Archive for the ‘Good One’ Category

Good Models and Bad Models

I have recently begun to spend a fair amount of time explaining the difference between a “good model” and a “bad model;” it seemed to me that this was a reasonable topic to put on the blog.

The difference between a good model and a bad model isn’t as obvious as it seems. Many people think that a “good model” is one that makes correct predictions, and a “bad model” is one that makes bad predictions. But that is not the case, and understanding why it isn’t the case is important for economists and econometricians. Frankly, I suspect that many economists can’t articulate the difference between a good model and a bad model…and that’s why we have so many bad models floating around.

The definition is simple. A good model is one which makes good predictions if high-quality inputs are given to the model; a bad model is one in which even the correct inputs doesn’t result in good predictions. At the limit, a model that produces predictions that are insensitive to the quality of the inputs – that is, whose predictions are just as accurate no matter what the inputs are – is pure superstition.

For example, a model of the weather that depends on casting chicken bones and rat entrails is a pretty bad model since the arrangement of such articles is not likely to bear upon the likelihood of rain. On the other hand, a model used to forecast the price of oil in five years as a function of the supply and demand of oil in five years is probably an excellent model, even though it isn’t likely to be accurate because those are difficult inputs to know. One feature of a good model, then, is that the forecaster’s attention should shift to the forecasting of the inputs.

This distinction is relevant to the current state of practical economics because of the enormous difference in the quality of “Keynesian” models (such as the expectations-augmented Phillips curve approach) and of monetarist models. The simplest such monetarist model is shown below. It relates the GDP-adjusted quantity of money to the level of prices.

This chart does not incorporate changes in money velocity (which show up as deviations between the two lines), and yet you can see the quality of the model: if you had known in 1948 the size of the economy in 2008, and the quantity of M2 money there would be in 2008, then you would have had a very accurate prediction of the cumulative rate of inflation over that 60-year period. We can improve further on this model by noting that velocity is not random, but rather is causally related to interest rates. And so we can state the following: if we had known in 2007 that the Fed was going to vastly expand its balance sheet, causing money supply to grow at nearly a 10% rate y/y in mid-2009, but at the same time 5-year interest rates would be forced from 5% to 1.2% in late 2010, then we would have forecast inflation to decline sharply over that period. The chart below shows a forecast of the GDP deflator, based on a simple model of money velocity that was calibrated on 1977-1997 (so that this is all out-of-sample).

That’s a good model. Now, even solid monetarists didn’t forecast that inflation would fall as far as it did – but that’s not a failure of the model but a failure of imagination. In 2007, no one suspected that 5-year interest rates would be scraping 1% before long!

Contrariwise, the E-A-Phillips Curve model has a truly disastrous forecasting history. I wrote an article in 2012 in which I highlighted Goldman Sachs’ massive miss from such a model, and their attempts to resuscitate it. In that article, I quoted these ivory tower economists as saying:

“Economic principles suggest that core inflation is driven by two main factors. First, actual inflation depends on inflation expectations, which might have both a forward-looking and a backward-looking component. Second, inflation depends on the extent of slack (or spare capacity) in the economy. This is most intuitive in the labor market: high unemployment means that many workers are looking for jobs, which in turn tends to weigh on wages and prices. This relationship between inflation, expectations of inflation and slack is called the “Phillips curve.”

You may recognize these two “main factors” as being the two that were thoroughly debunked by the five economists earlier this month, but the article I wrote is worth re-reading because it describes how the economists re-calibrated. Note that the economists were not changing the model inputs, or saying that the forecasted inputs were wrong. The problem was that even with the right inputs, they got the wrong output…and that meant in their minds that the model should be recalibrated.

But that’s the wrong conclusion. It isn’t that a good model gave bad projections; in this case the model is a bad model. Even having the actual data – knowing that the economy had massive slack and there had been sharp declines in inflation expectations – the model completely missed the upturn in inflation that actually happened because that outcome was inconsistent with the model.

It is probably unfair of me to continue to beat on this topic, because the question has been settled. However, I suspect that many economists will continue to resist the conclusion, and will continue to rely on bad, and indeed discredited, models. And that takes the “bad model” issue one step deeper. If the production of bad predictions even given good inputs means the model is bad, then perhaps relying on bad models when better ones are available means the economist is bad?

Pension Fund Perils: Why Conventional Pairing of LDI with De-risking Glide Paths Produces Inferior Outcomes

February 9, 2017 1 comment

Milla Krasnopolsky, CFA and Michael Ashton, CFA[1]

Combined use of traditional Liability Driven Investment (LDI) and funded status responsive de-risking strategies should be decoupled or rebuilt. Embedded inconsistencies in the treatment of risks in these two elements of what has become a popular pension strategy cause irreconcilable conflicts in their execution and imperils the positive pension fund outcome.

