Interpreting fed funds futures

Despite what you may have read elsewhere, the probability of a fed funds rate cut has increased significantly over the last few weeks.

Felix Salmon and Barry Ritholtz seemed to find more merit in this analysis from WSJ Real Time Economics than I did.

Since the stock market began to sink a week ago, the federal funds rate for next January, as implied by futures markets, has plummeted to 5% from 5.2%. As a result, the implied odds of a quarter-point rate cut from the current 5.25% are said to have risen from 20% to 100%.

Well, nobody in their right mind would ever describe the odds as 100%, but let us not get diverted.

Lou Crandall, chief economist at Wrightson Associates, says while such action is commonly attributed to increased expectations of a Federal Reserve rate cut, that would be a mistake. The real reason, he said, is that investors are fleeing risk and seeking safety in Treasury bonds and bills and other high-quality paper, sending their prices up and yields down. As a result, the entire yield curve has shifted down. To maintain parity with that lower yield curve, the implied federal funds rate also has to drop, he says.

Mr. Crandall says, “99% of the universe, including a lot of people in those trades, don’t do it because they think the Fed will ease but because that’s the way the yield curve is shaped.”

But wait a minute: isn’t that a violation of efficient markets? If fed funds futures were out of line with a realistic expectation of Fed action, couldn’t smart people take positions in the mispriced futures and make a bundle six months later when it turns out the Fed didn’t cut rates? And shouldn’t such arbitrage push expectations of the Fed and pricing of futures back into line?

No, says Mr. Crandall, for two reasons. First, the Fed has gotten more predictable but gives no guarantees on where rates will go, so there is no assured profit on such a trade (so it wouldn’t really be arbitrage). Second, “The amount of money backing people who have opinions about where the Fed will be in six or nine months is dwarfed by the amount of real money being invested in short-term credit markets.” Nervous investors are willing to accept a lower yield than what might ordinarily be justified based on the economics in exchange “for safety. Market participants know that perfectly well. That’s why it’s called a flight to quality.”

The first odd thing about this statement is that it seems to suggest that there are two competing theories of how fed funds contracts get priced. The first theory evidently claims that the contracts reflect investors’ expectations of Fed actions, and a second, supposedly contradictory theory claims that the contracts just follow the Treasury yield curve, as if we have to choose whether the fed funds futures contracts are priced in a way that is consistent with expectations of what the Fed is going to do or if instead they are priced in a way that is consistent with the yield curve.

But of course the answer is that they are priced in a way that is consistent with both. These and every other financial market are responding to exactly the same news that we’ve been discussing here, and drawing the same conclusions as we have. The latest economic news points to a considerably higher likelihood of economic softness, a situation in which the Fed will want to lower the funds rate and short-term interest rates will come down. That scenario is priced in the fed funds futures, in the term structure of Treasuries, in the stock market, in foreign exchange, and what not. Here’s what’s been happening over the last few weeks to the price of the November fed funds futures contract, the simple-minded interpretation of which (and the one that I favor) is that the expected fed funds rate for November has now fallen to 5%.

Price of November fed funds futures contract (subtract from 100 to get implied interest rate). Source: Chicago Board of Trade

A second idea in the statement quoted above is the suggestion that one needs to add a significant risk premium to that fed funds futures calculation in order to arrive at the objective expectation of what the fed funds rate will be. It is true that risk premia play a role
in the Treasury term structure, and fed funds futures should incorporate that same risk premia. A recent paper by Monika Piazzesi and Eric Swanson
finds some indication that risk premia may play a role in longer-horizon fed funds contracts. But evidence for significant risk premia operating in very short-horizon fed funds contracts is much harder to find,
as indeed theory predicts it would be. In recent years the Fed’s actions have become much easier to predict. As the accuracy of your forecast improves and the time horizon for your forecast gets smaller, the risk premium necessarily shrinks, and the risk premium on something you know with certainty has to be exactly zero. Perhaps Crandall is right that risk premia could be playing some role in the January fed funds futures contracts. But I find this story much less plausible for October or November contracts, and, as the figure demonstrates, movement in these was quite dramatic this week.

