*Via ConvergEx's Nick Colas,*

In the Q&A period during yesterday’s Federal Reserve Chair press conference, Janet Yellen was careful to describe the projections made by Fed officials on future interest rate policy as point estimates. **The implicit caveat here is that every “Dot” on the Fed’s chart of expected future Fed Funds rates carries its own confidence interval – a statistical range with the dot at the center.** Today we take Chair Yellen’s observation to heart, and ponder what range (rather than simple average) of potential future rates is most likely.

For example, the average projection for 2015 year-end Fed Funds is 1.27%, but the standard deviation of the 17 estimates that make up that mean is 0.71. Recall your college statistics: that means that a range of 0 to 2.7% covers 95% of the likely outcomes for Fed Funds by the end of next year. Based on this math, it isn’t until 2016 that an increase to Fed Funds becomes a statistical certainty, with a 2.7% mean estimate and a range of 0.75 – 4.7% Fed Funds at a 0.98 standard deviation.

**Bottom line: forget the averages - markets actually aren’t far off the Fed’s estimates – they’re just shading their bets to the lower end of the curve.**

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**Market sage and Yankee great Yogi Berra said it best: “It’s tough to make predictions, especially about the future.”** He would have hated working at the Federal Reserve – or Wall Street, for that matter – where forecasting is an important part of the job. At the same time both baseball and market projections do have one thing in common: it’s more about your averages than any specific at-bat or play. Even the best traders on the Street seldom have win ratios better than 60%. And Yogi “Only” had a .285 batting average over his career at the Yankees and Mets.

**All that is worth keeping in mind as you look at the projections made by Federal Reserve officials for where Fed Funds will be at the end of 2015, 2016, 2017, and the longer run.** This is the now-famous “Dot Plot” chart that got so much attention at today’s press conference with Fed Chair Janet Yellen. There’s a link to the document at the end of this note, but the basics are as follows:

The Federal Reserve regularly surveys members of the Federal Open Market Committee on their opinions regarding “Appropriate monetary policy in the future”.The Fed defines this as “The future path of policy that each participant deems most likely to foster outcomes for economic activity and inflation that best satisfy his or her interpretation of the Federal Reserve’s dual objectives of maximum employment and stable prices.” The information is part of the central bank’s “Summary of Economic Projections”, or SEP for short.

One of the more interesting nuances that Chair Yellen highlighted in her Q&A session with reporters today was the need to think about such projections as merely a point along a continuum.An estimate of 1% Fed Funds at the end of 2015, for example, did not include how certain the respondent actually was in making that projection. That’s an important point, for how valuable is an estimate of 2 percent if the respondent could also tell you that they really thought the range was zero to 4 percent?

The capital markets, however, do tend to focus their analysis on the average of these estimates.Today’s Fed dot plot, for example, showed a mean estimate for year-end 2015 Fed Funds of 1.27%, up from the average of 1.2% that the Fed published in June. For 2016, the average rose to 2.68% from June’s 2.52%. Longer dated bonds like the U.S. 10-year Treasury sold off after the Fed release, closing the day at a yield of 2.60%, up from the 2.56% level right before the release. The change in the Dot Plot seemed to play a role in that move.

**Taking Chair Yellen’s advice to heart, we got to wondering: just how much certainty does the Dot Plot actually express?** To assess that, we ran the standard deviation for each year’s projections: 2015, 2016, 2017, and what the Fed calls the “Longer run”. A few points here:

If you want 95% certainty that the Fed will raise interest rates, then 2015’s estimates in the Dot Plot will not provide that level of conviction.Here’s the problem in a nutshell. The mean estimate for the 17 projections in the SEP is for Fed Funds to end next year at 1.27%. At the same time, the standard deviation of those estimates is 0.71.

Recall your college statistics: in a normally distributed population, you need 2 standard deviations on either side of the mean to cover 95% of the dataset.In this case, that gives us a range of negative 15 basis points (essentially zero) to positive 2.69%. In other words, Fed Funds could stay at zero for another year and still be consistent with the probabilities expressed by the Fed’s Dot Plot.

The story changes for year-end 2016, where a similar statistical analysis shows that the FOMC absolutely believes Fed Funds will be at least 74 basis points.The math here: a mean observation of 2.70% for Fed Funds, and a standard deviation of the Fed’s estimates of 0.98. The same holds true for 2017, where Fed Funds should be at least 2.32% (mean of 3.54, standard deviation of 0.61).

Going out to the FOMC’s “Longer run” projections, the average here is 3.79% and a quite small 0.26 standard deviation.That’s a much higher degree of certainty than the 2015-2017 forecasts, indicating that the FOMC does have a lot of conviction over where they would like to see rates normalize. One odd historical point: the year end 2006 Fed Funds rate was 5.25%, and 4.25% in December 2005. Why doesn’t the FOMC think these (higher) rates are more appropriate than the lower point estimates for retarding the advancement of unwelcomed developments like asset bubbles?

This math provides an alternative explanation for another question posed in the press conference yesterday, highlighting a paper out of the San Francisco Fed (Chair Yellen’s “alma mater”).Essentially, the problem is this: why does the public (as expressed in the prices for financial assets, for example) “Expect a more accommodative policy than Federal Open Market Committee participants”?

Our statistical analysis shows one possible answer: the point estimates in the FOMC’s Dot Plot yield an artificial accuracy than markets and the public understand is actually a bit fuzzier than what the simple average shows.It’s not that asset prices are at real loggerheads with the FOMC. Rather they are handicapping the possibility that the Fed’s projections will change – modestly and in line with statistical ranges – downward over the course of the next 12 months.

__ In summary, the Fed’s Dot Plot may look like a precise set of forecasts, with a series of purposeful markings meant to portray certainty and conviction.__ The math, however, says something else entirely. Ambiguity is part of life, either as a central banker or investor. As Yogi once said while giving directions to his house: “When you come to a fork in the road, take it.”