This article provides a critique of the combined LDI / De-risking Glide Path strategy as currently implemented by many pension plan managers and also provides an example of an alternative solution that better improves pension plan outcomes.

deriskingboxApproaches to pension risk management have passed though many phases over the past 40+ years.  Higher rate environments of the 1980s made liability immunization programs with treasuries very attractive, but traditional 60/40 or balanced fund strategies persisted as the dominant strategy for pensions.  As rates began their secular decline, funding levels continued to deteriorate and while liability-driven investing became popular again in the beginning of the new millennium, significant levels of underfunding prevented most pensions from fully matching their assets and liabilities.  A variety of partial risk mitigation solutions began to emerge as the lower rate environment of the past 20 years forced institutional investors to be exposed to higher levels of market risk.  New asset classes were introduced into pension plan portfolios in order to achieve higher returns and higher levels of diversification.  Adverse market volatility was further reduced through creative solutions that incorporated smart beta and risk allocation strategies that delivered lower-volatility at similar levels of long term return.  Other strategies sold liquidity back to the market in order to generate additional return in a low yielding environment.  Some risk-based approaches also introduced interest rate derivative overlay programs to extend interest rate duration of total assets along with equity risk reduction programs to reduce equity market risk.  Finally, de-risking glide paths – and ultimately liability risk transfer to insurance companies – became in vogue as companies continued to struggle with their asset-liability risk and found it expedient to pay insurance companies to assume the problem for them.

In recent years, much has been written about whether pension funds have sufficient assets to support their liabilities, and clearly the source of much of this angst is that…many of them don’t.  One thing that is clear is that after decades of chasing new and creative solutions, the problem of underfunded pension plans is still here and the debate about who should manage the assets, and how they should be managed, continues with ever-increasing urgency.

This article represents our contribution to this debate, with a special focus on the asset allocation requirements for cost effective pension plan de-risking.


Two Shortcomings of Traditional LDI and De-risking Strategies, as Combined

Type of risk

At this point it is important to differentiate the assets that function as liability hedges and those assets that better assist with the process of de-risking as the plan glides towards a fully hedged status.  Long duration bonds function as the best hedge for the liabilities, and as the plan’s funded status improves and the de-risking process proceeds, the allocation to bonds increases.  While bonds and bond-like derivatives are a core staple of liability-driven investing (LDI) strategies, for most underfunded plans that have a goal of full funding with some help from asset performance it is economically infeasible to allocate 100% of the assets to the liability-matching portfolio.  A gradual increase in bond assets over time as funding status increases is part of the de-risking asset allocation process.  This is an important distinction between LDI and the process of de-risking.  If the liability-matching assets allow the plan to better lock in the current funded status level, then it is only the remaining assets that allow that plan to reach the next funded status threshold in order for the plan to de-risk further.  Traditionally, these non-LDI assets are exposed to a significant amount of equity beta, as the long-term expected compensation from taking equity risk is positive.  While it is thought to be true that, in the long term, equity beta risk is well compensated, the trouble is that in the shorter time horizon of de-risking process the equity beta is very much dependent on market valuations that are not related to the valuation of the pension liabilities. Therefore, it becomes a tactical rather than a strategic decision to hold equities for a de-risking plan.

While all pension models focus on longer-term horizons, pensions in a de-risking mode have a much lower risk tolerance in the short term.  This has caused many pensions to allocate assets to a variety of alternative investments in order to diversify away from equity beta risk.  However, this practice also introduces other risks to the plan, some of which are illiquidity, currency, and/or additional credit default risk.  So there is an inconsistency: while pension funds are known for taking the very long view when it comes to illiquidity, if the sponsors are pursuing an LDI/de-risking strategy the additional illiquidity is counterintuitive, given the objective to be dynamic and nimble in the de-risking process.

But assuming that potential illiquidity is at least somewhat of a concern to a pension fund manager, then the Hobson’s choice between equity risk or illiquidity likely means that underfunded pension plans that are pursuing joint LDI/de-risking strategies are still carrying too much equity beta risk, or are slowing down the de-risking process while equity risk is mitigated through other less liquid investments, or both. Pension fund managers and their advisors sense this, but tend to reach a type of asset allocation compromise where pension returns may be less optimal and de-risking results are less effective.

So if equity beta isn’t desirable as unrelated to the liability, and illiquidity of many other alternatives make them less-desirable for dynamic rebalancing into LDI assets, what is the most effective way to replace the equity beta for a de-risking plan?  What other forms of beta and/or alpha are appropriate in aiding in the process of de-risking?  From the standpoint of Markowitz efficient frontier generation, risk is a function of return variance and the covariance of the returns of the eligible portfolio elements. Beyond that, to the optimization routine risk is risk. That is, it doesn’t matter whether the risk comes from beta or from alpha.  From the standpoint of the de-risking process, when it comes to the non-LDI assets or return generating assets, alpha is preferred to most beta since alpha is more process-dependent as opposed to market-dependent.   In the shorter-term horizon of de-risking, non-LDI beta introduces more risk.  So our only choice seems to be some combination of liquid alpha and/or well compensated liquid beta that has some correlation to liabilities.  This particular beta may be different from how the liability matching or LDI assets are invested and doesn’t need to match the performance of the liabilities, but should have a positive correlation with liability performance.  That’s a tall order.

Some of the more publicized alpha alternatives are hedge funds, private investments in equity or debt of corporations, or real estate.  We don’t intend to dive into the merits and disadvantages of these or other alternative investments on a stand-alone basis but will only superficially observe their fit in a de-risking framework.  Many hedge funds return as much beta as alpha – indeed, the fact that there are successful hedge-fund replication techniques is virtual proof that many hedge funds are actually beta masquerading as alpha. The obvious visual correlation between hedge fund returns and equity returns, too, should make one suspicious that hedge funds are a pure source of alpha (see Chart, source Bloomberg, comparing the HFRI Fund of Funds Composite Index to the S&P 500).

hfriFigure 1: HFRI Fund of Funds Composite Index vs S&P 500

While those hedge funds or private investments that have a higher correlation to fixed income beta may benefit plans with a long time horizon, they suffer from varying degrees of illiquidity, which impedes the de-rising process as previously discussed.

