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Kicking Tails

February 12, 2018 2 comments

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Like many people, I find that poker strategy is a good analogy for risk-taking in investing. Poker strategy isn’t as much about what cards you are dealt as it is about how you play the cards you are dealt. As it is with markets, you can’t control the flop – but you can still correctly play the cards that are out there.[1] Now, in poker we sometimes discover that someone at the table has amassed a large pile of chips by just being lucky and not because they actually understand poker strategy. Those are good people to play against, because luck is fickle. The people who started trading stocks in the last nine years, and have amassed a pile of chips by simply buying every dip, are these people.

All of this is prologue to the observation I have made from time to time about the optimal sizing of investment ‘bets’ under conditions of uncertainty. I wrote a column about this back in 2010 (here I link to the abbreviated re-blog of that column) called “Tales of Tails,” which talks about the Kelly Criterion and the sizing of optimal bets given the current “edge” and “odds” faced by the bettor. I like the column and look back at it myself with some regularity, but here is the two-sentence summary: lower prices imply putting more chips on the table, while higher volatility implies taking chips off of the table. In most cases, the lower edge implied by higher volatility outweighs the better odds from lower prices, which means that it isn’t cowardly to scale back bets on a pullback but correct to do so.

When you hear about trading desks having to cut back bets because the risk control officers are taking into account the higher VAR, they are doing half of this. They’re not really taking into account the better odds associated with lower prices, but they do understand that higher volatility implies that bets should be smaller.

In the current circumstance, the question merely boils down to this. How much have your odds improved with the recent 10% decline in equity prices? Probably, only a little bit. In the chart below, which is a copy of the chart in the article linked to above, you are moving in the direction from brown-to-purple-to-blue, but not very far. But the probability of winning is moving left.

Note that in this picture, a Kelly bet that is less than zero implies taking the other side of the bet, or eschewing a bet if that isn’t possible. If you think the chance that the market will go up (edge) is less than 50-50 you need better payoffs on a rally than on a selloff (odds). If not, then you’ll want to be short. (In the context of recent sports bets: prior to the game, the Patriots were given a better chance of winning so to take the Eagles at a negative edge, you needed solid odds in your favor).

Now if, on the other hand, you think the market selloff has taken us to “good support levels” so that there is little downside risk – and you think you can get out if the market breaks those support levels – and much more upside risk, then you are getting good odds and a positive edge and probably want to bet aggressively. But that is to some extent ignoring the message of higher implied volatility, which says that a much wider range of outcomes is possible (and higher implied volatility moves the delta of an in-the-money option closer to 0.5).

This is why sizing bets well in the first place, and adjusting position sizes quickly with changes in market conditions, is very important. Prior to the selloff, the market’s level suggested quite poor odds such that even the low volatility permitted limited bets – probably a lot more limited than many investors had in place, after many years of seeing bad bets pay off.


[1] I suspect that Bridge might be as good an analogy, or even better, but I don’t know how to play Bridge. Someday I should learn.

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Categories: Analogy, Investing, Theory, Trading

Are Rising Yields Actually a Good Thing?

February 6, 2018 2 comments

I’ve recently been seeing a certain defense of equities that I think is interesting. It runs something like this:

The recent rise in interest rates, which helped cause the stock market swoon, is actually a good thing because interest rates are rising due to a strong economy and increasing demand for capital, which pushes up interest rates. Therefore, stocks should actually not mind the increase in interest rates because it’s an indication of a strong economy.

This is a seductive argument. It’s wrong, but it’s seductive. Not only wrong, in fact, but wrong in ways that really shouldn’t confuse any economist or strategist writing in the last twenty years.

Up until the late 1990s, we couldn’t really tell the main reason that nominal interest rates were rising or falling. For an increase in market rates there are two main potential causes: an increase in real interest rates, which can be good if that increase is being caused by an increasing demand for credit rather than by a decreasing supply, and an increase in inflation expectations, which is an unalloyed negative. But in 1995, we would have had to just guess which was causing the increase in interest rates.