My guess is that we will indeed see a cut in the fed funds rate by the October 30/31 meeting, if not sooner.

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31 thoughts on “Interpreting fed funds futures

  1. praguetwin

    I’d be curious to know what your view was late last year when the odds of a rate cut by May were also very high (although admittedly not as high as current levels). I have consistently maintained that the Fed will not cut rates due to persistent inflation pressures. I’ve been beating the street on this for nearly a year now.
    Unless the Fed sees a financial crisis looming, they really have no reason to cut rates as 5.25% is still quite low by historical standards.
    Should inflation remain persistent, and the dollar continues to weaken, how does the Fed justify a rate cut?

  2. stan jonas

    Pretty silly to read something like that in the Wall Street Journal….and from an ostensible professional..
    Of course your comments are dead on..
    Probability is a tricky word.. here we are dealing what should be called “definetti bilities”
    PROBABILITY DOESN’T EXIST.. its just your best guess today|given your information…
    There is no “objective” right anser out there.
    That said..if you look at what the market is pricing.. AN EASE BY OCTOBER IS THE LEAST OF IT..
    If the FED eases at the December FOMC (by December as you would say)… the December FED FUNDS futures would be at 94.93….
    The are trading now at 94.06 ++,,
    Ergo.. there is more than ONE EASE by DECEMBER being prices.. actualy in “probaiblity terms”
    35% probaiblity..
    That is and this is the only way probability makes sense.. you can today.. if you wish.. make a bet.. pay 35 dollars and get back 100 (make 65) if and only if the FED eases twice by December of 2007..
    By the same token the probability of an ease “at” the October FOMC is closer to 40%…
    The interesting “fact” is that the market is pricing around 15% probability that the FED will EASE at the August FOMC is you like… and then around 25/30% probability again (bet) that they will ease at the September FOMC..
    And since in this Universed October is after August and September… when you add up all those numbers you get close to 100% of something..
    But this are conditional numbers…
    What you can say is that if they don’t go in Augys and or September… I think the probability is 40% that they will go by October…
    This is the number “non professionals”… i.e those not in the Market or the FED which knows how to do the calcuations.. locks at…
    By the way one Question…
    On Friday… surveys were taken of all the economists working for banks etc. in the marketplace..
    Of the 20 Economists polled all gave a forecast that the FED was on hold till December.. i.e zero probability of an EASE.. except of Course Bear Stearns who “ironicaly” believes they will tighten… oh yes Cantor Fitzgerald apparently thikns they will ease next week..
    Now of course the right answer is either zero percent or 100%…but I’ve never seen such a disconnect ..

  3. Anarchus

    I was listening to Bear Stearns’ conference call on Friday — when the call started at 2 pm, BSC shares were trading up a tad at $116 and after 30 minutes of confidence-building by management the shares were down $7.50 to $108.50 where they later closed. The main problem seems to be that they honestly and credibly described this mortgage market as as difficult as any they’d ever seen, which is pretty similar to what Lyle Gramley had been saying earlier in the week but for some reason investors chose to be surprised by the description.
    Semi-credible sources suggest that the NY Fed was injecting liquidity on Thursday afternoon and Friday, which would be the intelligent thing to do under the circumstances but not likely adequate to forestall a financial crisis if in fact one is coming.
    The Fed meeting next week will be very interesting – if the FOMC only goes to neutral and says they’re monitoring market liquidity carefully, I suspect we’d see a frantic sell-off. And if the FOMC cuts rates by 25-50 bp to get in front of the liquidity crisis, we’d probably also have a sell-off for a half-day or day or two, but that’d be the right thing to do, I think.

