A portfolios duration, like a bonds duration, can be viewed as a measure of its price risk

PORTFOLIO CONSTRUCTION

Option-adjusted spread analysis of more than one security at a time is an extremely powerful tool. It allows for security selection that can take advantage of the natural hedging relationships among securities and for the evaluation of the portfolio as an entity.

For example, the portfolio manager might reject a given IO and a given PO as individual securities, because of high prepayment exposure or other risks. OAS analysis may show that the two securities in combination are very suitable candidates. Or it might reveal that the two securities do not complement each other over all possible interest rate paths. Such relationships are difficult to determine without OAS analysis. For example, investors are at an extreme disadvantage buying IOs or POs based upon simple, static yield tables, which typically do not account for any shifts in prepayment rates or changes in forward rates.

OAS can also be used for overall portfolio analysis. Merging the cash flows of an entire portfolio and running an OAS analysis can allow the manager to see how the risks inherent in some securities are offset by certain features of other securities. Virtually all mortgage securities have some positive and some negative characteristics. Combining securities with different flaws and different strengths in the same portfolio can allow the manager to minimize the hedging (and associated costs) required to create a market neutral portfolio.

This is where analysis of interest rate paths is important. We have noted that the discounted cash flows of a floater will give the same price for each interest rate path; the price of a nonfloater will vary over different paths. Although OAS analysis provides a weighted average price, some interest rate paths generate prices that are higher than the average, while others generate lower prices. Path analysis can be used to determine which interest rate scenarios are detrimental to a portfolio, and how they can best be hedged in order to achieve a market neutral portfolio that will replicate a floater and have the same price over all scenarios. As with OAS analysis of individual securities, OAS portfolio analyses should include estimation of prepayment and volatility derivatives. Additionally, at the portfolio level, the manager should perform OAS analyses across collateral, testing the sensitivity of the portfolio to relative errors in the prepayment model for each collateral type, coupon, and loan age. A portfolio might exhibit a very low prepayment derivative overall, but if the prepayment model is slow for one type of collateral and fast for another, actual results could differ dramatically from expected results. A prepayment derivative should thus be calculated for each different type of collateral to see if the risk is within reason, and whether it requires additional hedging.

HEDGING

The hedging function can be viewed as a means to convert the cheap security, which has a high weighted average return with a potentially large deviation over different interest rate paths, into a synthetic combination that has the same return, or spread, with very little deviation over all scenarios. Accomplishing this means eliminating the price risk, or the duration and convexity, of the portfolio.

Hedging is a full-time job. As interest rates and prepayments vary, it is necessary to evaluate constantly the efficiency and effectiveness of a hedge and to make adjustments as needed. A manager cannot sit back and observe. Hedging is an active process, as theory does not always apply in practice.

A portfolios duration, like a bonds duration, can be viewed as a measure of its price risk. A duration neutral portfolio can be thought of as exhibiting zero deviation in price over all interest rate paths. Unfortunately, duration alone does not accurately reflect a portfolios sensitivity to large moves in interest rates.

To be truly market neutral, a portfolio must be not only duration neutral, but also convexity neutral. A convexity neutral portfolio can be thought of as providing zero deviation in duration over all interest rate paths. Understanding duration and convexity and identifying the most

efficient hedges for achieving duration and convexity neutral portfolios represent the biggest challenges in managing market neutral CMO portfolios. The complexities of hedging are just as great as those involved in analyzing the securities themselves.

Key Rate Durations

Recent innovations in technology have allowed portfolio managers to determine not only the duration of a security, but also the key points for addressing duration. The importance of this becomes abundantly clear if one considers the problem of hedging planned amortization class (PAC) bonds against yield curve twists (i.e. steepenings, flattenings, and humps in the yield curve). For example, one would not want to hedge the interest rate risk of a five-year, tight-window PAC with a two-year swap, Treasury or futures contract. Nor would one propose to use long bonds or long bond futures.