But since 1997, we’ve had inflation-linked bonds, which trade on the basis of real yield. So we no longer have to guess why nominal rates are rising. We can simply look.

The chart below shows the decomposition of 10-year nominal yields since early December. The red line, which corresponds to the left scale, shows “breakevens,” or the simple difference between real yields and nominal yields; the blue line, on the right-hand scale, shows real yields. So if you combine the two lines at any point, you get nominal yields.

Real yields represent the actual supply and demand for the use of capital. That is, if I lend the government money for ten years, then in order to entice me to forego current consumption the government must promise that every year I will accumulate about 0.68% more ‘stuff.’ I can consume more in the future by not consuming as much now. To turn that into a nominal yield, I then have to add some premium to represent how much the dollars I will get back in the future, and which I will use to buy that ‘stuff’, will have declined in value. That of course is inflation expectations, and right now investors who lend to the government are using about 2.1% as their measure of the rate of deterioration of the value of the dollar.[1]

So, can we say from this chart that interest rates are mainly rising for “good” reasons? On the contrary! The increase in inflation expectations has been much steadier; only in the last month have real interest rates risen (and we don’t know, by the way, whether they’re even rising because of credit demand, rather than credit supply). Moreover – although you cannot see this from the chart, I can tell you based on proprietary Enduring Intellectual Properties research that at this level of yields, real yields are usually responsible for almost all of the increase or decrease in nominal yields.[2] So the fact that real yields are providing a little less than half of the selloff? That doesn’t support the pleasant notion of a ‘good’ bond selloff at all.

As I write this, we are approaching the equity market close. For most of the day, equities have been trading a bit above or a bit below around Monday’s closing level. While this beats the heck out of where they were trading overnight, it is a pretty feeble technical response. If you are bullish, you would like to see price reject that level as buyers flood in. But instead, there was pretty solid volume at this lower level. That is more a bearish sign than a bullish sign. However, given the large move on Friday and Monday it was unlikely that we would close near unchanged – so the last-hour move was either going to be significantly up or significantly down. Investors chose up, which is good news. But the bad news is that the end-of-day rally never took us above the bounce-high from yesterday’s last hour, and was on relatively weak volume…and I also notice that energy prices have not similarly rallied.


[1] In an article last week I explained why we tend to want to use inflation swaps rather than breakevens to measure inflation expectations, but in this case I want to have the two pieces add up to nominal Treasury yields so I am stuck with breakevens. As I noted in that article, the 2.1% understates what actual inflation expectations are for 10 years.

[2] TIPS traders would say “the yield beta between TIPS and nominals is about 1.0.”

Historical Context Regarding Market Cycles

February 5, 2018 4 comments

I really enjoy listening to financial media outlets on days like this. Six days removed from all-time highs, the equity guys – especially the strategists, who make their money on the way up – talk about “capitulation,” and how “nothing has changed,” and how people need to “invest for the long-term.” If equities have entered a bear market, they will say this all the way down.

It helps to have seen a few cycles. Consider the early-2000s bear market. In 2000, the Nasdaq crested in March. After a stomach-churning setback, it rallied back into August (the S&P actually had its highest monthly close for that cycle in August). The market then dropped again, bounced, dropped again, bounced, and so on. Every bounce on the way down, the stock market shills shrieked ‘capitulation’ and called it a buying opportunity. Eventually it was, of course. But if there is a bear market, there will be plenty of time to buy later. This was also true in ’09, which was much more of a ‘spike’ bottom but let’s face it, you had months and months to get in…except that no one wanted to get in at the time.

If it is not a bear market, then sure – it’s a buying opportunity. But what I know from watching this drama play out several times is that you cannot tell at the time whether it’s a buying opportunity, or a dead-cat bounce. It does not help at all to say “but the economy is okay.” Recalling that the Nasdaq’s peak was in March 2000: the Fed was still hiking rates in May of that year, and didn’t cut rates until 2001.  In late July 2000, GDP printed 5.2% following 4.8% in Q1. In October 2000, GDP for Q3 was reported to still be at 2.2%. Waiting for the economy to tell you that all was not well was very costly. By the time the Fed was alarmed enough to ease, in a surprise move on January 3, 2001, the S&P was down 16%. But fortunately, that ended it as stocks jumped 5% on the Fed’s move. Buy the dip!

