Archive for the ‘Theory’ Category

The F9 Problem

February 3, 2015 Leave a comment

All around the world, investors and traders and even fancy hedge-fund guys are dealing with something that denizens of the inflation-linked bond world have been dealing with for some time.

I call it the F9 problem. Please come with me as I descend into geekdom.

You would be surprised to learn how many of the world’s major traders of bonds and derivatives rely for a significant amount of their analysis on the infrastructure of Microsoft Excel. While many major dealers have sophisticated calculation engines and desktop applications, nothing has yet been designed that offers the flexibility and transparency of Excel for designing real-time analytical functions on the fly. Bloomberg and other data providers have also built add-ins for Excel such that a subscriber can pull in real-time data into these customized calculation tools, which means that an Excel-based platform can be used to manage real-time trading.

When I have taught bond math, or programs like inflation modeling at the New York Society of Securities Analysts, I have had students design spreadsheets that built yield curves, calculated duration and convexity, valued vanilla derivative products, and so on. There are few better ways to learn the nuts and bolts of bond math than to build a spreadsheet to build a LIBOR swap curve. And, if you are doing anything very unique at all, being able to see and follow the whole calculation (and possibly amend or append additional calculations as necessary) is invaluable. When I was trading at two different Wall Street shops, the inflation book’s risk was pulled into my spreadsheets daily and manipulated so that I could understand all of its dimensions. This is, in short, very common.

It turns out that two very important Excel functions in bond portfolio management are PRICE() and MDURATION(). And it also turns out that these functions return an error at negative bond yields. All over the world, right now, as nominal bonds in various countries are trading at negative yields, whole armies of portfolio managers are saying “why is my spreadsheet saying “#NUM!” everywhere? I call this the F9 problem because when you hit F9 in Excel, it calculates your workbook. And that’s when you see the problem.

There is nothing about the price-from-yield formula that is insoluble at negative yields. The price of a bond is simply the sum of the present values of its cash flows. If using a single yield to maturity to price such a bond, a negative yield simply means that the present-value factors become greater than 1, rather than less than 1, in the future. This is odd, but mathematically speaking so what? There is no reason that PRICE() should produce an error at negative yields. But it does.

There is also nothing about the modified duration formula that is insoluble at negative yields. Macaulay duration is the present-value-weighted average time periods to maturity, which (aside from the weirdness of future cash flows being worth more than present cash flows, which is what a negative yield implies) has a definite solution. And modified duration, which is what MDURATION() is supposed to calculate, is simply Macaulay Duration divided by one plus the yield to maturity. While this does have the weird property that modified duration is less than Macaulay duration unless yields are negative, there’s nothing disqualifying there either. So there is no reason why MDURATION() should produce an error at negative yields. But it does.

I don’t know why Microsoft implemented bond functions that don’t work at negative yields, except that, well, it’s Microsoft and they probably didn’t thoroughly test them.

The good news is that inflation-indexed bonds have long had negative yields, so inflation guys solved this problem some time ago. Indeed, it only recently occurred to me that there’s a whole new cadre of frustrated fixed-income people out there.

Let me help. Here are the Visual Basic functions I use for the price from yield of TIPS or other US Treasuries, and for their modified durations. They’re simply implementations of the standard textbook formulas for yield-to-price and for modified duration. They’re not beautiful – I hadn’t planned to share them. But they work. I believe they require the Analysis Toolpak and Analysis Toolpak – VBA add-ins, but I am not entirely sure of that. No warranty is either expressed or implied!



Function EnduringPricefromYield(Settlement As Date, Maturity As Date, Coupon As Double, Yield As Double)

Dim price As Double

accumulator = 0

firstcoup = WorksheetFunction.CoupPcd(Settlement, Maturity, 2, 1)

priorcoup = firstcoup

Do Until priorcoup = Maturity

   nextcoup = WorksheetFunction.CoupNcd(priorcoup, Maturity, 2, 1)

   If accumulator = 0 Then

       dCF = (nextcoup – Settlement) / (nextcoup – priorcoup)

       x = dCF / 2


       x = x + 0.5

   End If

   pvcashflow = Coupon * 100 / 2 / (1 + Yield / 2) ^ (2 * x)

   accumulator = accumulator + pvcashflow

   priorcoup = nextcoup


‘add maturity flow and last coupon

   accumulator = accumulator + 100 / (1 + Yield / 2) ^ (2 * x)

