Vinita Ittoop, vice president of product development at SunGard Treasury Systems, and Ira Kawaller, founder of Kawaller & Co., help to pin down some of the vagaries of the Financial Accounting Standards Board’s Statement 133.

It is one thing to understand the conceptual framework of FAS 133, the new hedge accounting standard; it’s quite another thing to try to apply it. The new rules will require firms to acquire or adapt their treasury systems to comply fully with the standard. Most critically, derivative instruments must be recorded in financial statements at their fair market values. Beyond that, additional analytics are required for even the most basic accounting efforts.

For cash-flow hedges, the critical issue is the determination of how to assess effectiveness.

The new rules, which become effective for fiscal years beginning after June 15, 2000, require users of derivative instruments to classify their use under one of the following categories: for speculative purposes; to hedge the exposure associated with the price fluctuations of an asset, liability or firm commitment; to hedge the exposure associated with an uncertain forecasted cash flow; or to hedge the exposure associated with the currency component of a net investment in a foreign operation.

The correct accounting treatment is indicated for each of these designations. For speculative applications, derivative gains or losses must be marked to market, and gains or losses must be realized in the current period’s income.

For fair-value hedges, the accounting for the derivative is the same as it is for speculative uses. However, the underlying exposures resulting from the risks being hedged must also be marked to market; and these results also flow through current income. Ideally, the hedge will produce gains or losses that will offset the losses or gains on the underlying exposure, such that there will be minimal impact to earnings.

For cash-flow hedges, derivative gains or losses must be evaluated, with a determination made as to how much of the result is effective and how much is ineffective. The ineffective component of the hedge must be realized in current income, while the effective portion is initially posted to “other comprehensive income” and later closed out to income in the same time frame in which the forecasted cash flows affect earnings. It’s important to note that the Financial Accounting Standards Board only recognizes hedges as being ineffective for accounting purposes when the hedge effects exceed the effects of the underlying forecasted cash flows, measured on a cumulative basis.

For hedges of the currency exposure of a net investment in foreign operations, hedges must be marked-to-market. This time, the treatment maintains the current provisions of FASB Statement 52, which requires effective hedge results to be consolidated with translation adjustments in other comprehensive income. Differences between total hedge results and the translation adjustments being hedged will flow through earnings.

Conceptually, these rules may appear to be straightforward, but implementation requires careful attention to some critical subtleties. Complicating the effort for those trying to follow the standard is the fact that basic terms may be defined to mean something within the context of FAS 133 other than what normal usage suggests. For cash-flow hedges, the critical issue is the determination of how to assess effectiveness. For fair-value hedges, it is the question of what is meant by the term fair value. In order to comply with the requirements of FAS 133, these definitions must be clearly understood, and this understanding must be incorporated into any FAS 133-compliant accounting system.

Effective hedges

In common usage, a hedge is typically deemed to be effective if it satisfies its intended economic objectives. For example, forward contracts and futures contracts are known to be effective price-fixing mechanisms. Both can be used to lock in the price of some associated underlying instrument, for some deferred value date. Moreover, if the terms of these contracts match those of the underlying risk or the hedged item (that is, the notional amounts, timing and so on), these tools will perfectly satisfy their intended objective. Similarly, if an option is purchased to cover the risk of an adverse price move beyond the threshold of the option’s strike price, again with the caveat that the critical terms match up, this option will perfectly satisfy its intended objective.

FASB defines effectiveness in a precise way, and perfect economic hedges often generate “ineffective” results.

Given the deterministic nature of these “perfect” hedges, one might expect that such instruments would be recognized as being entirely effective under FAS 133, such that no earnings effect would be recorded. This expectation, however, will not pan out. The problem is that FASB defines effectiveness in a precise way, and perfect economic hedges often generate “ineffective” results.

As a prerequisite to receiving favorable hedge accounting treatment under FAS 133, a hedge must be expected to be highly effective, and its effectiveness must be measured regularly. The accounting treatment only differentiates between the effective and ineffective results, however, in the case of a cash-flow hedge. Put another way, for fair-value hedges all of the derivative’s gain or loss is recorded in earnings, whether those results are effective or ineffective; for cash-flow hedges, on the other hand, effective and ineffective results are treated differently since only ineffective results go to earnings, while effective results go to other comprehensive income.

Under FAS 133, effectiveness for cash-flow hedges is measured by comparing the derivative’s gain or loss with the change in the cash flows (or the present value of the cash-flow changes) of the associated hedged item. It cannot be assumed, however, that hedges that perform perfectly in an economic sense will generate a perfect offset. Rather, in the general case, at least some degree of income volatility should be expected.