By mid-2002, stocks were down about 50% from the high. Buying the dip was in that case precisely wrong.

Then there is the bear market of a decade ago. The October 2007 market high happened when the economy was still strong, although there were clearly underlying stresses in mortgages and mortgage banking and the Fed was already easing. Yet, on January 10, 2008, Fed Chairman Bernanke said “the Federal Reserve is not currently forecasting a recession.” On January 18, he said the economy “has a strong labor force, excellent productivity and technology, and a deep and liquid financial market that is in the process of repairing itself.” In June 2008, he said “The risk that the economy has entered a substantial downturn appears to have diminished over the past month or so.” Stocks were already down 19%. It got somewhat worse…and it didn’t take long.

So the thing to remember is this: equities do not wait for earnings to suffer, or for forecasts of earnings to suffer, or for everyone to figure out that growth is flagging, or for someone to ring a bell. By the time we know why stocks are going down, it is too late. This is why using some discipline is important – crossing the 200-day moving average, or value metrics, or whatever. Or, decide you’ll hold through the -50% moves and ignore all the volatility. Good luck…but then why are you reading market commentary?

I don’t know that stocks are going to enter a bear market. I don’t know if they’ll go down tomorrow or next week or next month. I have a pretty strong opinion about expected real returns over the next 10 years. And for that opinion to be realized, there will have to be a bear market (or two) in there somewhere. So it will not surprise me at any time if a bear market begins, especially from lofty valuation levels. But my point in this article is just to provide some historical context. And my general advice, which is not specific to any particular person reading this, is that if anyone tells you that price moves like this are ‘capitulation’ to be followed by ‘v-shaped recoveries,’ then don’t just walk away but run away. They haven’t any idea, and that advice might make you a few percent or lose you 50%.

To be sure, don’t panic and abandon whatever plan you had, simply because other people are nervous. As Frank Herbert wrote, “fear is the mind-killer. Fear is the little-death that brings total obliteration.” This is why having a plan is so important! And I also think that plans should focus on the long term, and on your personal goals, and matching your long-term investments to those goals. Rebalancing and compounding are powerful tools, as is a value ethic of buying securities that have a margin of safety.

And, of course, diversification. Bonds today did what they’re supposed to do when ‘risky assets’ take a tumble: they rallied. As I noted on Friday: “I am not saying that interest rates are going directly from 3% to 6%. Indeed, the rates/equity ecosystem is inherently self-dampening to some degree (at least, until we reach a level where we’ve exceeded the range of the spring’s elasticity!) in that if equity prices were to head very much lower, interest rates would respond under a belief that central bankers would moderate their tightening paths in the face of weak equities.” The problem with nominal bonds at this point, though, is that they’re too expensive. At these yields, there is a limit to the diversification they can provide, especially if what is going to drive the bear market in stocks is rising inflation. Bonds will diversify against the sharp selloff, but not against the inflation spiral. (I’ve said it before and I will say it again. If you haven’t read Ben Inker’s piece in the latest GMO quarterly, arguing why inflation is a bigger risk for portfolios right now than recession, do so. “What happened to inflation? And What happens if it comes back?”)

Which brings us to commodities. If the factor driving an equity bear market turns out to be inflation, then commodities should remain uncoupled from equities. For the last few days, commodity indices have declined along with equities – not nearly as much, of course, but the same sign. But if the problem is a fear of inflation then commodities should be taking the baton from stocks.

So there you go. If the problem is rising interest rates, then that is a slow-moving problem that’s self-limiting because central banks will bring rates back down if stocks decline too far. If the problem is rising inflation, then commodities + inflation bonds should beat equities+nominal bonds. Given that commodities and inflation bonds are both relatively cheaper than their counterparts, I’d rather bet that way and have some protection in both circumstances.