‘subtract accrued int

   price = accumulator – WorksheetFunction.AccrInt(firstcoup, WorksheetFunction.CoupNcd(firstcoup, Maturity, 2, 1), Settlement, Coupon, 100, 2, 1)

   EnduringPricefromYield = price

End Function


Function EnduringModDur(Settlement As Date, Maturity As Date, Coupon As Double, Yield As Double)

Dim price As Double

firstcoup = WorksheetFunction.CoupPcd(Settlement, Maturity, 2, 1)

price = EnduringPricefromYield(Settlement, Maturity, Coupon, Yield) + WorksheetFunction.AccrInt(firstcoup, WorksheetFunction.CoupNcd(firstcoup, Maturity, 2, 1), Settlement, Coupon, 100, 2, 1)

accumulator = 0

priorcoup = firstcoup

Do Until priorcoup = Maturity

   nextcoup = WorksheetFunction.CoupNcd(priorcoup, Maturity, 2, 1)

   If accumulator = 0 Then

       dCF = (nextcoup – Settlement) / (nextcoup – priorcoup)

       x = dCF / 2


       x = x + 0.5

   End If

   pvcashflow = Coupon * 100 / 2 / (1 + Yield / 2) ^ (2 * x)

   accumulator = accumulator + pvcashflow / price * x

   priorcoup = nextcoup


‘add maturity flow and last coupon

   accumulator = accumulator + (100 * x / (1 + Yield / 2) ^ (2 * x)) / price

   EnduringModDur = accumulator / (1 + Yield / 2)

End Function

Crazy Spot Curves – Orderly Forwards

January 30, 2015 2 comments

This is an interesting chart I think. It shows the spot CPI swap curve (that is, expected 1y inflation, expected 2y compounded inflation, expected 3y compounded inflation), which is very, very steep at the moment because of the plunge in oil. It also shows the CPI swap curve one year forward (that is, expected inflation for 1y, starting in 1y; expected inflation for 2y, starting in 1y; expected inflation for 3y, starting in 1y – in other words, what the spot curve is expected to look like one year from today). The x-axis is the number of years from now.

efficientThe spot curve is so steep, it is hard to tell much about the forward curve so here is the forward curve by itself.

efficient2Basically, after this oil crash passes through the system, the market thinks inflation will be exactly at 2% (a bit lower than the Fed’s target, adjusting for the difference between CPI and PCE, but still amazingly flat) for 6-7 years, and then rise to the heady level of 2.10-2.15% basically forever.

That demonstrates an amazing confidence in the Fed’s power. Since inflation tails are longest to the high side, this is equivalent to pricing either no chance of an inflation tail, or that the Fed will consistently miss on the low side by just about exactly the same amount, and that amount happens to be equal to the value of the tail more or less.

But what is really interesting to me is simply how the wild spot curve translates so cleanly to the forward curve, at the moment.

Categories: Bond Market, Quick One, Theory Tags: ,

Commodities Re-Thunk

January 13, 2015 12 comments

I want to talk about commodities today.

To be sure, I have talked a lot about commodities over the last year. Below I reprise one of the charts I have run in the past (source: Bloomberg), which shows that commodities are incredibly cheap compared to the GDP-adjusted quantity of money. It was a great deal, near all-time lows this last summer…until it started creating new lows.


Such an analysis makes sense. The relative prices of two items are at least somewhat related to their relative scarcities. We will trade a lot of sand for one diamond, because there’s a lot of sand and very few diamonds. But if diamonds suddenly rained down from the sky for some reason, the price of diamonds relative to sand would plummet. We would see this as a decline in the dollar price of diamonds relative to the dollar price of sand, which would presumably be stable, but the dollar in such a case plays only the role of a “unit of account” to compare these two assets. The price of diamonds falls, in dollars, because there are lots more diamonds and no change in the amount of dollars. But if the positions were reversed, and there were lots more dollars, then the price of dollars should fall relative to the price of diamonds. We call that inflation. And that’s the reasoning behind this chart: over a long period of time, nominal commodities prices should grow with as the number of dollars increases.