The issue may be most severe in the case of purchased options serving as traditional, insurance-type hedges. In such cases, hedge effectiveness is typically assessed by comparing changes in the intrinsic value (the amount that can be extracted by exercising the option and then liquidating the resulting position in the underlying market, with the caveat that this amount must be beneficial or positive) of the option to the fair-value or cash-flow changes in the hedged item. That is, time-value changes (the difference between the full price of an option and its intrinsic value) will generally be excluded from the effectiveness consideration, because the intrinsic value changes, specifically, provide the intended offset. Given its decision to exclude the time value from the effectiveness consideration, FAS 133 requires time-value effects to be realized in current earnings. Long option hedges will thus inevitably contribute to income volatility and therefore will have the appearance of being ineffective. This consideration will likely be problematic for users of interest rate caps and floors, where individual instruments actually are a composite of multiple options, such that the magnitudes of these effects may more likely appear to be material.

Fair value

In the context of FAS 133, the term fair value is defined as the market price of the instrument in question; as a consequence, a market quotation is the preferred measure. FASB recognizes, however, that many markets may not have liquid or transparent pricing, and as a consequence those who prepare financial statements are expected to make use of valuation models to estimate fair values.

The precise measure of model-generated fair value will likely differ from case to case. These differences arise because no single model is universally accepted, and because model users may assume somewhat different values for the variables that serve as inputs to the model. These discrepancies aside, in the general case the fair value of a derivative is expected to reflect the present value of all of its expected future cash flows. Only the choice of the appropriate discounting factor will contribute to valuation variations.

It cannot be assumed that hedges that perform perfectly in an economic sense will generate a perfect offset. At least some degree of income volatility should be expected.

Beyond fair value, FAS 133 makes specific reference to fair-value changes. Those uninitiated to the ways of FAS 133 might reasonably expect this change to be calculated as the difference between the present value of the instrument in question at, say, the end of the accounting period, vs. the present value at the start of the accounting period. But this is not the difference FASB has in mind. FASB defines the change in the fair value of a hedged asset or liability to exclude changes in the present value that would result from factors other than the specific risk being hedged.

To illustrate the issue, consider the case of a fair-value hedge, in which an interest rate swap is used to swap a fixed-rate loan into floating. In assessing the effectiveness of this hedge, the derivative’s result should be compared with the change in the fair value of the loan. Both the hedge and the hedged item deserve further scrutiny.

With respect to the swap, the total gains or losses would consist of the change in the present value of the swap over the period, plus (minus) net cash inflows (outflows) during the period. This value is the amount that would be gained or lost if the swap were initially traded at time t-1 and liquidated at t. Note that a positive value would be assigned to the present value of an asset, while a negative value would be assigned to the present value of a liability.

The postponement of the implementation date should give users a window of opportunity to find a system that will appropriately suit their needs.

On the debt side, the economic profit (loss) is determined analogously, but the relevant basis adjustment would subtract from the gain or loss any change in the present value that would have occurred, independent of a change in interest rates (assuming the credit rating of the debt remained unchanged over the accounting period).

Unfortunately, at the time of this writing, the guidance from the FASB as to how to calculate PV*(t) had yet to be issued. Three possibilities might reasonably be considered:

• calculate PV*(t) using the yield to maturity of the instrument at the start of the accounting period;
• freeze the entire discount rate curve at the start of the accounting period, and discount each prospective cash flow by the initial discount rate appropriate for the time horizon at the end of the accounting period;
• generate forward rates from the original discount rate curve for each prospective cash flow at the end of the accounting period, and use these forward rates to discount those cash flows.

Suppose, for example, an entity issues fixed-rate debt with a six-month horizon and quarterly interest payments. Simultaneously, the firm enters into a swap to convert from a fixed to floating rate. In addition, assume that the quarters of the debt coincide perfectly with the accounting quarters. The issue at hand is how to measure PV* at the end of the first quarter.

Let’s say that at the start of the first quarter the spot three-month rate is 5 percent, the spot six-month rate is 6 percent, and the three-month rate, three months forward, is 7 percent.

Under the first methodology, PV* at the end of the first quarter would be calculated using the 6 percent interest rate (that is, reflecting the initial yield to maturity). Employing the second method, 5 percent would be used, while 7 percent would be used in the third method. It should be obvious that the different methodologies could result in substantially different basis adjustments for the hedged item, depending on the shape of the yield curve.

FASB has mandated an unprecedented level of reliance on valuation models and accounting systems.

This uncertainty notwithstanding, it is important to note that interest accruals associated with this debt—whether in connection with coupon accruals or amortization schedules—must also continue to be recorded in earnings, separate and apart from the FAS 133 requirements. Moreover, following each adjustment to the basis from the fair value hedge effects, a new calculation for prospective amortization becomes necessary to ensure that the retirement value of the debt will fully accrete to par at maturity.