  4. esb

    I agree with you completely that the ‘language’ of the next statement will be the ‘tell all’ which colors the character of trading in the financial markets (probably worldwide) for the period immediately ahead.
    BB will either signal that he embraces the Easy Al put or signal that the sea of liquidity is going to be allowed to go away.
    My position is this…having built an economic construct which REQUIRES massive lending to those who cannot pay in the absence of substantial and unending inflation was an act of insanity. Trying to make such borrowers and their lenders and successors in interest whole compounds the insanity and should not be done, come what may.
    The bat is swinging and should be allowed to interact with the financial teeth of those who participated as borrowers, intermediaries, enablers, lenders and successors in interest in the residential real estate mania now imploding. The consequences of assuming risk (knowingly or unknowingly) must be reintroduced into the decision making processes that are the foundation of resource allocation.
    Like you, I will be reading the statement very carefully at 11:15:01. And like you, I anticipate that the way it tips will have profound implications for my decisions and future wealth.
    And if the turn is in the direction of the Easy Al put, then I will leave you with just two words.
    ‘Got gold?’

  5. peter from oz

    I agree with you about the financial teeth and this is too widespread to focus on one LTCM as a signal!
    inflation already fuelled by such things as Iraq must be the overriding factor
    however there is nothing in gold or other commodities this time around to indicate they won’t be in lock step with an across the board asset sell off
    rgds pcm

  6. GWG

    I would be interested to hear your thoughts on the federal funds rate prediction as calculated by the Federal Reserve Bank of Cleveland using options on federal funds futures.
    The most recent data show that the most likely outcome from the October Meeting is that rates stay at 5.25%, but the implied probability (as they calculate it) has fallen to around 60% from as high as 90% about 1 month ago. The odds of a cut to 5.0% by October are less than 20% while the odds of a 75 b.p. cut are slightly greater than 20%.
    The FRB of Cleveland methodology seems that it would be more accurate than just using prices of fed funds futures since it takes into account more possible outcomes than just a 25 b.p. cut.

  7. Anonymous

    So I guess the question is will the Fed sacrifice the dollar to prop up Wall Street, yes?

  8. Anarchus

    I used to know a fellow who’d been a fairly senior undersecretary in Treasury back under James Baker. He swore that (a) the Fed didn’t care much at all about the dollar exchange level (in part because it was impacted by so many factors outside Fed control and in part because “dollar stability” isn’t in the Fed’s job description – THAT responsibility falls within the Treasury Dept’s portfolio of duties, and (b) defending soft currencies with only a couple of tools (intervention, monetary policy) was a bit of a fool’s errand.
    Based on that input and watching Fed actions over the past 25 years, at this time I think the odds of the Fed not reducing rates because of concerns over the dollar exchange rate are about 1/1,000.

  9. oops

    a year or so ago the fed funds fuures had a full point of cuts built in to the price of the mid ’07 contracts.
    maybe the macro crunchers will get somme of their money back after that crap trade.

  10. joe

    Dear Professor Hamilton,
    Is shrinking risk premia as the time to maturity approaches zero the same thing as saying that the expectations under the EMM measure is approaching the expectation under the physical measure? Are there any writings on this phenomenon in the macro literature?

  11. Mike Laird

    Deja vu. This is the same stuff that was all over Wall Street in the spring. The Fed didn’t cut rates. In the short term, markets over-react – especially in sharp down turns. That’s all we’re seeing. Praguespring (above) is correct. The Fed will not cut rates while overall inflation is 4% and the US dollar trades near a multi-year low. Just think about the domestic and international reactions if they were to do so in this situation. Forget about a couple numbers from a climactic trading day.

  12. JDH

    GWG, I’m thinking those Cleveland numbers are not based on Friday’s closing options prices. There were certainly big moves in the futures on Friday alone.

  13. JDH

    Joe, that’s exactly right. The pricing kernel is a random variable whose mean has to converge to unity and whose variance has to converge to zero as the time horizon becomes shorter. Here’s a link to my paper on this.

  14. muckdog

    The reality is that the two goals of the Federal Reserve (low inflation and low unemployment) are being met. Year over year rate in core inflation is under 2%. The unemployment rate is below 5%. The economy is growing moderately. Wages are up, but so is productivity.
    The only thing wrong right now is a small percentage of subprime loans. In addition, real estate speculation peaked in 2005 and the whole bubble is deflating. Not much of an impact to most of us who are employed and making our monthly mortgage payments.
    The folks taking the brunt of the pain are the latecomers. Those who bought $500,000 homes on a $40,000 income and had incorrect data on their loan applications.