Obviously, this has sent a poor signal for a while, and I have been looking for some other reasonable way to compute the expected return on commodities.[1] Some time ago, I ran across an article by Erb and Harvey called The Golden Dilemma (I first mentioned it in this article). In it was a terrific chart (their Exhibit 5) which showed that the current real price of gold – simply, gold divided by the CPI price index – is a terrific predictor of the subsequent 10-year real return to gold. That chart is approximately reproduced, albeit updated, below. The data in my case spans 1975-present.


The vertical line indicates the current price of gold (I’ve normalized the whole series so that the x-axis is in 2015 dollars). And the chart indicates that over the next ten years, you can expect something like a -6% annualized real return to a long-only position in gold. Now, that might happen as a result of heavy inflation that gold doesn’t keep up with, so that the nominal return to gold might still beat other asset classes. But it would seem to indicate that it isn’t a great time to buy gold for the long-term.

This chart was so magnificent and made so much sense – essentially, this is a way to think about the “P/E ratio” for a commodity” that I wondered if it generalized to other commodities. The answer is that it does quite well, although in the case of many commodities we don’t have enough history to fill out a clean curve. No commodities work as well as does gold; I attribute this to the role that gold has historically played in investors’ minds as an inflation hedge. But for example, look at Wheat (I am using data 1970-present).


There is lots of data on agricultural commodities, because we’ve been trading them lots longer. By contrast, Comex Copper only goes back to 1988 or so:


Copper arguably is still somewhat expensive, although over the next ten years we will probably see the lower-right portion of this chart fill in (since we have traded higher prices, but only within the last ten years so we can’t plot the subsequent return).

Now the one I know you’re waiting for: Crude oil. It’s much sloppier (this is 1983-present, by the way), but encouraging in that it suggests from these prices crude oil ought to at least keep up with inflation over the next decade. But do you know anyone who is playing oil for the next decade?


For the sake of space, here is a table of 27 tradable commodities and the best-fit projection for their next 10 years of real returns. Note that most of these fit a logarithmic curve pretty reasonably; Gold is rather the exception in that the historical record is more convex (better expectation from these levels than a pure fit would indicate; see above).


I thought it was worth looking at in aggregate, so the chart below shows the average projected returns (calculated using only the data available at each point) versus the actual subsequent real returns of the S&P GSCI Excess Return index which measures only the return of the front futures contract.


The fit is probably better in reality, because the actual returns are the actual returns of the commodities which were in the index at the time, which kept changing. At the beginning of our series, for example, I am projecting returns for 20 commodities but the 10-year return compares an index that has 20 commodities in 1998 to one that has 26 in 2008. Also, I simply equal-weighted the index while the S&P GSCI is production-weighted. And so on. But the salient point is that investing in spot commodities has been basically not pretty for a while, with negative expected real returns for the spot commodities (again, note that investing in commodity indices adds a collateral return plus an estimate 3-4% rebalancing return over time to these spot returns).

Commodities are, no surprise, cheaper than they have been in a long while. But what is somewhat surprising is that, compared to the first chart in this article, commodities don’t look nearly as cheap. What does that mean?

The first chart in this article compares commodities to the quantity of money; the subsequent charts compare commodities to the price level. In short, the quantity of money is much higher than has historically been consistent with this price level. This makes commodities divided by M2 look much better than commodities divided by the price level. But it merely circles back to what we already knew – that monetary velocity is very low. If money velocity were to return to historical norms, then both of these sets of charts would show a similar story with respect to valuation. The price level would be higher, making the real price of commodities even lower unless they adjusted upwards as well. (This is, in fact, what I expect will eventually happen).

So which method would I tend to favor, to consider relative value in commodities? Probably the one I have detailed here. There is one less step involved. If it turns out that velocity reverts higher, then it is likely that commodities real returns will be better than projected by this method; but this approach ignores that question.

Even so, a projected real return now of -2% to spot commodities, plus a collateral return equal to about 1.9% (the 10-year note rate) and a rebalancing return of 3-4% produces an expected real return of 2.9%-3.9% over the next decade. This is low, and lower than I have been using as my assumption for a while, but it is far higher than the expected real returns available in equities of around 1.2% annualized, and it has upside risk if money velocity does in fact mean-revert.