While there may be other examples for a better alternative, we can provide one strategic example that better fits the combined LDI / de-risking criteria we have discussed in this article.

 The Better Alternative

We have addressed above the type of risk that pension funds do not want to have. But it behooves us as well to point out one type of risk that pension funds really ought to have, and yet tend to be underinvested in: inflation exposure, or more accurately real interest rates.

There is a competent literature about the importance of inflation-linked assets to the pension plan.[2] Importantly, inflation-linked assets are relevant even if the pension benefits are not themselves inflation-linked, since for most pension plans the formula which links the work history of active participants to their future retirement benefits implicitly means that pension benefit accruals for a particular employee are higher the more that employee earns. Since wages generally rise at least partly because of inflation, this implies that any pension fund with active participants still accruing benefits does in fact have some inflation exposure.

But the importance of inflation to the pension plan goes beyond that liability-side insight. Additionally, pension assets are exposed to inflation – and, especially, large changes in inflation – because on the asset side the majority of the assets of most plans are invested in equities and nominal fixed-income. Both of these asset classes are terribly exposed to increases in inflation, especially when inflation rises above 3-4%.[3]

We can go still further. While the effects just mentioned are well-established in the literature, one additional benefit from owning inflation-linked assets has not been discussed as far as we can tell, and that is this: the relative value of inflation-linked bonds, compared to nominal bonds, is related to the business cycle and/or level of interest rates level in the same way that corporate spreads are – but without default risk. The chart below (source: Bloomberg data) highlights the connection between credit spreads and 10-year breakevens.[4] This is important because for most pension funds, the relevant interest rate for discounting liabilities is not the risk-free Treasury rate, but a risky corporate rate; therefore, the liability has credit spread risk and an asset that co-moves with credit spreads – especially without actually having credit risk – is valuable.

creditvsbreaksFigure 2: Inflation spreads (“Breakevens”) vs Credit spreads

In our opinion, given a choice between equity beta and inflation/real rate beta, there is no choice: inflation-linked assets are clearly the more valuable risk for a pension fund to own.

Now, pension plans that are pursuing de-risking along with LDI are typically loathe to replace equity risk, given its advantage (over a full cycle, although not necessarily at any given point) in expected return, with real interest rate risk. But inflation-linked markets have an additional benefit, at least in 2017 – they are inefficient, and produce myriad opportunities to generate alpha along with their useful beta. Indeed, we have designed an investment strategy that addresses all of these requirements:

  • Historical return commensurate with equity returns, with slightly lower total risk
  • Beta from inflation-linked bond markets, which is relevant to pension fund liabilities
  • Risk sourced from useful beta, as well as alpha
  • Implied credit spread exposure, without actual credit risks, which is relevant to pension fund liabilities
  • Superior liquidity to “alts” such as real estate, private equity, or hedge funds – which is more consistent with the de-risking mandate

We call this strategy “Enhanced Systematic Real Return.” In a nutshell, this strategy holds the combination of inflation-linked bonds and breakevens that most efficiently adds inflation protection for a given level of interest rates, and adjusts these proportions based on the richness or cheapness of inflation-linked bonds to capture additional alpha.[5]


Magnitude of risk

After determining a different, if not more efficient risk vehicle for the non-LDI assets we now turn to the discussion of how much of this risk should be taken at every point of the glide path.  Should the risk allocation to return generating risk assets (i.e non-LDI assets) only depend on the dollars allocated to these investments or should the risk allocation be independent of dollars allocated and vary based on the level of leverage and/or asset composition?

Not All Risk is Bad

As we have already alluded, prudent risk has some place in the management of a pension fund on a glide path. Yet, as with the villain in the black hat, we have been conditioned to look at the word “risk” and recoil. But not all risk is bad. Certainly, with LDI approaches risk is a negative – after all, the goal of LDI is to maximize the funded status (difference between assets and liabilities), subject to a limit on the maximum volatility (risk) of the funded status. In that construction, there is no doubt that risk is bad, or anyway that less risk is better. But risk is not necessarily bad for de-risking.

This seems counter-intuitive. If we are trying to remove risk, doesn’t that imply that risk is bad? Yes – as we just said, risk is bad for the LDI-driven mandate. But the plan that takes less risk has fewer opportunities to reach de-risking thresholds. That is, the more that you de-risk the longer the next increment of de-risking takes. In this context, it is actually helpful to retain more rather than less risk in the non-LDI assets at each de-risking step.

Here is an analogy from basketball: consider the player who constantly heaves up three-point shots. He shoots a lower percentage from beyond the arc, and so the variance of his scoring is quite a bit higher than his variance shooting short jumpers or layups. Let us suppose that on average, he scores the same amount per game whether he shoots three-pointers or short jumpers. In an asset management context, we would say that this is a “non-optimized” shooter. He should aim for the same average scoring with lower volatility, right?