This conclusion seems obvious in the case of securities with bullet-like amortizations. It is less clear when hedging wide-windowed securities, support bonds, or inverse floaters with constant-maturity Treasury (CMT) indexes. The problem here is determining the appropriate duration to hedge.

In most OAS analyses for mortgages, there are 360 (30 years times 12 months) time steps. Theoretically, the manager could short Treasuries or construct swap contracts to hedge almost all 360 time points, but it would be very expensive and time-consuming to do so. In practice, the manager has to choose what points on the yield curve he or she considers the key rates, or benchmark points, to hedge. Often the manager

chooses the maturities of the liquid, on-the-run Treasuries.

OAS analysis can then be used to calculate the price change relative to each key rate, in much the same way the effective duration is calculated for the whole yield curve. The portfolio manager can then determine the most appropriate hedges. A single security may have positive duration with respect to one point on the yield curve, while having negative duration with respect to another.

For example, a two-year PAC inverse IO has a duration similar to that of a two-year Treasury. However, if long rates fall, and mortgage rates follow, the securitys value will fall as the bond shortens as a result of the expected increase in prepayments. The security thus has negative duration with respect to the long end of the yield curve, but positive duration to the front end of the yield curve. These different exposures should be hedged.

Exhibit 6.3 illustrates, as an example, the FNR 1993-178 SD. This security is a short (approximately two-year) average life PAC inverse floater. However, because its coupon formula is based on the 10-year constant-maturity Treasury, its key rate duration shows a different exposure profile. The biggest exposure of this security is to the 10-year Treasury note.

Prepayment Hedging

Maintaining a market neutral portfolio means attempting to eliminate prepayment risk. Success in this endeavor depends upon the accuracy of the prepayment model used to determine the level of prepayment risk and on the ability of the hedging instruments to immunize against this risk. Prepayment risk can only be truly hedged with other mortgages or CMOs or with options on mortgages, as these are the only instruments that have prepayment risk.

Prepayment models assume slower prepayments in a rising interest rate environment and faster prepayments in a falling rate environment.

However, actual prepayments might not mimic model forecasts. Changes in the mortgage market, economic activity, and/or demographics could render some models less useful. We noted earlier that model error should be less important for securities that have low prepayment derivatives. However, this result may not hold if markets move.

Consider, for example, a security priced at par. This security has little prepayment risk, which may be adequately hedged with Treasuries or swaps. Given a large market movement, however, this security could become an $80 security with a large positive prepayment exposure that a Treasury or swap hedge will not cover. The portfolio manager can, however, purchase an IO product (with similar collateral, if not another tranche off the same CMO structure) that will serve to increase the overall portfolios yield and reduce the newly emerged prepayment risk.

Of course, in hedging a portfolio of mortgage securities in order to achieve market neutrality, the manager will have to take into account not only the portfolios prepayment risk, but also factors such as its overall sensitivity to underlying rate changes. The manager is likely to take advantage of a variety of instruments. These instruments, and their benefits and limitations, are discussed below.

Interest Rate Swaps

An interest rate swap, in its simplest form, is an agreement between two parties where one party pays a fixed rate of interest while receiving a floating rate of interest, usually LIBOR, and the other party takes the opposite position. Because most CMOs have fixed-rate coupons, interest rate swaps can be a valuable hedging mechanism.

Consider, for example, a portfolio that is benchmarked to LIBOR. The portfolio manager finds a fixed-rate security that appears to be cheap. The manager can buy the security and enter into a swap to pay fixed and receive floating. The portfolio will earn LIBOR plus any difference between the yield on the security and the fixed rate paid in the swap (adjusting for such factors as day count). To the extent that the security does turn out to have been purchased cheaply, this difference will be positive and the portfolio will earn a positive spread over LIBOR.

Swaps are over-the-counter agreements that can be tailored to the specific needs of the portfolio manager. They can thus provide very accurate hedges. Unfortunately, the more complicated or unique the swap, the more expensive it tends to be.