  15. SJONAS

    If you have access to a Bloomberg.. you might want to get acquainted with their page FFIP..
    It uses both the tradition futures binomial path methodology.. as well as the Cleveland fed’s option constrained method.. as well as calibrating it with Euro’s..
    It’s live.. and they store the data in a convenient format.. in the real world if the data isn’t on Bloomberg it doesn’t exist..
    By the way on Friday.. the clevland.. FED data.. implied appoximately a 50% probability that the FED would ease 50 basis points by December..
    not quite the same thing as certain of one EASE…

  16. Mike Laird

    Muckdog is just wrong on his facts and view of expenses. Year over year (June to June) core inflation is 2.6% – that’s greater than 2% the last time I looked. But real people purchase food and energy so core inflation is not a useful inflation measure for anything beyond month to month comparisons. The All Items measure is up 4.3% on the same year over year comparison. This is what real people spend. Its also a lot higher than 2%. Oops, productivity is declining – see todays announcements. And, the mortgage problems are a lot broader than sub-prime, if you have been reading recently. Alt-A and standard mortgage defaults are rising rapidly in recent months. Variable mortgage expenses will triple in October (over 1stQ levels) and bruise yet another large group of home owners. Yes, in the short term its the problem of over-stretched home buyers, but defaulting the house is the last thing to go. Before default, purchases of all other goods and services get cut back, hugely by most people, and this reduces GDP growth for all of us. The question is how many people stay employed making mortgage payments for how long? No one knows.

  17. Lord

    I wouldn’t say this is just a problem for late comers. Rates are skyrocketing and access declining even for prime buyers. A credit freeze is now underway.

  18. Jake Miller

    Fed statement seems to indicate they’re still worried about inflation, and the markets dive down as a result. My guess is that there’s an ease or two on its way over the next 6 months, as the mortgage mess continues to work its way through, but we’re too close to stagflation status for the Fed to want to cut much further.
    Of course, if we had members of Congress willing to look into fiscal policy as a way of controlling demand over the last 6 years (instead of constantly trying to expand it), maybe the Fed wouldn’t have to worry about inflation as such a risk.

  19. esb

    It appears that BB has a complete set of cojones as opposed to the “magnifying glass and tweezers” variety of Easy Al. How absolutely refreshing to witness an American central banker who understands the ultimate danger in attempting to ‘borrow ourselves rich.’
    And with reference to my earlier posts in this thread, the swinging bat is being allowed to come into contact with the financial teeth of all categories of the participants in the residential real estate insanity now imploding.
    To which I respond with an enthusisatic ‘Amen.’

  20. kio

    Likely it is associated with stocks an d bonds aswell. I would be interested in you opinions in the first place.
    Id like to explain macrovariables as driven by pure population effects.
    S&P500 is an example. I have carried out a research, which I did not finish yet for a publication.
    Imagine that SP500 is a linear function of the change rate of 9-year-olds. (Same I made for real GDP, as I mentioned in one of you previous posts). So, for returns
    dln[SP500(t)]= A+B*dln[N9(t)]
    A and B empirical coefficients.
    Having monthly readings of both variables one can obtain the following plots.
    Figure 1.
    Comparison of observed and predicted monthly returns. The observed returns are MA(12).
    Figure 2.
    Cumulative observed and predicted returns from Figure 1.
    Figure 3.
    Difference between the predicted and observed returns. Notice the absence of any trend and heteroskedasticity.
    Currently we are near the peak. Likely, a drop will come soon (It has come).
    Notice, however, that coefficients are different after 2

  21. GT

    “But of course the answer is that they are priced in a way that is consistent with both.”
    Yeah, I noticed.
    How about Stuart Staniford. How about the fact that 8.6 mbpd is looking consistent with the fact that he was and continues to be dead wrong.
    That oil production is a serious enough topic so that “a” situation cannot be “consistent” with both this and that.
    You can avoid this as long as you and Stuart like. Sooner or later you are going to have to pay the piper. For your sake, I suggest dumping Stuart as the intellectual fraud that he is.