Now let us suppose that in a particular game, this player’s team is down by 18 points in the final quarter. The coach sends the player onto the court. If this coach is from the pension industry, he instructs his shooter to take only safe shots, because that is how he maximizes his Sharpe Ratio. But if this is actually a basketball coach, he orders his player to take as many three-pointers as he can. Why? He does this because in this situation, risk is good. A strategy of only taking safe shots is guaranteed to lose in this context; only a highly-volatile strategy has a chance of working.[6]

In the same way, prudent addition of volatility as the plan is de-risking helps to de-risk a plan that is under water. So we can see that there is a tension here, and one that is routinely ignored in most LDI/de-risking plans: more volatility is helpful for de-risking, but hurtful inasmuch as it departs from the LDI mandate to maximize the return/risk tradeoff for the funded status. This leads to the phenomenon that is common today, of “hurry up and wait.” As we noted previously: the more that a fund has been de-risked, the longer the next increment of de-risking takes. Each reduction of the proportion of return generating assets to total assets significantly increases the average time until the next de-risking point is reached, as the table below[7],[8] illustrates:

table1Table 1: Reducing return-generating assets will tend to increase time to next trigger

This is problematic. By de-risking, this plan is becoming too conservative as it approaches being fully funded. We can show that the plan reaches a fully-funded status more quickly when it prudently avoids full de-risking. What happens when we allow leverage, and maintain the total portfolio risk even as the bond allocation increases at each trigger? The following table shows the significant result:

table2Table 2: By maintaining portfolio risk to return-generating assets, de-risking proceeds apace.


Combining the Right Type, and the Right Magnitude, of Risk

When the pension plan pursues a strategy that focuses on risks sourced from alpha and the “right kinds” of beta sources that will tend to match the liability, and de-risks in a way that recognizes that some risk helps the de-risking task, then the combined result can be powerful. The chart below (Source: Enduring Intellectual Properties, Inc) compares this new approach with the “classic” LDI plus de-risking approach. The dashed lines represent the “classic” approach, while the solid lines represent an approach that uses our “Enhanced Systematic Real Return” strategy as a substitute for the equity risk of the traditional strategy. In each case, this imaginary pension fund starts year zero at 60% funded, and liabilities grow with the Bloomberg/Barclays/Lehman U.S. Long Government/Credit Index. Also in each case, the top line represents the 90th percentile outcome of the Monte Carlo simulation; the bottom line represents the 10th percentile, and the middle line represents the median outcome.

comparativeglidepathsFigure 3: Proper types and magnitudes of risks produce preferable pension outcomes.

There are several facets of this chart worth noting.

Importantly, observe how the median outcome line is linear with our approach, but flattens out with the traditional de-risking approach. This phenomenon is the visual counterpart to Tables 1 and 2; it illustrates how the closer one gets to being fully funded with a traditional glide path, the slower the funded status converges. Our approach, as highlighted in Table 2, is designed to remove that effect. The benefits of that approach aren’t only felt on the median outcome, but are apparent on every path as the funded status moves above 75%.

Also, observe that the superior “good” outcomes aren’t “paid for” by much worse “bad” outcomes. After all, we could have had even better “good” outcomes if we took lots of extra risk. But in that case, the benefit would have come at a price, and we would see it manifesting in much worse “bad” outcomes. The outcomes here are actually skewed to the positive side.

Finally, although you cannot tell this from the illustration, you should know that this simulation assumes that stocks and bonds have expected returns that are somewhere near their historical mean returns. Unfortunately, presently this seems a generous assumption for the traditional approach. It seems more likely that, going forward, pension plans which are invested heavily in equities will be drawing from a distribution with worse-than-average characteristics due to the high starting valuations. Ditto, of course, for fixed-income…but at least bonds affect both sides of the LDI equation.


LDI and de-risking glide paths can be combined under certain conditions, but current implementation practices create inconsistencies in how risks are treated and do not facilitate achievement of strategic goals.

Asset beta risks that do not match liability beta risks are useful only in a tactical setting, and then only if they are associated with exceptional returns (that is, the market is cheap tactically).

More effort is required to search out new sources of liquid alpha and beta that facilitate the de-risking process. We have produced one that we believe is useful in this context.

As the plan de-risks along the glide path, the level of risk in the non-LDI assets should be adjusted to preserve a quantum of variance that is useful in the de-risking process, as opposed to just mechanically adjusting allocation dollars in a simple glide path.

[1] Milla Krasnopolsky is an investment strategist and investment manager. Milla held previous positions as a Managing Director of Fixed Income Markets and Strategic Solutions at General Motors Asset Management and as a Principal and Senior Investment Consultant at Mercer Investments.  Michael Ashton is the Managing Principal of Enduring Investments and CEO of Enduring Intellectual Properties, Inc.

[2] For the iconic example, see Siegel and Waring, “TIPS, the Dual Duration, and the Pension Plan” (Financial Analysts Journal, September/October 2004).

[3] Remarkably, the myth that common stocks confer some inflation protection has survived decades of contrary experience, both before and after Zvi Bodie’s classic “Common Stocks as a Hedge Against Inflation” (Journal of Finance, Vol. 31, No. 2, May 1976), in which he concluded forcefully “The regression results…leads to the surprising and somewhat disturbing conclusion that to use common stocks as a hedge against inflation one must sell them short.”

[4] The 10-year simple “breakeven” is merely the yield difference between the 10-year nominal Treasury yield and the 10-year TIPS real yield; it represents roughly the amount of future inflation at which an investor would be indifferent between the two types of bonds.

[5] It would be inappropriate to discuss the fine details of this strategy in a thought piece such as this. However, we thought it important to point out that demand for a solution with these characteristics is not hopeless or uninformed. There does exist at least one such solution, and probably others!

[6] This idea isn’t exactly alien in finance: if you own an out-of-the-money option, a higher implied volatility increases your delta while if you own an in-the-money option, a higher implied volatility decreases your delta. It’s just alien in pension fund management.