Why Commodities Are a Better Bet These Days

January 16, 2018 3 comments

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It’s been a long time since an article about commodities felt like ‘click bait.’ After all, commodity indices have been generally declining for about seven years – although 2016 saw a small advance – and the Bloomberg Commodity Index today sits 63% below its all-time high set in the summer of 2008. I’ve written before, quite a bit, about this absurdity of the market, represented in the following chart comparing one real asset (equities) to another real asset (commodities). The commodity index here is the Bloomberg spot index, so it does not include the drag (boost) from contango (backwardation).

This is the fair comparison for a forward-looking analysis. Some places you will see the commodity index plotted against the S&P, as below. Such a chart makes the correct inference about the historic returns to these two markets; the prior chart makes a more poignant point about the current pricing of stocks versus commodities.

There’s nothing that says these two markets should move in lock-step as they did from 2003-2007, but they ought to at least behave similarly, one would think. So it is hard to escape the reasoning that commodities are currently very cheap to equities, as one risk-asset to another.

Furthermore, commodity indices offer inflation protection. Here are the correlations between the GSCI and headline inflation, core inflation, and the change in those measures, since 1970 and 1987 respectively.

Stocks? Not so much!

So, commodities look relatively cheap…or, anyway, they’re relatively cheaper, having gone down for 7 years while stocks went higher for 7 years. And they give inflation protection, while stocks give inflation un-protection. So what’s not to like? How about performance! The last decade has been incredibly rough for commodities index investors. However, this is abnormal. In a watershed paper in 2006 called Facts and Fantasies about Commodity Futures, Gorton and Rouwenhorst illustrated that, historically, equities and commodity futures have essentially equivalent monthly returns and risks over the period from 1959-2004.

Moreover, because the drivers of commodity index returns in the long run are not primarily spot commodity prices[1] but, rather, the returns from collateral, from roll or convenience yield, from rebalancing, and from “expectational variance” that produces positive skewness and kurtosis in commodity return distributions,[2] we can make some observations about how expected returns should behave between two points in time.

For example, over the last few years commodities markets have been heavily in contango, meaning that in general spot prices were below forward prices. The effect of this on a long commodity index strategy is that when futures positions are rolled to a new contract month, they are being rolled to higher prices. This drag is substantial. The chart below shows the Bloomberg Commodity Index spot return, compared to the return of the index as a whole, since 2008. The markets haven’t all been in contango, and not all of the time. But they have been in serious contango enough to cause the substantial drag you can see here.

So here is the good news. Currently, futures market contango is the lowest it has been in quite a while. In the last two years, the average contango from the front contract to the 1-year-out contract has gone from 15% or so to about 2% backwardation, using GSCI weights (I know I keep switching back and forth from BCOM to GSCI. I promise there’s nothing sinister about it – it just depends what data I had to hand when I made that chart or when it was calculated automatically, such as the following chart which we compute daily).

That chart implies a substantial change in the drag from roll yield – in fact, depending on your weights in various commodities the roll yield may currently be additive.

The other positive factor is the increase in short-term interest rates. Remember that a commodity index is (in most cases) represents a strategy of holding and rolling futures contracts representing the desired commodity weights. To implement that strategy, an investor must put up collateral – and so an unlevered commodity index return consists partly of the return on that particular collateral. It is generally assumed that the collateral is three-month Treasury Bills. Since the financial crisis, when interest rates went effectively to zero in the US, the collateral return has approximated zero. However, surprise! One positive effect of the Fed’s hiking of rates is to improve projected commodity index returns by 1.5-2% per year (and probably more this year). The chart below shows 3-month TBill rates.

I hope this has been helpful. For the last 5 years, investing in commodities was partly a value/mean-reversion play. This is no longer so true: the change in the shape of the futures curves, combined with rising interest rates, has added substantially to the expected return of commodity indices going forward. It’s about time!