Interest rate swaps also suffer from two fundamental problems: they are somewhat illiquid, and they have counterparty credit risk. Illiquidity should not be a critical problem for a buy-and-hold portfolio manager. It can be more of a problem for an actively traded account, as it is likely to result in a wider bid-ask spread that can increase the portfolios transaction costs. Even here, however, the profit expected from the mortgage investment may exceed the bid-ask spread on the swap, making the mortgage-plus-swap combination attractive.

Furthermore, an active trading account does not generally sell off securities for purposes of liquidating the account, but in order to replace one asset with another, cheaper asset. The portfolio manager can thus maintain a core group of swaps while substituting assets opportunistically. If the manager does choose to sell off securities and maintain a large position in cash, a long position in Treasuries can be used to maintain the desired duration without liquidating the swaps. The illiquidity of swaps is thus not critical.

This leaves the problem of counterparty credit risk. A swap leaves each party exposed to the credit quality of the other. This is why banks with high credit quality have historically been the best candidates for swap transactions. More recently, the need for high credit quality counterparties has led to the creation of several AAA swap dealers, some of which are special purpose subsidiaries of broker-dealers, set up strictly for such transactions.

Fortunately, the swap market is efficient and competitive enough that, even with a limited number of high-quality swap counterparties, it is possible to obtain reasonable rates without sacrificing credit quality. Furthermore, portfolio managers and dealers now have daily marks to market and bilateral collateral arrangements that require counterparties to post margin to each other to cover the net present value of the swap. Such arrangements allow the manager to engage in swaps with lowerquality counterparties without incurring substantial credit risk.

The specific problem of swaps with regard to CMO hedging is that they generally have fixed maturities or deterministic amortization schedules, while mortgages are exposed to unpredictable prepayment risk. In order to hedge this risk, the portfolio manager will have to use options, either on the swap or on similar fixed-income instruments such as Treasuries or mortgages.

Theoretically, then, interest rate swaps can provide an important hedging instrument for CMO portfolios. However, practical considerations, including regulatory and balance sheet issues, must be explored to see if the cost of such a trade is compensated for by the yield pickup from the trade.

Financial Futures

Several futures contracts can provide an alternative to swaps as hedging vehicles. Futures offer liquidity, price transparency, and the high credit quality of the exchange clearinghouse. Eurodollar futures provide a very good proxy for short-term swaps and are particularly useful for LIBORbased funds. Eurodollar futures have maturities up to 10 years, although liquidity is relatively low for back contracts. As they are cash settled, there are no technical factors related to supply and demand, and no delivery options.

For longer-term securities, Treasury bond and note futures can be valuable hedging instruments. Contracts exist for the 2-, 5-, 10- and 20year Treasury securities. Treasury bond futures do not capture swap spreads, which can be a risk for LIBOR-based funds, but their liquidity and high credit quality may compensate for this, at least in the short term. Furthermore, swap spread risk can be hedged independently, without actually entering into swaps.

Nevertheless, hedgers using futures should be aware of some problems and complexities. First, technical situations with deliverable bonds can reduce the implied financing (repo) rate, causing negative carry for the short position in the contract and potentially wiping out the return of the asset.

Second, the short position in the contract has certain delivery options that are priced into the contract. These options can be classified as either timing or quality options. There is a great deal of academic research dealing with these options, and although their values are disputed, it is generally agreed that they have significant value and that the seller of a futures contract is selling at a price lower than the cash-andcarry price because of these options.

Finally, futures contracts are marked to market daily, and margin must be posted to either the buyers or the sellers account if the contract price changes. This is an additional complication that the manager using futures to hedge must consider.

Treasuries

Hedging can be accomplished by shorting appropriate Treasury securities. Treasuries have great liquidity, which makes it almost cost-free to unwind a trade. Furthermore, Treasuries can be sold along the entire yield curve, unlike futures contracts, which have only a limited number of maturities. Treasuries can allow more accurate hedging than futures and more efficient hedging, with less credit risk, than swaps.

In certain situations, however, the repo rate may be significantly lower than the short-term rate. Treasuries may thus be very expensive to borrow. The cost can reduce or even wipe out the spread of the CMO over time. A portfolio manager choosing to hedge by shorting Treasury bonds must have a thorough understanding of the Treasury and repurchase markets.