  22. kharris

    Not to be too nice to Muckdog, but Mike Laird is confused about what it means to be “just wrong on his facts and views of expenses.”
    The Fed is far more interested in the personal consumption deflator data that in CPI, finding it a better measure of consumer price inflation. The Fed also prefers core as a policy guide, for a number of reasons that are readily available in Fed research and speeches. Mike Laird disagreeing with Fed officials does not make Muckdog wrong. The core PCE deflator rose at a 1.4% annualized pace in Q2, and was up just 2.0% y/y, vs 2.4% in Q1. That shows both that the inflation measure that policy makers prefer as a policy guide has come down to the high end of the range most Fed officials prefer, and that the trend is toward lower inflation.
    Mike does has a better point when it comes to conditions in credit markets. Trouble has spread well past a narrow range of subprime borrowers from 2005. The issue for the Fed is the extent to which trouble in credit markets spreads to real economic activity. A low unemployment rate now is not the Fed’s main concern. The Fed attempts to figure out where the unemployment rate is most likely to be a few quarters down the road. If inventory finance becomes difficult (watch the commercial paper market) or orders begin to slip, the Fed will take that very seriously. Today’s “woopsie” by the ECB when the libor/funds spread spiked up is evidence that a major central bank was worried about a failure in short-term corporate finance.

  23. JDH

    GT, your hostility to Stuart remains somewhat puzzling to me. Whatever its explanation, I would encourage you to debate specific claims with specific facts, rather than just offer your dismissive opinions about personalities.

    You seem to have a zealous mission centered on what you regard as a prediction by Stuart Staniford that Saudi production will continue to decline at 8% per year. I do not know that Stuart ever made that prediction, and if you think he did, then I suggest that this is not the best forum in which to pursue that debating point.

    But since you raise the issue here, let me attempt once again to respond. The consensus assumption seemed to be that Saudi production would soon exceed 10 mb/d. Stuart offered arguments why that will never happen. So far, I would say the facts have been quite consistent with Stuart’s position.

    So let’s hear your prediction, GT. Will Saudi production exceed 10 mb/d soon? If so, why? If not, why not? I’d be much more interested in hearing you try to engage specific questions like these rather than continue to indulge your emotion-laden criticisms of Stuart.

  24. esb

    Actually, I think that the ‘major central bank’ just discovered that a major entity (financial or other) got caught leaning the wrong way with far too much leverage, and it will not be the last firm that is badly positioned.
    Ever notice that when the ‘illusion of wealth’ starts to disappear people begin to insult each other?
    We should all realize that calling someone an unpleasant name will do very little to restore the previous value of a portfolio.

  25. Hal

    A couple of points –
    First, here is a link to graphs from the Cleveland Fed showing their calculations of imputed market probabilities for Fed moves in the various meetings, based on Fed fund futures and options prices:
    The December situation looks a little pathological as the most likely outcome is to stay at 5.25%, but a drop to 4.75 or 4.5% is seen as more likely than 5.0%! Perhaps this oddball result points to the general turmoil and uncertainty in the markets. The Fed is, as they say in certain parts of the country, between a rock and a hard place, and some traders see the rock while others are more worried about the hard place.
    On the other point about “which interpretation is right”, the answer being “they both are”, the same thing arises with regard to oil futures. Some people say that oil futures predict future oil (spot) prices; others say that oil futures are merely today’s prices plus carrying charges (storage fees, interest rates, etc.). Which is right?
    The answer is, they both are. The resolution of the paradox is that today’s prices are the result of expectations of future prices as much as future prices are the result of today’s prices. These constraints keep both sets of prices consistent while still allowing futures market prices to match expectations of what future prices will be. The reason spot prices are high today is in part because of fears of serious oil shortages in the future. One example of how this can manifest is OPEC not knocking itself out to increase production today, when it sees oil as potentially being far more valuable in a few years.

