Here is how it compares to my very basic estimate, using treasury yields:

Now, the estimate I show in this graph is from a very broad analysis of treasury yields, with a blunt adjustment made to account for the asymmetry of the yield curve near the zero lower bound (ZLB). I have a more rigorous model that starts with Eurodollar futures data in September 2012, but the blunt estimate from treasury data fits the estimate from that model surprisingly well. (Below is a comparison of my two estimates since September 2012.) The graph above is similar to this previous graph that I posted. Keep in mind that the two graphs above measure the distance to the ZLB exit at any given time, whereas the graph in my previous post, and this little graph comparing my two models are showing the expected exit date on a fixed calendar.

And, the pattern fits the pattern of the estimate from the Fed pretty well, too, up to QE3. We both see a spike before QE2, which is reversed during QE2, before spiking again at the end of 2011 and moving sideways into 2012.

But, after that, they seem to move in opposite directions. My model shows the exit moving back, from 2.5 years to 1.5 years, from the beginning of QE3 until September 2013, when it levels off at about 1.5 years. The Fed model shows the exit date remaining fairly level, around 2 years, until September 2013, after which it declines steeply toward 1 year.

This is an important difference. My data would support what I would call the market monetarist version of events. The expected exit date had been moving ahead over time, so that we were not making progress on escaping ZLB. But, QE3 improved economic and inflation expectations, which stabilized the expected exit date until economic improvements in early 2013 caused the exit date to move toward us. Taper talk in June 2013, followed by the establishment of a tapering schedule later in the year, reversed some of these expansionary expectations, which moved the expected exit date back into late 2015. Continued improvements in the economic outlook, in spite of the taper, have continued to have a positive influence on the expected exit date. This is my interpretation, and I expect the exit date to remain fairly stable. I expect continued economic progress pulling the exit date back a little more, and my main fear is that the economy's inherent growth won't maintain enough momentum to overcome the slightly disinflationary effect of the taper, and the expected ZLB exit date will start to recede again. (Here is a more detailed review of summer 2013 rate changes.)

But, the Fed data would tend to support what I call the "Wizard of Oz" view of the Fed, which ascribes a powerful ability to target interest rate levels over time to the Fed. With this data, and in this view, QE3 signaled a plan from the Fed of holding rates lower for longer, so the expected exit date kept moving into the future, but with the talk of taper in June 2013 and the subsequent implementation after September 2013, the Fed has signaled that they will raise rates sooner than they had previously planned, so the expected date of the exit has moved back toward us.

**What's Up?**

My model is constructed by assuming that the range of possible dates for the ZLB exit is described by a normal curve. My model fits the forward yield curve to a curve defined by that normal distribution's mean and standard deviation, combined with the expected slope of the yield curve from that date. I am reporting the mean expected date of the ZLB exit, which, by assumption, is the same as the median expected date.

The Fed's model is much more sophisticated than mine, and they are measuring a set of inputs that, through Monte Carlo simulations, produce unique distributions of the expected exit date. These distributions tend to have a positive skew, which should be expected. The Fed is reporting the median expected date of the exit, which because of the skew, is sooner than the mean expected exit. This is why the Fed's expected median dates tend to be earlier than my expected mean dates.

It looks to me like the mean exit date from my model is stable, regardless of the shape of the distribution, at least within the range of skew that we have experienced. If the positive skew did become so excessive that a measurable percentage of potential ZLB exits would happen in the range of the yield curve where the slope levels off to the long term yield levels, it should cause my model to report a future yield curve slope that is slightly understated, and possibly slightly understate the amount of time to the mean. And some of the skew would increase the measured standard deviation of the distribution of the expected exit date, which makes the yield curve less convex around the exit date. I don't believe that these distortions were significant.

Now, while both the mean and the median would be useful if you are trying to assess the shape of expected outcomes and risks of taking positions on the yield curve, the mean date would be the more important measure for determining the intrinsic value of forward rate contracts. So, I believe that my measure is useful.

But, looking at both the mean and the median might allow a more fine interpretation of market reactions to Fed policies since the beginning of QE3.

Here is the mean from my model, compared to the median (estimated from the Fed graph above).

For a period in 2013, the median date of the ZLB exit was farther away than the mean date. That suggests a negatively skewed distribution, which seems implausible. I don't have the Fed's data, but either I am misunderstanding something here, or there seems to be either an error in the published chart or something wrong with the Fed data.

y-axis is Eurodollar contract price, which is 100 minus the interest rate. It is inverted, so that the graph represents the yield curve. |

Following are three charts comparing each of these specific yield curves, showing the estimated locations of the mean date of the exit from ZLB (from my model) and the median date of the expected exit from ZLB (estimated from the Fed's graph).

(A brief note on these charts.

The mean date appears to be shifted by 3 months, because
these are 3 month Eurodollar contracts.
So, if the first rate increase is in September 2015, the June 2015
contract would be the last contract settled at the ZLB and the September
contract would reflect the higher rate.)

On May 1, 2013, we can see the signatures of a positively skewed distribution of expected exits. A median date that is sooner than the mean date, and a long stretch of curvature that reflects a wide range of expectations. You can tell from the slope of the linear plot of my modeled forward curve that my model is able to pick up the expected slope of the post ZLB curve from the shape of the convexity, even though the slope of the actual yield curve never quite gets that high, because a measurable proportion of expected ZLB exits occur very far in the future.

By September 6, rates had risen substantially. My model shows a quicker ZLB exit and a steeper subsequent slope. Two issues are very clear in this graph. Because at this point, the ZLB exit had become very near, the yield curve became very convex around the mean date of the exit, nearly mimicking my linear model of future rates. The mean expected exit has to be at the center of that convex area.

I can't think of a plausible way for the mean and median dates to fall in these ranges in a way that leads to a yield curve with this shape. I don't see how the Fed's stated median date at this point in time can be accurate.

By December 16, 2013, rates had fallen from the September levels, and the mean and median exit dates return to their expected positions.

Since December, the curve has flattened slightly, and the mean expected exit date has moved back to about August 2015.

Anyone modeling the BOJ's expected exit from the ZLB?

ReplyDeleteWow, I hadn't looked that closely at Japanese yields. Here is the 10 year zero coupon rate:

Deletehttp://sdw.ecb.europa.eu/quickview.do;jsessionid=3A6493AACB543D598AE2E7BA9A5CFC89?node=2018775&SERIES_KEY=143.FM.M.JP.JPY.RT.BZ.JPY10YZ_R.YLDE

It still looks like the expected date is roughly "never", doesn't it?