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What's the Probability?

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Leading into the June 25 FOMC decision, market pundits speculated on what the FOMC might decide. Based on the Fed funds, many said, no rate hike was expected. Leading into the August 5 meeting, you'll hear speculation rise again.

They were right, but how exactly did they make that calculation? How does one calculate the probability of a rate hike or cut? Can you do it for yourself?

Certainly you can, but you don't have to. Someone else does it for you.

If you wanted to calculate that number for yourself, your calculations begin with a look at the CME Group's 30-Day Fed Funds futures contracts. A Fed fund rate is the rate that banks assess each other for overnight loans of reserves that the Fed holds. The futures track that effective overnight rate for a specific month. Originally traders would have found this information at the Chicago Board of Trade (CBOT), but the information is now migrating to the new CME Group website after the merger of the two.

CME Group says that the 30-Day Fed Funds Futures provide a "view on the direction of the Federal Open Market Committee (FOMC) policy," among other benefits. Options are available on those futures. If a trader looks at those options on the 30-Day Fed Funds futures for a specific month in the future, that trader should get a rough idea of what the FOMC will be deciding in that month.

Exactly how is that done? Well, there's a simple way and a complex way. Edward Talisse discussed a simple method in "Predicting the FED Funds Rate" in an article picked up by Yahoo. Those 30-Day Fed Fund futures have different maturity dates, of course. To calculate the market's prediction of where the Fed's target rate will be on a specified date in the future, you subtract the price of the 30-Day Fed Fund future for that date from one hundred.

For example, as this article was first prepared on June 27, 2008, the futures expiring March 9, 2009 were last at 97.360. If that's subtracted from 100, that results in an expected target Fed rate on March 9, 2009 of 100.000 - 97.360 = 2.64 or 2.64 percent. That's 64 basis points above the current Fed rate of 2.00 percent. As this article was edited prior to publication midmorning on July 25, 2008, futures expiring March 9, 2009 were then at 97.475. That results in a new expected target Fed rate on March 9, 2009 of 100.000 - 97.475 = 2.525 or 2.53 percent. That's still more than 50 basis points above the current Fed rate of 2.00 percent, but expectations for higher rates are ebbing.

Midmorning that Friday, July 25, 2008, futures expiring September, 2008 were 97.940. That equates to a Fed rate of 100.000 - 97.940 = 2.06, only six basis points above the current Fed rate of 2.00 percent. The FED tends to move in multiples of 25 basis points (or quarter-point moves), so the expectation did not seem high that the FOMC would raise rates between now and September.

Quotes for the 30-Day Fed Funds futures can be found at www.CMEgroup.com by clicking on "Quotes" in the blue bar on this page: http://www.cmegroup.com/cmegroup/trading/interest-rates/stir/30-day-federal-fund.html

A more difficult calculation may be arrived at by employing the Taylor Rule, developed by the Stanford economist and former U.S. Undersecretary of the Treasury John B. Taylor. That calculation requires inputs for the inflation rate and real GDP gap, and it's meant to tell us what the Fed Funds rate should be, not what the FOMC will necessarily do. Whether or not the Fed decides to hone in on that rate depends on whether they agree with the inputs, their expectations on how the economy might shift away from some of the current inputs, and a multitude of other factors. Does one use the PCE (Personal Consumption Expenditures) to estimate inflation or some other measure?

I don't know. I have enough difficulty determining what I think might happen next with the stock market without having to figure out the whole economy and whether the Fed will agree with my assessment. However, if you want to dig in, Talisse provides this simplified form of the Taylor Rule calculation, with r = the Fed Funds rate, p= the inflation rate and y = the real GDP gap: r = 1.5p + 0.5y + 1.0.

John Hussman of Hussman Funds (www.hussmanfunds.com) explains that what this formula is doing is adjusting for inflation. In the Fed's ideal economy, inflation would be two percent, so the FOMC would tighten if inflation rose above that and ease if the economy weakened too much. In a June 9, 2008 article, Hussman surmised that the Fed has to operate in a "regret-minimax" mode. When conflicting needs arise--such as a need to tame inflation and a need to not to put further dampers on a weakening economy--the Fed must act in the way that "minimizes the maximum possible loss." In other words, if it's going to ultimately cause more harm in a weakening economic climate to raise rates than to risk holding off on tackling inflation with the hope that it would ease anyway, the Fed is unlikely to move.

The Taylor Rule is not the only method for calculating where the Fed's target rate should be. But in most cases, when someone on CNBC discusses predictions for the Fed's target rate, that person is not referencing either the Taylor or any other such rule. That person is likely referencing the simpler calculations made from looking at where the 30-Day Fed Funds futures prices are at a particular maturity.

The Fed may be looking at it, too, gauging what the market's expectations is. Hussman says that "even the policy makers themselves don't know the 'true model' determining the course of economic growth, inflation, employment, exchange rates and other variables." We know, too, that our Fed doesn't like to shock markets, either, with an unexpected move, unless that shock is to shorts who are occasionally surprised by a pre-market move by the Fed when equity futures were getting slammed. Some believe that the Fed doesn't dictate to the markets where target rates should go: that it's the other way around, and that it's those prices on Fed Fund futures that do the talking.

We know that the Cleveland Fed is watching those futures, at least. For those of you who don't want to check the futures on the CME Group's site, the Cleveland Fed is glad to do all the calculations for you. The URL http://www.clevelandfed.org/Research/data/Fedfunds/index.cfm sends market watchers to the Federal Reserve Bank of Cleveland's research section titled "Fed Funds Rate Predictions."

You'll find charts that list the probabilities of all kinds of outcomes for the next couple of Federal Reserve meetings, updated daily. For example, as of midmorning on July 25, 2008, the August Meeting Outcomes chart showed the probability of a 2.00 percent rate--unchanged from the current rate--at the August FOMC meeting higher than the probabilities for any other rate graphed, with those rates ranging from 1.75 to 2.75 percent. The chart showed the probability of no change at the August meeting at almost 0.90 or 90 percent.

August Meeting Outcomes from the Federal Reserve Bank of Cleveland:

The Cleveland Fed's page currently has charts for the next two FOMC meetings, so also produces one for September. For a while in early June, the September Meeting Outcomes chart had shown that the possibility of a rate hike to 2.75 percent by the September meeting had gained favor. Currently, however, that chart shows a more than a 50 percent probability that the target Fed rate will remain the same, with all other probabilities being less than 20 percent.

As long as you don't try to read through the pages of information on all the assumptions that go into that chart, including assumptions required for the "single meeting estimation technique" and "nonnegative probability constraint," the easiest way to obtain a current take on probabilities might be to bookmark that Cleveland Fed page. One advantage is that market watchers are provided with a visual of how expectations are changing over time. The Cleveland Fed also nicely benchmarks such events as the Beige Book release. Some market watchers, however, will want to check those predictions more frequently than once a day. Looking directly at the Fed Funds futures and making that quick calculation will provide a rough-and-ready estimate of what might happen.

At least now, however, you'll know what they're talking about on CNBC when someone says that Fed funds futures are predicting a certain move by the Fed by a certain time.

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