  26. Anarchus

    Still can’t figure out what on earth triggered the inexplicable stock market rally for a day and a half in the wake of the FOMC announcement, but the credit/liquidity crisis is snowballing ahead at an accelerating pace:
    FROM the Financial Times – “ECB injects 95bn to help markets”
    Published: August 9 2007 12:59 | Last updated: August 10 2007 01:33
    The European Central Bank scrambled to head off a potential financial crisis on Thursday by pumping an emergency 94.8bn ($131bn) into the regions banking system after liquidity in the interbank market started to dry up, threatening banks access to short-term funds.
    The cash injection was the biggest in the ECBs history, exceeding the 69bn provided the day after the terrorist attacks of September 11 2001. The ECB also made an unprecedented one-day pledge to meet 100 per cent of all funding requests from financial institutions . . . . . .
    I am worried that Dr. Bernanke may be overly focused on inflation and not entirely cognizant of how difficult it can be to restore confidence when the financial system is utterly panicked to the core.
    There are a considerable number of very large cap financial companies in the U.S. and Europe that are COMPLETELY dependent on their ability to roll billions of $ of commercial paper on an overnight basis . . . . . . . “an unprecedented one day pledge to meet 100% of all funding requests” by the ECB is pretty telling, I think, and as much as I hate agreeing with Crazy Jimmy Cramer, I think the Fed Chairman is missing in action on this one.

  27. Ivan Kitov

    I was lucky to get scaling for tmy previous post on SP500. The new scale corresponds to the drop in yearly returns during the last several days. So, the new plot for the MA(12months) SP500 returns is as follows.
    In previous comment (
    July 9, 2007), timing of the current drop was perfect. SP500 will reach a new bottom value in the next two months of around 1330.
    Figure 1
    Comparison of observed and predicted monthly returns. The observed returns are MA(12).
    Figure 2.
    Cumulative obserevd and predicted returns from Figure 1
    Figure 3.
    Difference between the predicted and observed returns

  28. Anarchus

    Another tough night in the Euro markets:
    “The fact that [the ECB is offering more funds] means there’s a serious problem,” said David Mackie, European economist with J.P. Morgan in London, “but if they weren’t responding to the serious problem you’d be even more worried.”
    Today’s tender differs from Thursday’s, when unlimited funds were offered at a guaranteed fixed 4% rate, as the money-market overnight rates shot up to 4.7%. Now, the ECB says it will assess how much liquidity the market needs, and – just as in the ECB’s weekly refinancing operations — market participants must submit bids for the cash, at a minimum 4% bid rate.
    Earlier Friday, Japan’s central bank injected 1 trillion yen ($8.39 billion) into money markets amid a stock-market plunge in Friday morning trading there following a sharp decline on Wall Street overnight.
    If not today, I’d guess the U.S. Fed is going to have to step in next week or the week after at the latest. As the subprime problem has become an alt-a problem has become a CDO problem, we’re perhaps not far from a more significant institution running into overnight liquidity issues the way that American Home Mortgage got sucked under by its lenders. Stay tuned.

  29. Mike Laird

    kharris, I’d like to respond to your comments about the Fed and the PCE deflator.
    You are, of course, correct that the Fed, especially since Greenspan, prefers the core PCE deflator over the CPI. I find this a bit like the fox guarding the hen house – or at least defining the measures of how many hens remain. PCE is almost always lower than CPI. Of course, Greenspan or Bernanke would prefer that measure of inflation. Their preference doesn’t make it the best measure. As you know, PCE uses averages of category weights from the beginning and end of the period, whereas CPI uses a constant basket of category weights. Proponents of PCE say it captures consumers actual purchases as they make decisions while prices shift. I view that as budget adjustment action in the face of inflation. If budget adjustments are included along with inflation, one gets a mush in the resulting index. That is my opinion of PCE. CPI on the other hand keeps a constant basket of goods and services – hence the index change is price related – the very nature of inflation. The 12 months ending CPI in April had all items CPI of 3.5%. In June, this measure rose to 4.3%. This is what people buy, or attempt to buy if they don’t have to make budget adjustments because things become too expensive for their budget. The Fed can say PCE is 2% and declining, but this is not the common man’s purchasing experience in the past few months. Its just the fox getting to measure his own hen count. 🙂 And as Bernanke has said to Congress, things look good. It all depends on your perspective.

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