Options

Options are an important aspect of CMO portfolio management, as the underlying assets virtually always have embedded options. Only options or instruments with option-like characteristics can truly hedge the convexity element of mortgage portfolios.

If a portfolio of mortgage securities has negative convexity, the manager can purchase options; long option positions have positive convexity. The option purchases increase the cost of the hedged portfolio, hence reducing the yield relative to the unhedged portfolio; but they also offset the negative convexity. If the options are priced fairly, the OAS should remain the same, but the performance of the hedged portfolio should remain more stable over various rate paths, which is the goal for a market neutral portfolio.

Of course, a portfolio may have positive convexity. Positive convexity can result from positive response to changes in prepayments, as when a rise in prepayments increases the price of POs, or from embedded options such as a cap on an inverse floater. In this case, the manager can sell options; short option positions have negative convexity. The premium received from option sales will reduce the cost of the overall portfolio and increase its yield. (Of course, in selling options, the manager gives up any potential windfalls from the options going in the money.)

It is important to understand that it is not necessary to buy or sell actual options in order to offset the options embedded in a CMO portfolio. Rather, the portfolio manager can dynamically hedge the effective duration of the portfolio, using interest rate futures. In effect, dynamic hedging replicates the option position that would offset the portfolios embedded options. Dynamic, or delta, hedging, however, is very sensitive to underlying assumptions. If volatility turns out to be materially different from the volatility assumed, for example, a dynamic hedge can turn out to be significantly more expensive than expected. Furthermore, conditions such as gaps in the price of the underlying assets can cause the hedge to fail to replicate the desired option.

Options can be bought or sold on Treasuries, on any of the futures contracts mentioned, on a specific interest rate or index, or on swaps themselves. Portfolio managers using options must use pricing models to compare option prices across different markets in order to ensure that only the fairly priced options are purchased. Paying too much for options diminishes the returns of a CMO portfolio. A thorough understanding of option instruments and option pricing is required for successful CMO portfolio management.

HISTORICAL EXAMPLES

In the 1990s, there were two instances of intense stress in the mortgage market. From the end of 1993 to late 1994, interest rates rose dramatically and prepayments slowed dramatically. From the first quarter of 1998 to the end of 1998, interest rates fell dramatically and prepayments increased significantly. These periods best demonstrate the value of the analysis discussed above and the validity of the market neutral trading strategy.

Hedging Duration

The FHLMC 1468 SC is an inverse floating-rate security that is a planned amortization class (PAC). In January 1993, the effective duration of the security was approximately 22, indicating that a 100-basispoint move in interest rates would induce a 22-point move in the securitys price. Because this is a PAC bond, there is not much convexity due to prepayments. In other words, its duration would remain relatively constant over large rate changes.

So, where do profit opportunities come from? If the bond is purchased at a cheap level, there is a good chance it will tighten (on an OAS basis) and a profit can be realized without any change in interest rates. Furthermore, profits can be made from market moves and the changing characteristics of the security.

Exhibit 6.4 shows the bonds price as well as the 10-year Treasury yield at various dates in 1993 and 1994, the time of the trade. It also shows the price at which the bond would be ownedthat is, its price net of the gain or loss on a duration-equivalent hedgeand the profit or loss on the position (without taking the positive carry on the portfolio into consideration).

It can be seen that there were significant profit opportunities as the market moved. In 1993, the bond traded at 99.53 in January and at 116 in August. Had it been duration-hedged, the price of the bond net of the hedge would have been 111.32. Had the bond been purchased in January, hedged, and sold in August, there would have been a 4.68-point profit.

This profit reflects in part the fundamental cheapness of the security at purchase. However, it also reflects the fact that prepayments accelerated in a low-rate, steep yield curve environment.

