# Using Regression to Keep Derivatives off the Income Statement

Since the adoption of FAS 133 in 1999, many companies have avoided the complexities of hedge effectiveness testing by applying shortcut accounting treatment. By documenting that the hedging instrument matched the critical terms of the underlying hedged item, it could be assumed that the hedge would be highly effective and the derivative would automatically qualify for preferential cash flow or fair value hedge accounting without the headache and risks of periodic assessments. The most common path to shortcut hedge accounting has been through the ‘critical terms match’ interpretation (see paragraph 65 and DIG G9 or paragraph 68 and DIG E4 for interest rate swap hedges of fixed rate debt).

However, over the past 18 months, there has been growing pressure from the SEC and the large audit firms to restrict shortcut hedge accounting. This newfound concern stems from the increasing number of restatements since 2004, many of them due to poor hedge documentation and misapplication of shortcut methods. Recent public statements from SEC and FASB staff have encouraged a literal interpretation of paragraphs 65 and 68 and this banner has been duly advanced by the Big 4. Use of shortcut or critical terms match is now an audit flag at best and a cause of de-designation and restatement at worst. The fact that your hedging program has passed muster for the past six years is no longer an indicator of what the next audit opinion will be.

With the bar on shortcut hedge accounting raised, there are three alternatives:

- Defend your application of shortcut. You must have meticulously documented the hedge and satisfied every provision of paragraph 68 or matched every critical term of the hedged item. Depending on the auditor, even this may not be sufficient due to ambiguity as to whether a hedge should be designated on the execution date or the funding date of the hedged item, whether settlement dates are considered a critical term that must be matched, whether all non-diminimus forms of risk have been truly hedged and whether the derivative truly has an initial fair value of zero.
- De-designate the hedge and take the gain or loss on the derivative to the income statement. This option may become more attractive once FAS 159 is adopted and certain hedged items can be carried at fair value, but for now it will only create the earnings volatility we are trying to avoid.
- Re-designate the hedge and document a long-haul effectiveness test that will be performed each period to justify hedge accounting. This can be done by looking at the historical performance of the derivative, or a similar instrument, against the performance of the hedged item, or a similar transaction. Let’s take a closer look at the long-haul effectiveness approach.

There are two basic methods of long-haul effectiveness testing:

*Dollar offset method*– this method considers the change in value of the derivative versus the change in value of the hedged item due to the risk being hedged since inception of the hedge or since the last measurement date.*Statistical methods*– these methods, which include regression, rely on a series of observations of the change in the derivative versus that of the hedged item over a duration relative to that of the hedge – for instance, monthly price changes over the past three years. From these observations, a statistical analysis is performed to determine whether the variation in the derivative is substantially explained by the variation in the hedged item.

The dollar-offset method is easy to understand and apply, but it has a significant shortcoming. The ‘law of small numbers’, whereby an immaterial change in the derivative may be large in relation to the change in the hedged item, can cause the hedge to fall out of the effectiveness band (e.g. 80 – 125) and force the gains/losses to be reported as earnings and/or the hedge’s termination. Regression, on the other hand, reduces the impact of such outliers and better reflects the long-term relationship between the change in the derivative and the hedged item. Regression is far less likely to produce a false positive or a false negative on whether the hedge is highly effective.

Applying regression analysis to hedge effectiveness testing requires considering a number of factors. These factors are discussed in the following sections.

First and most importantly, you must document the hedge in specific detail. FAS 133 is a rules-driven process and all of the facts and circumstances pertaining to your hedge must be spelled out in advance. You must identify the derivative and the hedged item, what risk you are hedging, what accounting treatment you are applying (cash flow or fair value), what the objective of the hedge is, and how you are going to evaluate whether you have effectively hedged that risk. This means not only deciding whether to use regression or dollar offset, but also which method is to be used for retrospective effectiveness testing and which method for prospective effectiveness testing. You are required to perform both tests quarterly or whenever accounting results are reported. The retrospective test might be dollar offset and the prospective test regression, or they may both be the same kind of test. If regression is used for both retrospective and prospective effectiveness, the same regression test may be used or two different regression tests may be used. For instance, you may want to limit the amount of data that you use for your retrospective test to the actual historical data for the period in which the hedge was in place; but for the prospective test you might want to go back over a longer period of time.