[7] Both Table 1 and Table 2 represent simplified examples where LDI hedging assets and pension liabilities are proxied by the same long-duration bonds, and future pension contributions are excluded from the analysis.

[8] Table is based on a Monte Carlo simulation of a pension fund that begins with the indicated funding status and allocated as shown until it reaches the next de-risking trigger. Returns for stocks and bonds are simulated; the correlation from the last five years is used. The importance of the table isn’t derived from the precision of the assumptions, but from the illustration of the increased difficulty in reaching the next de-risking increment when the fund is already de-risked substantially.

A (Very) Long History of Real Interest Rates

December 23, 2016 3 comments

One of the problems that inflation folks have is that the historical data series for many of the assets we use in our craft are fairly short, low-quality, or difficult to obtain. Anything in real estate is difficult: farmland, timber, commercial real estate. Even many commodities futures only go back to the early 1980s. But the really frustrating absence is the lack of a good history of real interest rates (interest rates on inflation-linked bonds). The UK has had inflation-linked bonds since the early 1980s, but the US didn’t launch TIPS until 1997 and most other issuers of ILBs started well after that.

This isn’t just a problem for asset-allocation studies, although it is that. The lack of a good history of real interest rates is problematic to economists and financial theoreticians as well. These practitioners have been forced to use sub-optimal “solutions” instead. One popular method of creating a past history of “real interest rates” is to use a nominal interest rate and adjust it by current inflation. This is obvious nonsense. A 10-year nominal interest rate consists of 10-year real interest rates and 10-year forward inflation expectations. The assumption – usually explicit in studies of this kind – is that “investors assume the next ten years of inflation will be the same as the most-recent year’s inflation.”

We now have plenty of data to prove that isn’t how expectations work – and, not to mention, a complete curve of real interest rates given by TIPS yields – but it is still a popular way for lazy economists to talk about real rates. Here is what the historical record looks like if you take 10-year Treasury rates and deflate them by trailing 1-year inflation:

dumbrealThis is ridiculously implausible volatility for 10-year real rates, and a range that is unreasonable. Sure, nominal rates were very high in the early 1980s, but 10%? And can it be that real rates – the cost of 10-year money, adjusted for forward inflation expectations – were -4.6% in 1980 and +9.6% in 1984? This hypothetical history is clearly so unlikely as to be useless.

In 2000, Jay Shanken and S.P. Kothari wrote a paper called “Asset Allocation with Conventional and Indexed Bonds.” To make this paper possible, they had to back-fill returns from hypothetical inflation-linked bonds. Their method was better than the method mentioned above, but still produced an unreasonably volatile stream. The chart below shows a series, in red, that is derived from their series of hypothetical annual real returns on 5-year inflation-indexed bonds, and backing into the real yields implied by those returns. I have narrowed the historical range to focus better on the range of dates in the Shanken/Kothari paper.


You can see the volatility of the real yield series is much more reasonable, but still produces a very high spike in the early 1980s.

The key to deriving a smarter real yield series lies in this spike in the early 1980s. We need to understand that what drives very high nominal yields, such as we had at that time in the world, is not real yields. Since the real yield is essentially the real cost of money it should not ever be much higher than real potential economic growth. Very high nominal yields are, rather, driven by high inflation expectations. If we look at the UK experience, we can see from bona fide inflation-linked bonds that in the early 1980s real yields were not 10%, but actually under 5% despite those very high nominal yields. Conversely, very low interest rates tend to be caused by very pessimistic real growth outcomes, while inflation expectations behave as if there is some kind of floor.

We at Enduring Investments developed some time ago a model that describes realistically how real yields evolve given nominal yields. We discovered that this model fits not only the UK experience, but every developed country that has inflation-linked bonds. Moreover, it accurately predicted how real yields would behave when nominal yields fell below 2% as they did in 2012…even though yields like that were entirely out-of-sample when we developed the model. I can’t describe the model in great detail because the method is proprietary and is used in some of our investment approaches. But here is a chart of the Enduring Investments real yield series, with the “classic” series in blue and the “Shanken/Kothari” series in red:


This series has a much more reasonable relationship to the interest rate cycle and to nominal interest rates specifically. Incidentally, when I sat down to write this article I hadn’t ever looked at our series calculated that far back before, and hadn’t noticed that it actually fits a sine curve very well. Here is the same series, with a sine wave overlaid. (The wave has a frequency of 38 years and an amplitude of 2.9% – I mention this for the cycle theorists.)


This briefly excited me, but I stress briefly. It’s interesting but merely coincidental. When we extend this back to 1871 (using Shiller data) there is still a cycle but the amplitude is different.


So what is the implication of this chart? There is nothing predictive here; about all that we can (reasonably) say is what we already knew: real yields are not just low, but historically low. (Current 10-year TIPS yields are higher than our model expects them to be, but not by as much as they were earlier this  year thanks to a furious rally in breakevens.) Money is historically cheap – again, we knew this – in a way it hasn’t been since the War effort when nominal interest rates were fixed by the Fed even though wartime inflation caused expectations to rise. With real yields that low, how did the war effort get funded? Who in the world lent money at negative real interest rates like banks awash in cash do today?

That’s right…patriots.

1986-004-223Frankly, that makes a lot more sense than the reason we have low real interest rates today!

Categories: Good One, Investing, Theory, TIPS

Who Keeps Selling These Free Options?