I will add one final point. This column is never meant to be a “timing” column. I am a value guy, which means I am always seen to be wrong at the time (and often reviled, which goes with the territory of being a contrarian). This says absolutely nothing about what the returns to commodities will be over the next month and very little about returns over the next year. But this analysis is useful for comparing other asset classes on similar long-term horizons, and for using useful projections of expected real returns in asset allocation exercises.

[1] In what follows, I will focus on the expected return to individual spot commodities. But remember that an important part of the expected return to commodity indices is in rebalancing and collateral return. Physical commodities should have a zero (or less) real return over time, but commodity indices still have a significantly positive return.

Growth-Sapping Effect of the Minimum Wage

December 10, 2014 1 comment

I just saw this interesting article in Econbrowser called “New estimates of the effects of the minimum wage.” It is both good news, and bad news.

It is good news because it clarifies a debate about the effect of the minimum wage which has been raging for a long time, but without much actual data. This article summarizes a clever approach by a couple of academic economists to examine the actual effects of increasing the minimum wage. The research produces solid numbers and confirms some theories about the effects of the minimum wage.

The bad news is that the effect of the minimum wage is just what theory says it should be, but liberal politicians have insisted isn’t true in practice. And that’s a net negative effect on overall welfare, albeit divided between winners and losers. However, even that ought to be good news, because this analysis also means that we can reverse the policy and reap immediate gains in consumer welfare.

First, the theory: microeconomics tells us that an increase in the minimum wage, if it is above the equilibrium wage for some types of labor, should decrease employment while increasing the wages of those who actually retain their jobs. (The usual argument for increasing the minimum wage is that the people who earn minimum wage aren’t making enough to live on, and supporters tend to forget that if people lose their jobs because the minimum wage is raised, then those people are making even less.) We often say things are “Econ 101,” but this really is Econ 101 in the sense that it is taught in every introductory economics class. There is no excuse not to know this:

sdoflaborIn the chart above, the supply of labor is S and the demand for labor is D. In the absence of a floor (minimum wage), the clearing wage and quantity of jobs is at the intersection; at a minimum wage of a, however, there is a shortage of jobs equal to c-b. If the minimum wage is raised to a’, then the shortage of jobs increases to c’-b’. The question for society is whether the increase in joblessness is an acceptable cost to accept, in order to increase the minimum wage from a to a’. (Of course, the political calculation might also include the fact that people who become unemployed will be supported by the welfare state, and potentially vote to preserve and expand those public institutions that constitute it).

The problem for those who argue against the minimum wage, or for it being increased, is that they can point out this economic truism until they are blue in the face, while the other side simply says “nuh-uh” and denies it is true with the same fervor that they insist that Obamacare has actually lowered premiums and deductibles. The façade only cracks, maybe, when actual data is presented that shows the argument to be bankrupt.

This academic study does that cleverly, by examining changes in employment and wages in states where the federal minimum wage was binding (because the state minimum wage was lower, or non-existent) and states where it was not binding (because the state minimum wage was higher, so the federal minimum wage didn’t matter). Their conclusion:

“Over the late 2000s, the average effective minimum wage rose by 30 percent across the United States. We estimate that these minimum wage increases reduced the national employment-to-population ratio by 0.7 percentage point.”

That’s the sterile conclusion. Now let’s count the cost. Between July 2007 and December 2009, the national employment-to-population ratio (which is similar to, but not the same as, the labor force participation rate) declined from 62.7% to 58.3%; it has since risen to 59.2%. As the chart below (source: Bloomberg) shows, the labor force participation rate (in yellow) shows a more gradual decline but no recovery – as has been well-documented.


Now, some numbers. In November, the Civilian noninstitutional population (the denominator for the employment-to-population rate) was reported by the Bureau of Labor Statistics (BLS) to be 248,844,000. That means that if the authors are correct, the minimum wage has boosted the wages of unemployed workers at the bottom of the scale at the cost of about 1.74 million jobs (0.007 * 248,844,000).

Imagine what having another 1.74 million workers would do for GDP? Do you think it could make a difference for one of the worst recoveries on record?