Some companies have used a single regression test as a proxy to prove effectiveness for a whole program of similar hedges. While this approach saves time, it does not show that each particular hedge is necessarily effective. A derivative may not be as effective as the general test indicates due to differences in seasonality and time value, credit risk, or timing of cash flows. A regression test must be performed for the unique circumstances of each hedge to show that it is highly effective.

In addition, the regression test must be repeated at the beginning of every period to show that the hedge is expected to continue to be effective. It is not sufficient to perform a regression at the outset of the hedge and to assume that the result carries forward so long as the hedge does not change (unless the hedge has qualified separately for shortcut accounting). Even if the hedge is unchanged, the statistical relationship between the derivative and the hedged item may no longer be empirically supportable due to changing market conditions. Furthermore, as the derivative draws closer to maturity the regression may be performed on nearer term forward prices which may not exhibit the same relationship as longer term forward prices.

Companies that conduct one regression test for an entire program or one test at the outset of the hedge will certainly invite scrutiny. But performing a regression for every hedge in every period can be a daunting task. Large hedge portfolios using regression may need to be managed through a software solution. Any such solution should allow you to customize your elections and perform the regression calculations consistently while controlling access to the inputs, documentation, and results and providing traceability for your auditors.

A regression test can and should be configured to meet the specific facts and circumstances of each hedge or hedging program. Neither FASB nor the SEC provides any specific guidance on regression other than that the choices must be defensible and the test applied consistently across all similar hedges. It would be wise to discuss with an auditor what factors need to be considered before embarking on a hedging program, as the audit firms tend to have their own guidelines on a properly structured regression test.

There are a few critical questions that must be decided when designing an appropriate regression test. The answers should be based on the hedging objective, the characteristics of the derivative and the hedged item, and the risk being hedged. For instance, if you are hedging foreign exchange or commodity risk, you need to decide whether you are going to regress on spot prices or forward prices. For commodities, ineffectiveness is due mostly to basis differences, so a regression on the future prices of the derivative versus the contracted prices for future delivery of the hedged item would be appropriate. For foreign exchange, forward prices are probably the best indicator as the most common source of ineffectiveness is time value.

With forward prices, there are additional considerations. Consider an 11 month derivative designated to hedge a forecasted transaction expected to occur in 12 months. We could regress on 11 month rates versus 12 month rates observed at weekly intervals over the past year. This is known as ‘constant maturity’, and treats the current terms of the hedge as static. The alternative is to regress on prices to a specific maturity date. Assuming our derivative matures 30 April 2008 and our hedged item on 31 May 2008, then we could regress on the prices to 30 April 2008 versus the prices to 31 May 2008 observed at weekly intervals over the past year. This ‘declining maturity’ method gradually removes the time value factor just as we would expect to happen as the derivative approaches maturity. Declining maturity is more complex than constant maturity but more accurately reflects the expected behavior of the derivative versus the hedged item over the remainder of the hedge and thus can be a better predictor of whether the hedge is expected to be highly effective.

Another consideration is whether to regress on price levels or the changes in price. The changes in price are likely to be more volatile than price levels, but it is the change in the hedged item that is being hedged after all, not its absolute level, so a regression on changes in price may be a better reflection of the effectiveness of the hedge.