At this point, it should be clear that in addition to imposing a new conceptual framework on the accounting for derivative instruments, whether intentionally or unintentionally, FASB also has mandated an unprecedented level of reliance on valuation models and accounting systems. The calculations that are required for even the most straight forward derivative instruments are simply too mathematically challenging to leave to the back of an envelope. Achieving a comfort level with a system—that is, understanding what it’s doing and having confidence that it is compliant with FAS 133 requirements—is no trivial task. Luckily, the postponement of the implementation date should give users a window of opportunity to find a system that will appropriately suit their needs.

A longer version of this article appeared in TMA Journal, September/October 1999. Ittoop is the chief resident expert on FAS 133 at SunGard Treasury Systems. Kawaller is a member of the Financial Accounting Standards Board’s Derivatives Implementation Group. He can be reached at kawaller@idt.net.

William Margrabe, president of the William Margrabe Group, explains statistical arbitrage

Dear Dr. Risk,
Where can I find information about different kinds of statistical arbitrage?
—Dilip

Dear Dilip,
Statistical arbitrage is one of those paradoxical but soothing labels—like “conservative Democrat,” “compassionate conservative” and “safe sex”—that sells. Dr. Risk’s informal polling establishes that nine out of 10 investors are much more likely to hand money over to a manager who says he is doing statistical arbitrage than to one who says he’s following a gambling system. Statistical arbitrage covers a lot of ground, and the definition is fuzzy. We’ll survey the topic and identify synonyms and special cases, so you can better focus further inquiries on specific areas that interest you.

Textbook, classical, hard or pure arbitrage consists of buying something that’s cheap in one market and immediately selling it for more in another market—without tying up any capital or taking on any risk. The classic arbitrageur is the currency dealer on the phone with two customers—for example, a buyer who would pay $1.0450 per euro and a seller who would sell for $1.0445. So the dealer buys from the seller, and then—within a few seconds, at most—sells to the buyer and makes $0.0005 per euro—times 10 million euros, for a total of $5,000.

A textbook arbitrage trade is to an ambitious trader as a mirage of an oasis is to a thirsty bedouin. The existence of an arbitrage opportunity for more than a moment defies common sense. How could a single trader see lasting opportunities that his professional peers couldn’t? If two or more traders saw the same opportunities, wouldn’t they bid prices up or down, until the arbitrages disappear? Ask Joe Jett, who lost hundreds of millions of dollars doing reconstitutions, while attempting to arbitrage the discrepancies between the prices of strips and Treasuries.

As early as the Modigliani-Miller (M&M) articles on optimal capital structure, academics found it useful to assume that arbitrage opportunities couldn’t exist—for even a moment. M&M used this notion to prove that an optimal capital structure didn’t exist—at least, in a world of perfect markets. The seminal 1973 Black-Scholes paper assumed that the option dealer would try and would fail to arbitrage price discrepancies across the markets for riskless debt, equity and options on the equity. This allowed Black and Scholes to derive the equilibrium option price that would eliminate any opportunity for arbitrage.

Tough fit

While perfect markets and the absence of arbitrage may sound like academic oversimplifications, traders have found that looking for classical arbitrage in financial markets is a lot like looking for that perfect outfit in Filene’s Basement when the doors open on a special sale day. Sure, there’s lots of barbaric excitement, but any opportunity lasts only an instant, and buyers end up paying for their bargains in time and energy, if not in dollars. Consequently, in practice as well as theory, the business of doing pure arbitrage is risky. You could conceivably do real arbitrages all day for months, making pennies on each trade but bleeding financially the whole time, because you didn’t cover the fixed costs of salary, office rent, computers, data feeds and so on.

Dr. Risk wasn’t able to find a definition of statistical arbitrage that everyone accepts, so here is his own definition. Statistical arbitrage is a family of multivariate trading strategies with positive expected profit, where the correlations between pairs of component positions work to reduce overall risk. Often, statistical arbitrage involves a spread trade, and the two underlying prices are positively correlated—for example, long a call and short the underlying. It could also involve two long positions, with negatively correlated underlying prices—for example, long a put and long the underlying. It never involves even the attempt to do pure arbitrage—otherwise, probability and statistics would be irrelevant. Michael Gamze of Chicago Partners adds, “In order to perform statistical arbitrage, one should trade frequently enough and have enough capital to support this trading to justify the statistical law of large numbers.” Definitions of some statistical arbitrage strategies appear in Figure 1.