It probably isn’t fair to assume that all of those 1.74 million workers is currently “unemployed” by the BLS definition. Many of them are likely not looking for work, in which case they would not be counted as unemployed. It is interesting to note, although surely spurious, that the series “Not in Labor Force, Want a Job Now” is about 1.7 million higher than would be expected given the unemployment rate (see chart, source BLS).

wannajobAlternatively, we could consider what it would mean to the Unemployment Rate if those 1.74 million workers were employed. This means they would also be in the Civilian Labor Force, so the participation rate (see above) would be 63.5% rather than 62.8%. If instead of coming from the “Not in Labor Force, Want a Job Now” group they came from the “Unemployed” group, the Unemployment Rate would be 4.7% instead of 5.8%. (Personally, I think that most of them are probably in the former category, as the Unemployment Rate has declined at approximately the rate we would expect from past recoveries, despite tepid GDP growth.) That is not inconsistent, of course, if GDP growth is lower because the labor force is simply smaller than it should be – and that is exactly the implication of this bit of research.

Again, the good news is that we can help the country and the downtrodden “structurally” unemployed with the same simple policy: reverse all increases in the Minimum Wage that have happened since 2007.

Dollar Rally Does Not Demand Deflation – Duh

November 6, 2014 2 comments

There are many funny stories out about disinflation these days. The meme has gotten amazing momentum, even more than it usually does at this time of year (see my post last month, “Seasonal Allergies“).  One of the most amusing has been the idea that the decision by the Bank of Japan to greatly increase its quantitative easing would be disinflationary in the U.S., because the yen would decline so sharply against the dollar, and dollar strength is generally assumed to be disinflationary.

The misunderstanding of the dollar effect is amazing, considering how easy it is to disprove. Sure, I understand the alarm at the dollar’s recent robust strength. Of course, such a large and rapid move must be disinflationary, right? Because who could forget the inflationary spiral of 2002-2008 in this country, when the value of the dollar fell 25%?


For the record, when the dollar hit its high in February 2002, core inflation was at 2.6%. It declined to 1.1% in 2003, before rebounding to 2.9% in 2006 and was at 2.3% in April 2008, when the dollar reached its pre-crisis low. That is, the dollar’s protracted and large decline caused essentially no meaningful change in core inflation. Indeed, without the housing bubble, core inflation would have declined markedly over this period.

Now, headline inflation rose during that period, because energy prices rose. This may or may not be the result of the dollar, or the causality may run at least partly the other way (because the dollar was cheaper, and oil is priced in dollars, oil got comparatively cheaper in foreign currencies, leading to greater demand). But what is very clear is that the underlying rate of inflation was not impacted by the dollar.

The bifurcation of inflation into core inflation and energy inflation (or food and energy inflation, if you like, but most of the volatility comes from energy inflation) is a critical point for both investors and policymakers. Much ink has recently been spilled about how the Saudi decision to lower the price of oil to better compete with U.S. shale supply, and the burgeoning shale supply itself, is disinflationary. But it isn’t, and it is important to understand why. Inflation is a rate of change measure, and more to the point a change in prices is not inflation per se unless it is persistent. Policymakers don’t focus on core inflation because they don’t care about food or energy or think that we don’t buy them; they focus on core inflation because it is more persistent than food or energy inflation.

So if gasoline prices aren’t merely in their usual seasonal dip, but actually continue lower for another year, it will result in headline inflation that is lower than core inflation over that period. But once it reaches a new equilibrium level, that downward pressure on headline inflation will abate, and it will re-converge with core.

Oil prices, in fact, are almost always a growth story rather than an inflation story, and some of the big monetary policy crack-ups of the past have occurred when the Fed addressed oil price spikes (plunges) with tighter (looser) monetary policy. In fact, if any policy response is warranted it would probably be the opposite of this, since higher oil prices cause slower broad economic growth and lower oil prices cause faster broad economic growth. (However, long time readers will know that I don’t believe monetary policy can affect growth significantly anyway.)

Back, briefly, to the BOJ balance sheet expansion story. This was a very significant event for global inflation, assuming as always that the body follows through with their stated intention. Money printing anywhere causes the equilibrium level of nominal prices globally to rise. To the extent that this inflation is to be felt idiosyncratically only in Japan, then the decline of the currency will offset the effect of this global increase in prices so that ex-Japan prices are steady while prices in Japan rise…which is the BOJ’s stated intent. Movements in foreign exchange are best understood as allocating global inflation between trading partners. However, for money-printing in Japan to lead to disinflation ex-Japan, the movement in the currency would have to over-react to the money printing. If markets are perfectly efficient, in other words, the movement in currency should cause the BOJ’s idiosyncratic actions to be felt only within Japan. There are arbitrage opportunities otherwise (although it is very slow and risky arbitrage – better thought of as arbitrage in an economic sense than in a trading sense).

