Negative skewness, or: bulls walk up stairs, bears jump out of windows

Recent market action is a good reminder of the asymmetry in markets. In general, stock market rises don't look like stock market declines. Stock indexes slowly eke out gains over a period of months, but lose all of those gains just a few days. There are plenty of famous meltdowns in stocks, including 1914, 1929, 1987, and 2008, but almost no famous "melt ups."

Just like the Inuit have multiple words for snow because they are surrounded by the stuff, equity commentators have many words for crashes (panics, selloff, etc). These events are not uncommon. In the same way that many indigenous African languages have no word for snow, we lack a good word to describe one or two day melt-ups in equity markets since these aren't part of our landscape.

There are a number of trader's adages that describe this pattern, including bulls walk up the stairs, bears jump out the window and variations on that theme. In the economic literature, this phenomenon is referred to as negative skewness. If you look at the distribution of daily percent returns for the S&P 500 Index over a long period of time, you'll notice that there are more extreme negative results than extreme positive results, with the majority of results being slightly positive. Whereas a normal distribution, or the bell shaped curve we've all seen in statistics class, is symmetrical with 95% of values dwelling within two standard deviations of the mean, a negatively skewed distribution has a fat left tail where declines extend far beyond what you would expect for a normally distributed data set.

The chart below illustrates this. Out of 22,013 trading days going back to 1928, just 47.8% of days resulted in negative outcomes while 52.2% resulted in positive outcomes. This makes sense given the generally upward trajectory of equity markets over that period. If we sort each day's return into buckets, we start to see asymmetries develop. For instance, there were 10,973 days on which markets moved higher or lower by by 0.5%, just 48.4% of which were lower. The majority of 0.5 to 1% and 1 to 2% changes were to the positive side as well. The distribution changes once we look at the 2% and over bucket. Out of 1485 days with "extreme" returns, the majority (51.9%) of changes were declines of 2% or greater rather than rises of +2% or greater.

Figure: Distribution of daily changes in the S&P 500 index going back to 1928

Financial economists have a number of hypothesis for negative skewness. One theory blames leverage, whereby a drop in a firm's equity price raises its leverage, or the amount of debt it uses to finance itself. This makes an investment in the company more risky and leads to higher volatility of its shares. Conversely, when a stock rises, its leverage decreases, making the shares less risky. For that reason, rises in equities are tame while falls are wild. While an attractive theory, data shows that as stock prices decline, all-equity financed companies experience jumps in volatility of the same magnitude as leveraged companies, indicating that leverage is not a good explanation for a pattern of negative skewness.

Another explanation is the existence of "volatility feedback." When important news arrives, this signals that market volatility has increased. If the news is good, investor jubilation will be partially offset by an increase in wariness over volatility, the final change in share price being smaller than it would otherwise have been. When the news is bad, disappointment will be reinforced by this wariness, amplifying the decline.

Other theories blame short sale constraints for the asymmetry. If bearish investors are restricted from expressing their pessimism, they will be forced to the sidelines and their information will not be fully incorporated into prices. When the bulls start to bail out of equities, the bearish group becomes the marginal buyer, at which point bearish information is finally "discovered" by the market, the result being large price declines.

Putting the reasons aside, behavioral finance types have some interesting things to say about how investors perceive skewness. According to prospect theory, investors are not perfectly rational decision makers. To begin with, returns are not appraised in a symmetrical manner; a 5% loss hurts investors more than a 5% gain feels good. Next, investors overweight unlikely events and underweight average ones. Given these two quirks, investors may prefer positively skewed assets (like government bonds), which have far fewer large declines than normally skewed assets, as this distribution reduces the potential for psychological damage. The possibility of large lottery-like returns, the odds of which investors overweight relative to the true odds of a positive payout, also drive preferences for positive skew assets. Negatively skewed assets like equity ETFs, which expose investors to tortuous drops while not offering much potential for large melt-ups, are to be avoided.

Put differently, positive skew is a feature that investors will pay to own. Negative skew is a "bad" and people need to be compensated for enduring it.

If you buy this theory, then in order to coax investors into holding negatively skewed assets like stocks, sellers need to offer buyers a higher expected return. The presence of this carrot could be one of the reasons why equities tend to outperform bonds over time. For equity owners who are suffering through the current downturn, here's the upshot: negative skew events like the current one, while stressful, may be the price you have to pay in order to harvest the superior returns provided by stocks over the long term.

How many bullets does the Bank of Canada have left in its chamber?

It's been a while since I blogged about Canadian monetary policy, but Luke Kawa's recent tweet on the topic of Canada's effective lower bound got me thinking.