November 22, 2016 Leave a comment

It seems that recently I’ve developed a bit of a theme in pointing out situations where the market was pricing one particular outcome so completely that it paid to take the other side even if you didn’t think that was going to be the winning side. The three that spring to mind are: Brexit, Trump, and inflation breakevens.

Why do these opportunities exist? I think partly it is that investors like to be on the “winning side” more than they like ending up with more money than they started. I know that sounds crazy, but we observe it all the time: it is really hard (especially if you are a fund manager that gets paid quarterly) to take losses over and over and over, even if one win in ten tries is all you need to double your money. It’s the “wildcatter” mindset of drilling a bunch of dry holes but making it back on the gusher. It’s how venture capital works. There are all kinds of examples of this behavioral phenomenon. I am sure someone has done the experiment to prove that people prefer many small gains and one large loss to many small losses and one large gain. If they haven’t, they should.

I mention this because we have another one.

December Fed Funds futures settled today at 99.475. Now, Fed funds futures settle to the daily weighted average Fed funds effective for the month (specifically, they settle to 100 minus the average annualized rate). Let’s do the math. The Fed meeting is on December 14th. Let’s assume the Fed tightens from the current 0.25%-0.50% range to 0.50%-0.75%. The overnight Fed funds effective has been trading a teensy bit tight, at 0.41% this month, but otherwise has been pretty close to rock solid right in the middle except for each month-end (see chart, source Bloomberg) so let’s assume it trades in the middle of the 0.50%-0.75% range for the balance of the month, except for December 30th (Friday) and 31st (Saturday), where we expect the rate to slip about 16bps like it did in 2015.


So here’s the math for fair value.

14 days at 0.41%  (December 1st -14th)

15 days at 0.625% (December 15th-29th)

2 days at 0.465% (December 30th-31st)

This averages to 0.518%, which means the fair value of the contract if the Fed tightens is 99.482. If the Fed does not tighten, then the fair value is about 99.60. So if you buy the contract at 99.475, you’re risking…well, nothing, because you’d expect it to settle higher even if the Fed tightens. And your upside is 12.5bps. This is why Bloomberg says the market probability of a 25bp hike in rates is now 100% (see chart, source Bloomberg).


There is in fact some risk, because theoretically the Fed could tighten 50bps or 100bps. Or 1000bps. Actually, those are all probably about equally likely. And it is possible the “turn” could trade tight, rather than loose. If the turn traded at 1%, the fair value if the Fed tightened would be 99.448. So it isn’t a riskless trade.

But we come back to the same story – it doesn’t matter if you think the Fed is almost certainly going to tighten on December 14th. Unless you think there’s a chance they go 50bps or that overnight funds start trading significantly higher before the meeting, you’re supposed to be long December Fed funds futures at 99.475.

The title of this post is a question, because remember – for everyone who is buying this option at zero (or negative) there’s someone selling it too. This isn’t happening on zero volume: 7207 contracts changed hands today. That seems weird to me, until I remember that it has been happening a lot lately. Someone is losing a lot of money. What is this, Brewster’s Millions?


An administrative announcement about upcoming (free!) webinars:

On consecutive Mondays spanning December 5, December 12, and December 19 at 11:00ET, I will be doing a series of one-hour educational seminars on inflation. The first is “How Inflation Works;” the second is “Inflation and Asset Classes;” and the third is “Inflation-aware Investing.” These webinars will also have live Q&A. After each session, a recording will be available on

Each of these webinars is financially sponsored by Enduring Investments.

Brexit and Trump and Free Options

November 9, 2016 1 comment

As the evening developed, and it began to dawn on Americans – and the world – that Donald Trump might actually win, markets plunged. The S&P was down 100 points before midnight; the dollar index was off 2%. Gold rose about $70; 10-year yields rose 15bps. Nothing about that was surprising. Lots of people predicted that if Trump somehow won, markets would gyrate and move in something close to this way. If Clinton won, the ‘status quo’ election would mean much calmer markets.

So, we got the upset. Despite the hyperbole, it was hardly a “stunning” upset.[1] Going into yesterday, the “No Toss Ups” maps had Trump down about 8 electoral votes. Polls in all of the “battleground” states were within 1-2 points, many with Trump in the lead. Yes, the “road to victory” was narrow, requiring Trump to win Florida, Ohio, North Carolina, and a few other hotly-contested battlegrounds, but no step along that road was a long shot (and it wasn’t like winning 6 coin flips, because these are correlated events). Trump’s victory odds were probably 20%-25% at worst: long odds, but not ridiculous odds. (And I believe the following wind to Trump from the timing of Obamacare letters was underappreciated; I wrote about this effect on October 27th).

And yet, stock markets in the two days prior to the election rose aggressively, pricing in a near-certainty of a Clinton victory. Again, recall that pundits thought that a Clinton victory would see little market reaction, but a violent reaction could obtain if Trump won. Markets, in other words, were offering tremendous odds on an event that was unlikely, but within the realm of possibility. The market was offering nearly-free options. The same thing happened with Brexit: although the vote was close to a coin-flip, the market was offering massive odds on the less-likely event. Here is an important point as well – in both cases, the error bars had to be much wider than normal, because there were dynamics that were not fully understood. Therefore, the “out of the money” outcome was not nearly as far out of the money as it seemed. And yet, the market paid you handsomely to be short markets (or less long) before the Brexit vote. The market paid you handsomely to be short markets (or less long) before yesterday’s election results were reported. And, patting myself on the back, I said so.