Statistical arbitrage is a popular approach to trading. According to information available at HedgeFund.net, Dr. Risk estimates that about 35 percent of hedge funds claim to follow various statistical arbitrage strategies, including 25 percent claiming long-short and market-neutral strategies. The number of hedge funds appears to run from around 3,000 (according to HedgeFund.net) to more than 5,800 (according to Van Hedge Fund Advisors International), which suggests that 1,000–2,000 funds do statistical arbitrage. Swap, futures and options market-makers (both OTC and on exchanges) are typically statistical arbitrageurs.

Statistical arbitrage is a matter of opinion, and one person’s statistical arbitrage is another’s speculation. But typically, all the opinions imply a probability distribution of possible returns for which the expected return exceeds that of a riskless investment by an amount that more than compensates for the risk. Of course, that begs important questions: What is the expected return? How do we measure risk? How does the investor compare reward and risk?

Professionals have developed standard—although not perfect—ways of measuring and comparing reward and risk. A typical way to summarize a hedge fund’s performance, for example, is with its alpha, Sharpe ratio and maximum drawdown. The alpha is the fund’s average return, adjusted for risk and the market’s average return. The intercept in the regression of a fund’s excess rate of return (above the riskless rate) against the market’s excess rate of return is an alpha. The Sharpe ratio equals the ratio of the fund’s excess rate of return to its volatility. Thus, the Sharpe ratio tells you how many standard deviations the average rate of return is from the riskless rate. Of course, evaluating a track record based on only alpha and Sharpe ratio would be simplistic. Readers can find additional information about alpha, the Sharpe ratio and other measures of reward and risk at www.margrabe.com, in the mathematical appendix.

If you want to learn more about statistical arbitrage, Sheldon Natenberg’s Option Volatility & Pricing is an authoritative resource for option spread trades. Nassim Taleb’s Dynamic Hedging: Managing Vanilla and Exotic Options is perhaps definitive on dynamic hedging. Once you have a handle on a few types of statistical arbitrage, I think you will have a better idea of the rest.

You didn’t ask if statistical arbitrage works, but here’s my opinion: It works with varying degrees of success for different people at different times. Victor Niederhoffer had been minting money by shorting out-of-the-money index put options—until the market crashed, he failed to meet his margin calls, and Refco closed him out. Statistical arbitrage (fixed-income arbitrage and convergence strategies) worked spectacularly well as a marketing tool for Long-Term Capital Management, which was able to amass a large sum of money under management in a short time and on favorable terms. Then, for a couple of years, it provided spectacular returns to LTCM’s investors. In 1998, it performed disastrously, leading to the notorious bailout. LTCM’s future performance—even survival—is a matter of speculation.

Figure 1: Statistical arbitrage’s many flavors Long-short—Long and short positions that tend to offset each other, so market swings don’t dominate overall portfolio performance. Supposed to beat a money market rate in up and down markets. Pairs trading—A pair of trades, one long and one short, involving similar companies with better and worse prospects. Tends to eliminate sector and style as factors that explain performance, and emphasizes the ability to pick winning and losing stocks. Market-neutral or zero-beta—An equity portfolio consisting of long and short positions that are net insensitive to a move in the market portfolio. Convergence trading—Assumes that a price relationship is out of line, but likely to come back. Involves buying the position that is likely to outperform and shorting the one likely to underperform. Risk arbitrage—Typically, bets that an announced takeover will actually happen. Often called event arbitrage. One arbitrage trader explains, “Investors don’t like to hear the word risk, unless you follow it with management.” Convertible arbitrage—Long (short) convertible bonds vs. short (long) shares and ordinary corporate bonds. Distressed securities arbitrage—Investment in debt or equity securities of companies that are distressed, bankrupt or in reorganization. Fixed-income arbitrage—Covers a variety of long-short strategies involving fixed-income instruments. A parade of traders—including David Askin—did this with mortgages and mortgage-backed securities vs. Treasuries and Treasury options. Others try to profit from changes in credit spreads. Derivatives arbitrage (includes options arbitrage)—Long (short) a complex contract and short (long) the replicating portfolio of simpler, more-liquid underlying instruments. Sometimes the replicating portfolio is dynamic (changing), sometimes “static” (unchanging). For example, the swap desk that uses part of its book (receiving fixed, say) to hedge another part (paying fixed), then hedges the mismatch with money-market futures contracts and/or Treasure notes, bonds, and/or zeros. Equity index arb—Buying (shorting) index futures and shorting (buying) the corresponding basket of shares. Equity volatility arb—Going long (short) volatility on a basket of shares and short (long) the volatilities of the component shares. Basis trading—For example, long WTI crude and short Brent.

Was this information valuable? Subscribe to Derivatives Strategy by clicking here!