For interest rate hedges, you might want to regress on fair value rather than price. While changes in a variable rate index (the price of the swap) might fairly illustrate hedge effectiveness for a floating-to-fixed-rate cash flow hedge, it is extremely complex to perform a similar calculation for a fixed-to-floating-rate fair value hedge. Instead, regressing on the fair value of the swap versus the fair value of the hedged item can clearly illustrate how effective the swap has been at offsetting changes in the hedged item. At this point the next choice is whether to regress on fair value or the change in fair value between each observation. For the same reasons as change in price, change in fair value may be more relevant to the question of hedge effectiveness.

Regressing on fair value is much more computation-intensive than regressing on price and requires management of discount curves (and, for options, volatility curves). This is a formidable task to complete using a spreadsheet. Inadequate tools is one of the biggest obstacles to proper application of regression analysis. Valuation is a concern as well as the security and consistency of the inputs and results. If you are going to apply regression analysis you will want to do so consistently and predictably over a wide range of hedges and be able to track your inputs and repeat your results for your auditors.

Obtaining appropriate market data is another critical part of designing your regression test. As part of your documentation, you must define what market data will be used to test for effectiveness. This is more than simply indicating that fixings will be taken from Bloomberg or another rate source. For instance, if you have already decided that you have a commodity risk and that you will regress on futures prices, the next question will be at what frequency will the futures prices be observed? Weekly? Monthly? Quarterly? For a short-term hedge, you might even require daily prices.

The frequency is driven by how many data points you need to perform a valid statistical analysis – most auditors recommend a minimum of 24 to 30 – and by the length of the look-back period. The look-back period should generally be consistent with the duration of the hedge, though it may need to be longer if market data is not available at sufficient frequency to obtain the required number of data points. For instance, if futures prices for linerboard are only available on a monthly basis, then you may need to look back two years or more to obtain a sufficient number of data points even though your hedge is only one year forward.

A final factor to consider and document is what you will do when a gap is found in the data. For instance, if you need a monthly price for 31 May 2005 and it is not available you might look back to 30 May or forward to 1 June to find an approximately contemporaneous price. Or, you might interpolate between the 30 April and 30 June prices to estimate the 31 May price. Finally, you might drop the 31 May price altogether and perform the regression without it, thereby increasing the importance of the remaining prices.

Once you have defined a regression test, the final task is deciding how to interpret the output and translate it into a determination of whether the hedge is highly effective. Many statistics are produced from a regression and the analysis of variance that goes with it, but which statistics are important and what do they mean? The statistic predominantly discussed is R2, which explains the portion of the change in the derivative that is explained by changes in the exposure. The SEC and audit firms agree that a value for R2 higher than 0.8 is a precondition for determining that the hedge is effective. Another often-quoted statistic is the slope of the best-fit line between the data points. The slope is frequently interpreted in the same way as a dollar offset test and should be between 0.8 and 1.25 when regressing on price or -0.8 and -1.25 when regressing on fair value since the derivative should offset the hedged item. R2 and slope and are often recommended together.

R2 and slope indicate whether there is a high correlation and thus potentially a highly effective hedge; but it is important to look also at the statistical validity of the regression. A t-test or f-test is necessary to prove that the results of the regression – namely R2 and slope – are valid at a given confidence level, typically 95%. The values related to these tests include the t-statistic, the p-value, the f-statistic, and significance f. All of these statistics can be calculated using Excel. Whether using Excel or another software package, however, it is important to understand which are the key statistics and how they are used. Above all, you must document which statistics you will rely on and what values are necessary to determine that the hedge is effective.

Regression analysis is a proven and accurate method for hedge effectiveness testing that is now preferred by most audit firms. By considering the factors addressed in this article you will be able to document a test that will accurately represent and reliably assess your hedge and withstand an audit.

Regression analysis is flexible and may be tailored to the hedging program and risk management objective. Whatever test you decide to use, you must ensure that it accurately reflects the risk you are hedging and that it is applied consistently.

Reliability, consistency and flexibility come at the cost of complexity and time. A small hedge program might be effectively managed within a spreadsheet, but for a larger program or multiple hedge programs, a dedicated software solution is the most cost-effective and audit-proof way to implement regression.