BoC has referred to 0.25% as its "effective lower bound" -- Shenfeld suggested that any lower, BoC thinks there'll be problems in money mkts

— Luke Kawa (@LJKawa) August 4, 2015

Luke is referring here to CIBC chief economist Avery Shenfeld's recent missive on how the Bank of Canada might react if the Canadian economy's losing streak were to continue. According to Shenfeld, the Bank of Canada has one final quarter point cut left in its quiver—from 0.5% to 0.25%. Should the bleeding continue, Governor Stephen Poloz can then turn to forward guidance and only when that has been exhausted will quantitative easing become a possibility.

Really? The Bank of Canada can't go below 0.25%? Has Shenfeld not been following what has been occurring outside Canada's borders over the last twelve months? Sweden's central bank, the Riksbank, has cut its repo rate to -0.35% while the European Central Bank has ratcheted its deposit rate down to -0.2%. The Swiss National Bank is targeting an overnight interest rate of -0.75%, down from 0% the prior year, at the same time that the Danmarks Nationalbank currently maintains a certificate of deposit rate of -0.75%. I've been covering this stuff pretty exhaustively here, here, here, here, and here.

After digging a bit further, I was surprised to find that the sort of interest rate emasculation implied in Shenfeld's piece is endemic here in Canada. David Rosenberg of Gluskin Sheff, for instance, recently said that Poloz has "just one bullet left in the chamber" while the FP's John Schmuel wonders what will happen if the Bank of Canada is forced to use its "last remaining lifeline and cut its rate to zero." The Bank of Canada is also a transgressor in spreading the meme: on its FAQ, the Bank says that the overnight rate's lowest possible level—its effective lower bound—is 0.25%.

One reason the faux 0.25% lower bound continues to circulate in the public discourse is the somewhat lazy reliance commentators have on the Bank of Canada's credit crisis playbook as a model for how low rates can go. In addition to implementing forward guidance during the crisis, the Bank reduced the overnight rate to 0.25% by flooding the system with excess balances. But this playbook has gone stale. As I've already pointed out, a number of European central banks have demonstrated the possibility of going below zero. A Bank of Canada deposit rate cut to as deep as, say, -0.50%, combined with an overnight target of -0.25, effectively buys Poloz three more 25 basis point interest rate cuts, not just one.

Ask folks why Canadian markets can't bear negative interest rates and there's typically a lot of arm-waving and mumbling about money markets. Case in point is Shenfeld on the +0.25% level: "In the Canadian money market structure that’s as low as she gets, and effectively represents the zero lower bound for monetary policy." I'm not aware of a single Canadian fixed income product that can't bear slightly negative interest rates. Would maple syrup commercial paper markets come to a standstill if the Bank of Canada cut rates to -0.25%? Would the market for Gordie Howe bonds collapse? While no doubt a nuisance, the transition to negative rates has been managed by money markets in Denmark, Sweden, Switzerland, and the rest of Europe without major mishap. There's simply no justification for Canadian exceptionalism.

While slightly negative rates won't cause structural problems in money markets, deeply negative rates would certainly be problematic. Send rates low enough and bank runs will begin as people cash in their negative-yielding money market instruments for paper dollars. At some point the banking system would cease to exist. But this doesn't occur at Shenfeld's so-called 0.25% lower bound, nor at -0.75%. Thanks to the carrying costs of bulky banknotes, it probably only starts to be a problem somewhere between -1.0% to -3.0%. The existence of a wide safe zone before hitting those levels gives the Bank of Canada a lot more lifelines than just one.

The last reason for the circulation of a false lower bound in Canadian monetary policy discussion is vested interests. I doubt that Canada's big banks are fond of incurring the frictional costs associated with transitioning to a negative rate world. Better to "wipe out" that possibility from the Overton Window and push something less-threatening like forward guidance.

Let me be clear that I have no specific insight into whether the Bank of Canada should be loosening or not. What is important is that the Bank has flexibility to the downside should it decide that easing be necessary. Breathing space is important because pound-for-pound, actual interest rate cuts are always better than unconventional policies like forward guidance—the promise to keep interest rates too low in the future—or quantitative easing. A move to -0.15% or -0.25%, should it be necessary, represents a continuation of the Bank of Canada's decades' long method of implementing conventional monetary policy via direct interest rate adjustments. It's not fancy, but it has been in place for a long time and everyone pretty much gets it by now. Central bank guidance, on the other hand, is complicated and suffers from the fact that the public can never be sure that a three-year promise initiated by a Conservative-appointed governor will stay in place should an NDP-appointed governor take his place. As for quantitative easing, it doesn't even work in theory, as pointed out by none other than Ben Bernanke. (Or see how New Zealand's cashing up the system had no influence on prices)

Incidentally, if Canada were to suffer a broader shock than the current one and the Bank of Canada found it necessary to go deep into negative territory, say -6%, there are all sorts of ways it can go about doing so without causing stress in money markets. In fact, economist & blogger Miles Kimball recently visited the Bank of Canada to explain how to go about implementing extremely low rates without igniting a run into paper dollars, or what he refers to as massive paper storage. I've written about some "lite" ways to go about doing so as well.