[1] This is a really important point. When people say “commodities always go down in the long run because of increased production,” they’re talking about spot commodity prices. That may be a good reason not to own spot gold or silver, or any physical commodity. Commodity spot returns are mean reverting with a downward slant in real space, true. But a commodity index gets its volatility from spot returns, but its main sources of long term return are actually not terribly related to spot commodities prices.

[2] In other words while stocks “crash” downwards, commodities tend to “crash” upwards. But this isn’t necessary to understand what follows. I just want to be complete. The term “expectational variance” was coined by Grant Gardner.

Point Forecast for Real Equity Returns in 2018

January 3, 2018 2 comments

Point forecasts are evil.

Economists are asked to make point forecasts, and they oblige. But it’s a dumb thing to do, and they know it. Practitioners, who should know better, rely on these point forecasts far more than they should. Because, in economics and especially in markets, there are enormous error bars around any reasonable point forecast, and those error bars are larger the shorter-term the forecast is (if there is any mean-reversion at all). I can no more forecast tomorrow’s change in stock market prices than I can forecast whether I will draw a red card from a deck of cards that you hand me. I can make a reasonable 5-year or 10-year forecast, at least on a compounded annualized basis, but in the short term the noise simply swamps the signal.[1]

Point forecasts are especially humorous when it comes to the various year-end navel-gazing forecasts of stock market returns that we see. These forecasts almost never have fair error bars around the estimate…because, if they did, there would be no real point in publishing them. I will illustrate that – and in the meantime, please realize that this implies the forecast pieces are, for the most part, designed to be marketing pieces and not really science or research. So every sell-side firm will forecast stock market rallies every year without fail. Some buy side firms (Hoisington springs to mind) will predict poor returns, and that usually means they are specializing in something other than stocks. A few respectable firms (GMO, e.g.) will be careful to make only long-term forecasts, over periods of time in which their analysis actually has some reasonable predictive power, and even then they’ll tend to couch their analysis in terms of risks. These are good firms.

So let’s look at why point forecasts of equity returns are useless. The table below shows Enduring’s year-end 10-year forecast for the compounded real return on the S&P 500, based on a model that is similar to what GMO and others use (incorporating current valuation levels and an assumption about how those valuations mean-revert).[2] That’s in the green column labeled “10y model point forecast.” To that forecast, I subtract (to the left) and add (to the right) one standard deviation, based on the year-end spot VIX index for the forecast date.[3] Those columns are pink. Then, to the right of those columns, I present the actual subsequent real total return of the S&P 500 that year, using core CPI to deflate the nominal return; the column the farthest to the right is the “Z-score” and tells how many a priori standard deviations the actual return differed from the “point forecast.” If the volatility estimate is a good one, then roughly 68% of all of the observations should be between -1 and +1 in Z score. And hello, how about that? 14 of the 20 observations fall in the [-1,1] range.

Clearly, 2017 was remarkable in that we were 1.4 standard deviations above the 12/31/2016 forecast of +1.0% real. Sure, that “forecast” is really a forecast of the long-term average real return, but that’s not a bad place to start for a guess about next year’s return, if we must make a point forecast.

This is all preliminary, of course, to the forecast implied by the year-end figures in 2017. The forecast we would make would be that real S&P returns in 2018 have a 2/3 chance of being between -10.9% and +11.1%, with a point forecast (for what that’s worth) of +0.10%. In other words, a rally this year by more than CPI rises is still as likely as heads on a coin flip, even though a forecast of 0.10% real is a truly weak forecast and the weakest implied by this model in a long time.

It is clearly the worst time to be invested in equities since the early 2000s. Even so, there’s a 50-50 chance we see a rally in 2018. That’s not a very good marketing pitch. But it’s better science.[4]


[1] Obligatory Robert Shiller reference: his 1981 paper “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends” formulated the “excess volatility puzzle,” which essentially says that there’s a lot more noise than signal in the short run.

[2] Forecasts prior to 2009 predate this firm and are arrived at by applying the same methodology to historical data. None of these are discretionary forecasts and none should be taken as implying any sort of recommendation. They may differ from our own discretionary forecasts. They are for illustration only. Buyer beware. Etc.