Of course, if the BOJ money-printing is not idiosyncratic – if other central banks are also printing – then prices should rise around the world and currencies shouldn’t move. This is why the Fed was able to get away with increasing M2 significantly without cratering the dollar: everyone was doing it. What is interesting is that the global price level has not yet fully reflected the rise in the global money supply, because of the decline in global money velocity (which is due in turn to the decline in global interest rates). This is the story that is currently being written, and will be the big story of the next few years.

Seasonal Allergies

October 14, 2014 8 comments

Come get your commodities and inflation swaps here! Big discount on inflation protection! Come get them while you can! These deals won’t last long!

Like the guy hawking hangover cures at a frat party, sometimes I feel like I am in the right place, but just a bit early. That entrepreneur knows that hangover cures are often needed after a party, and the people at the party also know that they’ll need hangover cures on the morrow, but sales of hangover cures are just not popular at frat parties.

The ‘disinflation party’ is in full swing, and it is being expressed in all the normal ways: beat-down of energy commodities, which today collectively lost 3.2% as front WTI Crude futures dropped to a 2-year low (see chart, source Bloomberg),


…10-year breakevens dropped to a 3-year low (see chart, source Bloomberg),


…and 1-year inflation swaps made their more-or-less annual foray into sub-1% territory.


So it helps to remember that none of the recent thrashing is particularly new or different.

What is remarkable is that this sort of thing happens just about every year, with fair regularity. Take a look at the chart of 10-year breakevens again. See the spike down in late 2010, late 2011, and roughly mid-2013. It might help to compare it to the chart of front Crude, which has a similar pattern. What happens is that oil prices follow a regular seasonal pattern, and as a result inflation expectations follow the same pattern. What is incredible is that this pattern happens with 10-year breakevens, even though the effect of spot oil prices on 10-year inflation expectations ought to be approximately nil.

What I can tell you is that in 12 of the last 15 years, 10-year TIPS yields have fallen in the 30 days after October 15th, and in 11 of the past 15 years, 10-year breakevens were higher in the subsequent 30 days.

Now, a lot of that is simply a carry dynamic. If you own TIPS right now, inflation accretion is poor because of the low prints that are normal for this time of year. Over time, as new buyers have to endure less of that poor carry, TIPS prices rise naturally. But what happens in heading into the poor-carry period is that lots of investors dump TIPS because of the impending poor inflation accretion. And the poor accretion is due largely to the seasonal movement in energy prices. The following chart (source: Enduring Investments) shows the BLS assumed seasonality in correcting the CPI tendencies, and the actual realized seasonal pattern over the last decade. The tendency is pronounced, and it leads directly to the seasonality in real yields and breakevens.


This year, as you can tell from some of the charts, the disinflation party is rocking harder than it has for a few years. Part of this is the weakening of inflation dynamics in Europe, part is the fear that some investors have that the end of QE will instantly collapse money supply growth and lead to deflation, and part of it this year is the weird (and frustrating) tendency for breakevens to have a high correlation with stocks when equities decline but a low correlation when they rally.

But in any event, it is a good time to stock up on the “cure” you know you will need later. According to our proprietary measure, 10-year real yields are about 47bps too high relative to nominal yields (and we feel that you express this trade through breakevens rather than outright TIPS ownership, although actual trade construction can be more nuanced). They haven’t been significantly more mispriced than that since the crisis, and besides the 2008 example they haven’t been cheaper since the early days (pre-2003) when TIPS were not yet widely owned in institutional portfolios. Absent a catastrophe, they will not get much cheaper. (Importantly, our valuation metric has generally “beaten the forwards” in that the snap-back when it happens is much faster than the carry dynamic fades).

So don’t get all excited about “declining inflation expectations.” There is not much going on here that is at all unusual for this time of year.

What Risk-Parity Paring Could Mean for Equities

October 9, 2014 14 comments

The stock market, the bond market, the commodities markets (to a lesser extent), FX markets – they are all experiencing a marked increase in volatility.