Had the bond been purchased in January 1993 and held until November 1994, the price net of the hedge would have been 65.34, whereas the bond actually traded at 69 on this date. Had the bond been purchased in January 1993, hedged, and traded in November 1994, there would have been a 3.66-point profit. This profit reflects the fact that, as rates rose and the inverse floater approached its cap, it tended to exhibit substantial positive convexity, and therefore its price decline was mitigated relative to fixed-coupon securities (i.e. Treasuries). In this scenario, the PAC protection prevented extension, thus keeping the duration of the bond within the duration of the hedge. This trade is one of many examples that demonstrate the liquidity of the market in 1994 was not as bad as many thought.

This portfolio of a PAC bond and its hedge would have been profitable regardless of the move in interest rates. PAC bonds were cheap in 1993 because, lacking the yield of a support bond, they were disregarded by most investors. This may seem obvious now, but at the time investors were sacrificing protection for higher yield.

Hedging Convexity

Using the example of the FHR 1983 S, a support bond that exhibited great variability of average life, Exhibit 6.5 illustrates problems that arise in attempting to hedge mortgage security convexity. When issued, in July 1997, the security had an attractive and stable OAS. The anticipated average life of the security was approximately four years, with an effective duration of approximately 14.

Hedging this security would have been quite complicated, as it was purchased at a price close to par. If interest rates declined, and prepayments increased, owning the bond at too high a dollar price could have resulted in a substantial loss. In fact, from July 1997 to January 1999, the 10-year Treasury yield decreased 157 basis points. If managers had hedged the bonds effective duration with a short 10-year Treasury position, they would have seen their cost basis on the security increase to approximately 125to catastrophic effect.

This security clearly needed to be hedged with options. An optionbased hedge would have provided interest rate protection while controlling for changes in the dollar price of the security. Additionally, even the model that assumed a fast prepayment rate underestimated the actual negative convexity of the security. An option hedge would have been the only type of effective hedge, as any losses on the security due to an unexpected increase in volatility would have been offset by a profit on the option hedge. As the security paid off in January 1999, this hedging strategy was the only effective one.

CONCLUSION

The CMO market encompasses hundreds of security types as well as different collateral types and, for floating-rate securities, different interest rate indices in the coupon formula. A thorough understanding of the market requires quantitative analysis and adequate systems and models. In general, however, portfolio managers use more rudimentary pricing methods, even though these methods are not accurate. As a consequence, the market is relatively inefficient, and the astute manager may be able to identify relatively cheap securities that will yield positive excess returns.

Identifying fundamentally cheap mortgage securities requires comprehensive quantitative analysis and an understanding of the practical aspects of the market. If it is done correctly, the rewards can be substantial. If it is done incorrectly, or in an incomplete manner, the risks can be substantial. It is important to remember that mortgage securities can be synthetically created in more liquid, more straightforward markets that are less susceptible to the vagaries of underlying rate movements. Therefore, unless the manager can identify relatively cheap securities with some accuracy, mortgage securities should probably not be purchased.

Option-adjusted spread analysis can provide the portfolio manager with an invaluable tool for evaluating individual mortgage securities and portfolios as a whole. OAS analysis can be used, for example, to identify cheap securities with high expected returns. It can also be used to evaluate combinations of securities, in order to arrive at a portfolio that maximizes the return contribution of each security while using the offsetting characteristics of different securities to minimize overall portfolio risk.

OAS analysis provides a single number that is a weighted average of a comprehensive set of possible interest rate paths. Some of these paths may be good for portfolio returns and some may be bad. A market neutral portfolio, by contrast, exhibits the same return regardless of the interest rate path. This can be achieved to a large extent by hedging.

Hedging in essence converts the portfolio of cheap mortgage-backed securities, which has a high expected return but potentially large return deviations, into a hedged portfolio that provides the same high expected return but displays little deviation. For sophisticated managers, hedging opens the door to a wide range of assets that might not be considered eligible investments in the absence of hedging. Thus a floating-rate mortgage fund does not have to confine itself to floating or adjustablerate securities, but can pursue higher returns in mortgage securities, while using hedging to reduce their risk to acceptable levels.