This is not a political blog, but an investing blog. And my point here about investing is simple: any competent investor cannot afford to ignore free, or nearly-free, options. Whatever you thought the outcome of the Presidential election was likely to be, it was an investing imperative to lighten up longs (at least) going into the results. If the status-quo happened, you would not have lost much, but if the status quo was upset, you would have gained much. As I’ve been writing recently about inflation breakevens (which was also a hard-to-lose trade, though less dramatic), the tail risks were really underpriced. Investing, like poker, is not about winning every hand. It is about betting correctly when the hand is played.

At this hour, stock markets are bouncing and bond markets are selling off. These next moves are the difficult ones, of course, because now we all have the same information. I suspect stocks will recover some, at least temporarily, because investors will price a Federal Reserve that is less likely to tighten and the knee-jerk response is to buy stocks in that circumstance. But it is interesting that at the moment, while stocks remain lower the bond market gains have completely reversed and are turning into a rout. 10-year inflation breakevens are wider by about 9-10bps, which is a huge move. But there will be lots of gyrations from here. The easy trade was the first one.

[1] And certainly not “the greatest upset in American political history.” Dewey Defeats Truman, anyone?

Why Are Inflation Expectations Rising?

November 2, 2016 5 comments

A persistent phenomenon of the last couple of months has been the rise in inflation expectations, in particular market-based measures. The chart below (source: Bloomberg) shows that 10-year inflation swap quotes are now above 2% for the first time in over a year and up about 25-30bps since the end of summer.


The same chart shows that inflation expectations remain far below the levels of 2014, 2013, and…well, actually the levels since 2004, with the exception of the crisis. This is obviously not a surprise per se, since I’ve been beating the drum for months, nay quarters, that breakevens are too low and TIPS too cheap relative to nominals. But why is this happening now? I can think of five solid reasons that market-based measures of inflation expectations are rising, and likely will continue to rise for some time.

  • Inflation itself is rising. What is really amazing to me – and I’ve written about it before! – is that 10-year inflation expectations can be so low when actual levels of inflation are considerably above 2%. While headline inflation oscillates all the time, thanks to volatile energy (and to a lesser extent, food) markets, the middle of the inflation distribution has been moving steadily higher. Median inflation (see chart, source Bloomberg) is over 2.5%. Core inflation is 2.2%. “Sticky” inflation is 2.6%.


Moreover, as has been exhaustively documented here and elsewhere, these slow-moving measures of persistent inflationary pressures have been rising for more than two years, and have been over the current 2% level of 10-year inflation swaps since 2011. At the same time inflation expectations have been declining. So why are inflation expectations rising? One answer is that investors are now recognizing the likelihood that the inflation dynamic has changed and inflation is not going to abruptly decelerate any time soon.

  • It is also worth pointing out, as I did last December in this article, that the inflation markets overreact to energy price movements. Some of this recovery in inflation quotes is just unwinding the overreaction to the energy swoon, now that oil quotes are rising again. To be sure, I don’t think oil prices are going to continue to rise, but all they have to do is to level off and inflation swap quotes (and TIPS breakevens) will continue to recover.
  • Inflation tail risk is coming back. This is a little technical, but bear with me. If your best-guess is that inflation over the next 10 years will average 2%, and the distribution of your expectations around that number is normal, then the fair value for the inflation swap is also 2%. But, if the length of the tail of “outliers” is longer to the high side than to the low side, then fair value will be above 2% even though you think 2% is the “most likely” figure. As it turns out, inflation outcomes are not at all normal, and in fact demonstrate long tails to the upside. The chart below is of the distribution of overlapping 1-year inflation rates going back 100 years. You can see the mode of the distribution is between 2%-4%…but there is a significant upper tail as well. The lower tail is constrained – deflation never goes to -12%; if you get deflation it’s a narrow thing. But the upper tail can go very high.

longtailsWhen inflation quotes were very low, it may have partly been because investors saw no chance of an inflationary accident. But it is hard to look at what has been happening to inflation over the last couple of years, and the extraordinary monetary policy actions of the last decade, and not conclude that there is a possibility – even a small possibility – of a long upside tail. As with options valuation, even an improbable event can have an important impact on the price, if the significance of the event is large. And any nonzero probability of double-digit inflation should raise the equilibrium price of inflation quotes.

  • The prices that are changing the most right now are highly salient. Inflation expectations are inordinately influenced, as noted above, by the price of energy. This is not only true in the inflation markets, but in forming the expectations of individual consumers. Gasoline, while it is a relatively small part of the consumption basket, has high salience because it is a purchase that is made frequently, and as a purchase unto itself (rather than just one more item in the basket at the supermarket), and its price is in big numbers on every corner. But it is not just gasoline that is moving at the moment. Also having high salience, although it moves much less frequently for most consumers: medical care. No consumer can fail to notice the screams of his fellow consumers when the insurance letter shows up in the mail explaining how the increase in insurance premiums will be 20%, 40%, or more. While I do not believe that an “expectations anchoring” phenomenon is important to inflation dynamics, there are many who do. And those people must be very nervous because the movement of several very salient consumption items is exactly the sort of thing that might unanchor those expectations.
  • Inflation markets were too low anyway. When 10-year inflation swaps dipped below 1.50% earlier this year, it was ridiculous. With actual inflation over 2% and rising, someone going short inflation markets at 1.50% had to assess a reasonable probability of an extended period of core-price disinflation taking hold after the first couple of years of inflation over 2%. By our proprietary measure, TIPS this year have persistently been 80-100bps too cheap (see chart, source Enduring Investments). This is a massive amount. The only times TIPS have been cheaper, relative to nominal bonds, were in the early days when institutions were not yet investing in TIPS, and in the teeth of the global financial crisis when one defaulting dealer was forced to blow out of a massive inventory of them. We have never seen TIPS as cheap as this in an environment of at least acceptable liquidity.