Some observers want to call this bearish for equities, mainly because they already are bearish. This is a very bad reason. While really bad equity returns almost always occur coincident with a rise in volatility – the old maxim is that stocks go ‘up on the staircase and down on the escalator’ – that does not mean that volatility causes bad returns. Or, put another way, there are also periods of increased volatility that do not precede and are not coincident with bad returns.

However, there actually is a reason that increased volatility might lead to poor short- to medium-term returns, that isn’t based on technical analysis or spurious correlations. Moreover, a relatively new phenomenon (the rise of so-called ‘risk-parity’ strategies) is starting to institutionalize what was already a somewhat natural response to volatility.

In ‘risk-parity’ strategies, the weight of an asset class (or a security within an asset class, sometimes) is inversely proportional to the risk it adds to the portfolio. Generally speaking, “risk” here is defined as variance, because it is easy to estimate and there are markets where symmetrical variance trades – i.e., options markets. But what this means is that when volatility (sometimes realized volatility, and sometimes option “implied” volatility) rises in stocks, then risk parity strategies tend to be shedding equities because they look riskier, and vice-versa. Right now, risk parity strategies are likely to be overweight equities because of the long period of low realized and implied volatility (even though the valuation measures imply quite high risk in the sense most of us mean it, in terms of the probability of return shortfall). Risk parity strategies are probably superior to ‘return-chasing’ methodologies, but by being ‘risk-chasing’ they end up doing something fairly similar when they are all operating together.

Note that while risk-parity strategies are comparatively new – well, not exactly because it is an oldish idea, but they have only recently become a big fad – this general phenomenon is not. The natural response to greater equity market volatility is to pare back exposure; when your broker statement starts to swing around wildly it makes you nervous and so you may start to take some profits. This is also true of other asset classes but it seems to me to be especially true in equities. Nobody who gets involved in commodities is surprised at volatility: the asset class suffers from a midguided belief that it is terribly volatile even though commodity indices are just about exactly as volatile as equity indices over time. But equity investors, contrariwise, seem perennially surprised at 2% moves.

So, while the recent volatility doesn’t mean that a move lower in equities is assured, it increases the probability of such because risk-parity strategies (and other investors reacting nervously to overweights in their equity exposure) will begin to scale back positions in the asset class in favor of positions in other asset classes, probably mostly bonds and commodities. At this point it would be good for me to point out that only the very short-term volatility measures have moved up dramatically; the VIX is well off its bottom but only up to 18.8 and it has been there numerous times in the last few years (see chart, source Bloomberg). But the longer the volatility continues like we have seen it for the last week or two, the bigger the chances that the asset-allocation boxes start to make important shifts (and the quant hedge fund boxes will probably move a bit before those asset allocation boxes do).


As an aside, the tendency for asset allocation shifts to follow volatility shifts is not the reason that the VIX displays a strong inverse directionality. Neither is the main reason for this inverse directionality because the VIX is a “fear gauge.” The main reason is that the VIX weights near-the-money options more heavily than out-of-the-money options. Because options skews almost always imply more downside volatility for stocks than upside volatility[1], when the market declines it tends to bring more “high volatility” strikes into play and so part of the VIX increase in a down market is simply mechanical.

I am not calling for a sharp decline in stocks, nor for an extended decline in stocks. My position and view is as it has long been, that the prospect for attractive real returns from equities over the next 5-10 years is quite small and beaten handily by commodities’ prospective returns at that end of the risk spectrum. I don’t think that most investors (me included!) should swing asset allocations around frequently in response to technical indicators or such things as “momentum”, but rather should focus on evaluating expected long-term returns (which are somewhat predictable) and invest for value. And I must admit I also think that “risk-parity” is a clever marketing gimmick but a pretty absurd way to assemble a portfolio for almost everyone. My point here is to highlight one little-considered aspect of herd behavior, and how that herd behavior may have become more institutionalized as late, and to consider the risks that herd behavior may create.

[1] This in turn is not due so much from the tendency of markets to have more downside volatility than upside volatility, but from the fact that buying protective puts and selling “covered” calls are both considered “conservative” options strategies. So, out-of-the-money puts tend to be too expensive and out-of-the-money calls too rich.


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