[3] The spot VIX is an annualized volatility but incorporating much nearer-term option expiries than the 1-year horizon we want. However, since the VIX futures curve generally slopes upward this is biased narrow.

[4] And, I should hasten point out: it does have implications for portfolio allocations. With Jan-2019 TIPS yielding 0.10% real – identical to the equity point forecast but with essentially zero risk around that point – any decent portfolio allocation algorithm will favor low-risk real bonds over stocks more than usual (even though TIPS pay on headline CPI, and not the core CPI I am using in the table).

Retail Investors Aren’t As Stupid As They Tell You

December 11, 2017 Leave a comment

Let’s face it, when it comes to the bullish/bearish argument about equities these days, the bears have virtually all of the arguments in their favor. Not all, but almost all. However, I always think the bears hurt their case with certain poor arguments that tend to be repeated a lot – in fact, it’s one way to tell the perma-bears from the thoughtful bears.

One of the arguments I have seen recently is that retail investors are wayyy out over their skis, and are very heavily invested in stocks with very low cash assets. This chart, which I saw in a recent piece by John Mauldin, is typical of the genre.

Now, bears are supposed to be the skeptics in the equation, and there is just nowhere near enough skepticism being directed at the claim that retail investors are being overly aggressive. Gosh, the first place a person could start is with asking “shouldn’t allocations properly be lower now, with zero returns to cash, than they were when yields were higher?”

But as it turns out, we don’t even have to ask that question because there’s a simpler one that makes this argument evaporate. Consider an investor who, instead of actively allocating to stocks when they’re “hot” (stupid retail investor! Always long at the top!) and away from them when they’re “cold” (dummy! That’s when you should be loading up!), is simply passive. He/she begins in mid-2005 (when the chart above begins) with a 13% cash allocation and the balance of 87% allocated to stocks. Thereafter, the investor goes to sleep for twelve years. The cash investments gain slowly according to the 3-month T-Bill rate; the equity investments fluctuate according to the change in the Wilshire 5000 Total Market index. This investor’s cash allocation ends up looking like this.

How interesting! It turns out that since the allocation to cash is, mathematically, CASH / (CASH+STOCKS), when the denominator declines due to stock market declines the overall cash ratio moves automatically! Thus, it seems that maybe what we’re looking at in the “scary” chart is just the natural implication of fluctuating markets and uninvolved, as opposed to returns-chasing, investors.

Actually, it gets better than that. I put the second chart on top of the first chart, so that the axes correspond.

It turns out that retail investors are actually much more in cash than a passive investor would be. In other words, instead of being the wild-and-woolly returns chasers it turns out that retail investors seem to have been responding to higher prices by raising cash, doing what attentive investors should do: rebalancing. So much for this bearish argument (to be clear, I think the bears are correct – it’s just that this argument is lame).

Isn’t math fun?

The Limits to Trusting the Robots

October 20, 2017 1 comment

After another day on Thursday of stocks starting to look mildly tired – but only mildly – only to rally back to a new closing high, it hardly seems unusual any more. I have to keep pinching myself, reminding myself that this is historically abnormal. Actually, very abnormal. If the S&P 500 Total Return Index ends this month with a gain, it will be the second time in history that has happened. The other time was in 1936, as stocks bounced back from a deep bear market (at the end of those 12 months, in March 1936, stocks were still 54% off the 1929 highs). A rally this month would also mean that stocks have gained for 19 out of the last 20 months, the longest streak with just one miss since…1936 again.

But we aren’t rebounding from ‘oversold.’ This seems to be a different situation.

What is going on is confounding the wise and the foolish alike. Every dip is bought; the measures of market constancy (noted above, for example) are at all-time highs and the measures of market volatility such as the VIX are at all-time lows. It is de rigeur at this point to sneer “what could go wrong?” and you may assume I have indeed so sneered. But I also am curious about whether there is some kind of feedback loop at work that could cause this to go on far longer than it “should.”