So, why did breakevens rally? Among the other reasons, they rallied because they were ridiculously too low. They’re still ridiculously too low, but not quite as ridiculously too low.

What happens next? Well, I look at that list and I see no reason that TIPS shouldn’t continue to outperform nominal bonds for a while since none of those factors looks to be exhauster. That doesn’t mean TIPS will rally – indeed, real yields are ridiculously low and I don’t love TIPS on their own. But, relative to nominal Treasuries (which impound the same real rate expectation), it’s not even a close call.

Why Does the Fed Focus on a Flawed PCE?

On Friday, I was on Bloomberg TV’s “What’d You Miss?” program to talk about the PCE inflation report from Friday morning. You can see most of the interview here.

I like the segment – Scarlet Fu, Oliver Renick, and Julie Hyman asked good questions – but we had to compress a fairly technical discussion into only 5 or 6 minutes. As a result, the segment might be a little “wonky” for some people, and I thought it might be helpful to present and expand the discussion here.

The PCE report itself was not surprising. Core PCE came in as-expected, at 1.7%. This is rising, but remains below the Fed’s 2% target for that index. I think it is interesting to look at how PCE differs from CPI to see why PCE remains below 2%. After all, core PCE is the only inflation index that is still below 2% (see chart, source Bloomberg). And, as we will see, this raises other questions about whether PCE is a reasonable target for Fed policy.

fourmeasuresThere are several differences between CPI and PCE, but the main reasons they differ can be summarized simply: the CPI measures what the consumer buys, out-of-pocket; the PCE measures not only household expenditures but also spending on behalf of consumers, including such things as employer-purchased insurance and some important government expenditures. As pointed out by the BEA on this helpful page, “the CPI is based on a survey of what households are buying; the PCE is based on surveys of what businesses are selling.”

This leads to two major types of differences: weight effects and scope effects.

Weight effects occur because the PCE is a broader index covering more economic activity. Consider housing, which is one of the more steady components of CPI. Primary rents and owners’-equivalent rent constitute together some 32% of the CPI and those two components have been rising at a blended rate of about 3.4% recently. However, the weight of rent-of-shelter in PCE is only 15.5%. This difference accounts for roughly half of the difference between core CPI and core PCE, and is persistent at the moment because of the strength in housing inflation.

However, more intriguing are the “scope” differences. These arise because certain products and services aren’t only bought in different quantities compared to what businesses sell (like in the case of housing), but because the two surveys include and exclude different items in the same categories. So, certain items are said to be “in scope” for CPI but “out of scope” for PCE, and vice-versa. One of the places this is most important is in the category of health care.

Most medical care is not paid for out-of-pocket by the consumer, and therefore is excluded from the CPI. For most people, medical care is paid for by insurance, which insurance is usually at least partly paid for by their employer. Also, the Federal government through Medicare and Medicaid provides a large quantity of medical care goods and services that are different from what consumers buy directly – at least, purchased at different prices than those available to consumers!).

This scope difference is enormously important, and over time accounts for much of the systematic difference between core CPI and core PCE. The chart below (source: BEA, BLS) illustrates that Health Care inflation in the PCE essentially always is lower than Medical Care inflation in the CPI.

pceandcpiMoreover, thanks in part to Obamacare the divergence between the medical care that the government buys and the medical care consumers buy directly has been widening. The following chart shows the spread between the two lines above:

pceandcpispreadIt is important to realize that this is not coincidental, but likely causal. It is because Medicare and other ACA control structures are restraining prices in certain areas (and paid by certain parties) that prices to the consumer are rising more rapidly. Thus, while all of these inflation measures are likely to continue higher, the spread between core CPI and core PCE is probably going to stay wider than normal for a while.

Now we get to the most interesting question of all. Why do we care about PCE in the first place? We care because the Fed uses core PCE as a policy target, rather than the CPI (despite the fact that it has ways to measure market CPI expectations, but no way to measure PCE expectations). They do so because the PCE covers a wider swath of the economy. To the Fed, this means the PCE is more useful as a broader measure.

But hang on! The extra parts that PCE covers are, substantially, in parts of the economy which are not competitive. Medicare-bought prices are determined, at least in the medium-term, by government fiat. The free market does not operate where the government treads in this way. The more-poignant implication is that there is no reason to suspect that these prices would respond to monetary policy! Ergo, it seems crazy to focus on PCE, rather than CPI (or one of the many more-useful flavors of CPI), when setting monetary policy. This is one case where I think the Fed isn’t being malicious; they’re just not being thoughtful enough.

Every “core” inflation indicator, including the ones above (and you can throw in wages and the Employment Cost Index as well!), is at or above the Fed’s target even accounting for the typical spread between the CPI and PCE. Not only that, they are above the target and rising. The Fed is most definitely “behind the curve.” Now, as I have noted before in this space I don’t think there’s anything the Fed can do about it, as raising rates without restraining reserves will only serve to accelerate inflation further since it will not entail a slowing of money supply growth. But it seems to me that, for starters, monetary policymakers should focus on indices that are at least in principle (and in normal times) more responsive to monetary policy!


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