better handle yield curve risk.

It is appropriate to look at the risk point concept as a more complete description of risk than just as a way to handle yield curve risk. This view is supported by the fact that the risk point method is useful in several situations. It can accurately highlight yield curve risk in an asset/liability context. In portfolio management it can help evaluate bond swap opportunities more precisely. It can help create more robust immunization strategies. And it also provides more insight into the current crop of exotic investments.

Several years of use of the duration concept has imparted the ability to most financial institutions to virtually eliminate market risk via prudent hedging activities. As a result of this, other residual risks have gained prominence. The most important of these, yield curve risk, deserves a detailed treatment. In particular, yield curve risk can be significant in portfolios containing options, some mortgage derivatives and most exotic securities.

Basis risk

As usually stated, duration of a fixed income asset (or liability) is the price sensitivity relative to its own yield. Therefore, when we use duration for hedging purposes, we are implicitly assuming that the yield levels of the various assets and liabilities move in parallel, that is, in equal amounts. In fact, however, different credit, coupon or maturity sectors of the market move differently in terms of their yield. This difference is known as the basis risk among the sectors.

In general, basis risk is difficult to measure and hedge. Most hedging vehicles address market risk, that is, changes in the Treasury rates, not basis risk. It is possible to take the view that only market risk is hedgeable and treat basis risk as a prudent business risk that an institution has to take. This is the only approach in dealing with certain types of basis risk, like credit risk.

Asset/liability matching

One method is to divide assets and liabilities into smaller maturity baskets and analyze each basket separately. If each basket covers a sufficiently small maturity range, then we can assume that the yield curve risk is acceptably small within that range. In a hedging application, we would use hedging instruments suitable for that maturity range to match dollar durations. In an asset/liability context, if each basket or sector is matched, using appropriate hedges as required, then the assets and liabilities are matched as a whole because of the additivity property of dollar duration.

There is a problem, however. It turns out that an asset of a given maturity might react to changes in rates in another maturity. Consider, for example, a 10-year bond with a coupon of 10 percent. The cash flow from this bond occurs every six months throughout its life. Since the value of a bond is simply the sum of the present values of the individual cash flows, it stands to reason that the value of the 10-year bond could be influenced by rate changes not just in the 10-year maturity, but also in all shorter maturities representing the cash flows. Therefore, we need to do more than simply group the assets and liabilities in maturity sectors.

The cash flow approach

One way to handle this problem is to first break down each asset and liability into its cash flow components. Then the individual cash flows can be grouped into maturity buckets. Now, the price sensitivity of each sector is more clearly defined, at least with respect to spot rates corresponding to each sector.

The cash flow approach provides very valuable insight into the relative natures of the assets and the liabilities. However, it represents risk in terms of spot rate, that is, in terms of zero-coupon bonds, which are rarely used for hedging. A more sophisticated approach is the risk point method, discussed below.

The risk point method

Since risk is a measure of change in value, it stands to reason that risk management and security valuation ought to be closely related. Therefore, it is advantageous to use a model that integrates these two aspects. The risk point method attempts such integration. It also has the practical advantage that it measures risk relative to available hedging instruments.

We define the risk point of a security or portfolio with reference to a specific hedge instrument. For this reason, it can also be called relative dollar duration. It represents the change in the value of the security or portfolio due to a one-basis-point change in the yield of the hedge. If we divide the risk point by the dollar duration of the hedge, we get the dollar amount of the hedge instrument to be used as a hedge. This hedge amount will protect the portfolio against risk from small changes in the market sector represented by the hedge instrument.

Unlike dollar duration, which measures the total interest rate risk, the risk point measures only one component of the total risk. This component represents the risk due to a change in rates in a given maturity sector. Thus, to determine a complete risk or hedge, we need a full set of risk points relative to a set of hedge instruments. From this set of risk points we can determine the portfolio of hedge instruments that will hedge a given portfolio.

The risk point method consists of three main steps:

(1) We first list the hedge vehicles that we are willing to use.

(2) We then apply a model that values the assets and liabilities relative to the prices of the hedge vehicles.

(3) We change the yield or price of one of the hedge instruments by a small amount, keeping all other yields and prices the same. With the new yield we revalue the portfolio again. The change in its value (expressed as dollars per one-basis-point change) is the risk point of the portfolio. We get the amount of the hedge instrument needed for hedging by simply equating the dollar duration of the hedge to the risk point of the portfolio.

Applications for the risk point method

The risk point method can be used wherever other simple measures such as duration are currently being used.

Hedging

This is the most common use of duration, and therefore, of risk points. Common duration analysis not only gives us just a crude approximation for the hedge, but also fails to provide critical information as to which hedge instruments are optimal to use. On the other hand, the risk point method correctly identifies the major risks in a portfolio and directly generates the portfolio of hedge instruments best suited for the hedging task. Since the starting point for the risk point method is the selection of hedge instruments, we have full control over which hedge instruments will be considered for hedging from the outset.

The par amount of any hedge instrument required to hedge a portfolio can be determined by dividing the risk point of the portfolio by the dollar duration of the hedge instrument.

Indexing

As a structured portfolio methodology, indexing is quite common. Indexing requires one to manage a portfolio in such a way that the returns from the portfolio track that from a given bond index, for instance, various Lehman Brothers indexes or the Merrill Lynch Government Bond Index. A common technique is to purchase, as far as possible, the same bonds as in the index in the same proportions. The effectiveness of this technique is limited because indexes almost always have too many bonds in them and most of these are not available at fair prices in the quantities required. An alternative is to manage the portfolio duration to match the published duration of the index as closely as possible. This technique allows the manager to pick bonds that are relatively cheap for the portfolio.

A portfolio manager is running an indexed fund tied to an index with a duration of five years. Given the bearish mood of the market, the manager decides to keep the duration of the fund short, at four-and-a-half years. Rates do climb. However, the manager finds that the fund has barely kept up with the index, and has not outperformed the index as expected. Further analysis reveals that the yield curve has steepened as the rates rose. The fund holds a relatively large amount of 10-year bonds which have suffered a loss. Thus duration matching in normal situations, and using a shorter duration in a bearish market, provide no guarantee that expected results will be obtained. The reason is that duration is an oversimplification.

A superior way to index is first to determine the full risk-point profile of the index and then manage the fund against this profile as a guide. Then the manager will know what types of yield curve bets are implied in the fund's portfolio.

Immunization and dedication

Another popular application of duration is in immunization. If we are managing a portfolio in order to meet a specific liability in the future, immunization calls for balancing the portfolio so the duration of the portfolio equals the duration of the liability. This procedure is a based on a parallel shift assumption for yield curve moves. Therefore, it is subject to the same types of surprises suffered by the index fund manager above.

A more robust approach is to determine the risk point profile of the liability and match this to the risk profile of the portfolio. In this sense, immunization is not much different from index fund management. In dedicated portfolios, a common strategy is to cash-match in the early years and use immunization in later years.

Benchmarking

In many industrial corporations, the performance of the liability portfolio is measured against a benchmark portfolio. In many ways this procedure resembles indexing. Again we recommend use of the risk point profile for managing the liabilities. Perhaps the creation of the benchmark portfolio itself can benefit from this method.

Scenario analysis

One use of duration is in scenario analysis. Under parallel shift assumptions we can quickly determine the change in the value of a portfolio from its duration. This use of duration is limited to parallel shifts and fails to reveal risks due to reshaping shifts of the yield curve. Using the risk point profile of the portfolio, it is easy to carry out scenario analysis including yield curve twists and other reshaping shifts.

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