To be sure, it shouldn’t. By many measures, equities are at or near all time measures of richness. The ones that are not at all-time highs are still in the top decile. Buying equities (or for that matter, bonds) at these levels ought to be a recipe for a capitalistic disaster. And yet, value guys are getting carried out left and right.

Does the elimination (with extreme prejudice) of value traders have any implications?

There has been lots of research about market composition: models, for example, that examine how “noise” and “signal” traders come together to create markets that exhibit the sorts of characteristics that normal markets do. Studies of what proportion of “speculators” you need, compared to “hedgers,” to make markets efficient or to cause them to have bubbles form.

So my question is, what if the combination of “buy the dip” micro-time-frame value guys, combine with the “risk parity” guys, represents a stable system?

Suppose equity volatility starts to rise. Then the risk-parity guys will start to sell equities, which will push prices lower and tend to push volatility higher. But then the short-term value guys step in to ‘buy the dip.’ To be clear, these are not traditional value investors, but rather more like the “speculators” in the hedger/speculator formulation of the market. These are people who buy something that has gone down, because it has gone down and is therefore cheaper, as opposed to the people who sell something that has gone down, because the fact that it has gone down means that it is more likely to go down further. In options-land, the folks buying the dip are pursuing a short-volatility strategy while the folks selling are pursuing a long-volatility strategy.[1]

Once the market has been stabilized by the buy-the-dip folks, who might be for example hedging a long options position (say, volatility arbitrage guys who are long actual options and short the VIX), then volatility starts to decline again, bringing the risk-parity guys back into equities and, along with the indexed long-only money that is seeking beta regardless of price, pushing the market higher. Whereupon the buy-the-dip guys get out with their scalped profit but leaving prices higher, and volatility lower, than it started (this last condition is necessary because otherwise it ends up being a zero-sum game. If prices keep going higher and implied volatility lower, it need not be zero-sum, which means both sides are being rewarded, which means that we would see more and more risk-parity guys – which we do – and more and more delta-hedging-buy-the-dip guys – which we do).

Obviously this sort of thing happens. My question though is, what if these different activities tend to offset in a convergent rather than divergent way, so that the system is stable? If this is what is happening then traditional value has no meaning, and equities can ascend arbitrary heights of valuation and implied volatility can decline arbitrarily low.

Options traders see this sort of stability in micro all the time. If there is lots of open interest in options around, say, the 110 strike on the bond contract, and the Street (or, more generally, the sophisticated and leveraged delta-hedgers) is long those options, then what tends to happen is that if the bond contract happens to be near 110 when expiry nears it will often oscillate around that strike in ever-declining swings. If I am long 110 straddles and the market rallies to 110-04, suddenly because of my gamma position I find myself long the market since my calls are in the money and my puts are not. If I sell my delta at 110-04, then I have locked in a small profit that helps to offset the large time decay that is going to make my options lose all of their remaining time value in a short while.[2] So, if the active traders are all long options at this strike, what happens is that when the bond goes to 110-04, all of the active folks sell to try and scalp their time decay, pushing the bond back down. When it goes to 99-28, they all buy. Then, the next time up, the bond gets to 110-03 and the folks who missed delta-hedging the last time say “okay, this time I will get this hedge off” and sell, so the oscillation is smaller. Sometimes it gets really hard to have any chance of covering time decay at all because this process results in the market stabilizing right at 110-00 right up until expiration. And that stabilization happens because of the traders hedging long-volatility positions in a low-volatility environment.

But for the options trader, that process has an end – options expiration. In the market process I am describing where risk-parity flows are being offset by buy-the-dip traders…is there an end, or can that process continue ad infinitum or at least, “much longer than you think it can?”

Spoiler alert: it already has continued much longer than I thought it could.

There is, however, a limit. These oscillations have to reach some de minimus level or it isn’t worth it to the buy-the-dip guys to buy the dip, and it isn’t worth reallocation of risk-parity strategies. This level is much lower now than it has been in the past, thanks to the spread of automated trading systems (i.e., robots) that make the delta-hedging process (or its analog in this system) so efficient that it requires less actual volatility to be profitable. But there is a limit. And the limit is reach two ways, in fact, because the minimum oscillation needed is a function of the capital to be deployed in the hedging process. I can hedge a 1-lot with a 2 penny oscillation in a stock. But I can’t get in and out of a million shares that way. So, as the amount of capital deployed in these strategies goes up, it actually raises the potential floor for volatility, below which these strategies aren’t profitable (at least in the long run). However, there could still be an equilibrium in which the capital deployed in these strategies, the volatility, and the market drift are all balanced, and that equilibrium could well be at still-lower volatility and still-higher market prices and still-larger allocations to risk-parity etc.

It seems like a good question to ask, the day after the 30th anniversary of the first time that the robots went crazy, “how does this stable system break down?” And, as a related question, “is the system self-stabilizing when perturbed, or does it de-stabilize?”

Some systems are self-stabilizing with small perturbations and destabilizing with larger perturbations. Think of a marble rolling around in a bowl. A small push up the side of the bowl will result in the marble eventually returning to the bottom of the bowl; a large push will result in the marble leaving the bowl entirely. I think we are in that sort of system. We have seen mild events, such as the shock of Brexit or Trump’s electoral victory, result in mild volatility that eventually dampened and left stocks at a higher level. I wonder if, as more money is employed in risk parity, the same size perturbation might eventually be divergent – as volatility rises, risk parity sells, and if the amount of dip-buyers is too small relative to the risk parity sellers, then the dip-buyers don’t stabilize the rout and eventually become sellers themselves.

If that’s the secret…if it’s the ratio of risk-parity money to dip-buyer money that matters in order to keep this a stable, symbiotic relationship, then there are two ways that the system can lose stability.

The first is that risk parity strategies can attract too much money. Risk parity is a liquidity-consumer, as they tend to be sellers when volatility is rising and buyers when volatility is falling. Moreover, they tend to be sellers of all assets when correlations are rising, and buyers of all assets when correlations are falling. And while total risk-parity fund flows are hard to track, there is little doubt that money is flowing to these strategies. For example one such fund, the Columbia Adaptive Risk Allocation Fund (CRAZX), has seen fairly dramatic increases in total assets over the last year or so (see chart, source Bloomberg. Hat tip to Peter Tchir whose Forbes article in May suggested this metric).

The second way that ratio can lose stability is that the money allocated to buy-the-dip strategies declines. This is even harder to track, but I suspect it is related to two things: the frequency and size of reasonable dips to buy, and the value of buying the dip (if you buy the dip, and the market keeps going down, then you probably don’t think you did well). Here are two charts, with the data sourced from Bloomberg (Enduring Intellectual Properties calculations).

The former chart suggests that dip-buyers may be getting bored as there are fewer dips to buy (90% of the time over the last 180 days, the S&P 500 has been within 2% of its high). The latter chart suggests that the return to buying the dip has been low recently, but in general has been reasonably stable. This is essentially a measure of realized volatility. In principle, though, forward expectations about the range should be highly correlated to current implied volatility so the low level of the VIX implies that buying the dip shouldn’t give a large return to the upside. So in this last chart, I am trying to combine these two items into one index to give an overall view of the attractiveness of dip buying. This is the VIX, minus the 10th percentile of dips to buy.

I don’t know if this number by itself means a whole lot, but it does seem generally correct: the combination of fewer dips and lower volatility means dip-buying should become less popular.

But if dip-buying becomes less popular, and risk-parity implies more selling on dips…well, that is how you can get instability.

[1] This is not inconsistent with how risk parity is described in this excellent paper by Artemis Capital Management (h/t JN) – risk parity itself is a short volatility strategy; to hedge the delta of a risk parity strategy you sell when markets are going down and buy when markets are going up, replicating a synthetic long volatility position to offset.

[2] If this is making your eyes glaze over, skip ahead. It’s hard to explain this dynamic briefly unless I assume some level of options knowledge in the reader. But I know many of my readers don’t have that requisite knowledge. For those who do, I think this may resonate however so I’m plunging forward.

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