Interestingly, Kimball writes that the Bank of Canada already has an “Effective Lower Bound” working group that is focused on "exploring the possibilities for negative interest rate policy in the next recession." So while the public discourse on Canadian monetary policy seems to have settled on the "one remaining lifeline" view, it appears that internally that is not the case—the Bank of Canada knows that it has much more up its sleeve.

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Various charts:

Freshwater macro, China's silver standard, and the yuan peg

1934 Chinese silver dollar with Sun Yat-sen on the obverse side. The ship may be in freshwater.

I have been hitting my head against the wall these last few weeks trying to understand Chinese monetary policy, a project that I've probably made harder than necessary by starting in the distant past, specifically with the nation's experience during the Great Depression. Taking a reading break, I was surprised to see that Paul Krugman's recent post on the topic of freshwater macro had surprising parallels to my own admittedly esoteric readings on Chinese monetary history.

Unlike most nations, China was on a silver standard during the Great Depression. The consensus view, at least up until it was challenged by the freshwater economists that people Krugman's post, had always been that the silver standard protected China from the first stage of the Great Depression, only to betray the nation by imposing on it a terrible internal devaluation as silver prices rose. This would eventually lead China to forsake the silver standard. This consensus view has been championed by the likes of Milton Friedman and Anna Schwartz in their monumental Monetary History of the United States.

This consensus view is a decidedly non-freshwater take on things as it it depends on features like sticky prices and money illusion to generate its conclusions. After all, given the huge rise in the value of silver, as long as Chinese prices and wages—the reciprocal of the silver price—could adjust smoothly downwards, then the internal devaluation forced on China would be relatively painless. If, however, the necessary adjustment was impeded by rigidities then prices would have been locked at artificially high levels, the result being unsold inventories, unemployment, and a recession.

Just to add some more colour, China's internal devaluation was imposed on it by American President Franklin D. Roosevelt in two fell swoops, first by de-linking the U.S. from gold in 1933 and then by buying up mass quantities of silver starting in 1934. The first step ignited an economic rebound in the U.S. and around the world that helped push up all prices including that of silver. As for the second, Roosevelt was fulfilling a campaign promise to those who supported him in the western states where a strong silver lobby resided thanks to the abundance of silver mines. The price of silver, which had fallen from 60 cents in 1928 to below 30 cents in 1932, quickly rose back above its 1928 levels, as illustrated in the chart below. According to one contemporary account, that of Arthur N. Young, an American financial adviser to the Nationalist government, "China passed from moderate prosperity to deep depression."

As I mentioned at the outset, this consensus view was challenged by the freshwater economists, no less than the freshest of them all, Thomas Sargent (who was once referred to as "distilled water"), in a 1988 paper coauthored with Loren Brandt (RePEc link). New data showed that Chinese GDP rose in 1933 and only declined modestly in 1934, this due to a harvest failure, not a monetary disturbance. So much for a brutal internal devaluation.

According to Sargent and Brandt, it appeared that "that there was little or no Phillips curve tradeoff between inflation and output growth in China." In non econo-speak, deflation.not.bad. They put forth several reasons for this, including a short duration of nominal contracts and village level mechanisms for "haggling and adjusting loan payments in the event of a crop failure." In essence, Chinese prices were very quick to adjust to silver's incredible rise.

Four years later, Friedman responded (without Schwartz) to what he referred to as the freshwater economists' "highly imaginative and theoretically attractive interpretation." (Here's the RePEc link). His point was that foreign trade data, which apparently has a firmer statistical basis than the output data on which Sargent and Brandt depended, revealed that imports had fallen on a real basis from 1931 to 1935, and particularly sharply from 1933 to 1935. So we are back to a story in which, it would seem, the rise in silver did place a significant drag on the Chinese economy, although Friedman grudgingly allowed for the fact that perhaps he may have "overestimated" the real effects of the silver deflation.

So this battle of economic titans leads to a watered-down story in which Roosevelt's silver purchases probably had *some* deleterious effects on China. China would go on to leave the silver standard, although what probably provided the final nudge was a bank run that kicked off in the financial centre of Shanghai in 1934. Depositors steadily withdrew the white metal from their accounts in anticipation of some combination of a devaluation of the currency, exchange controls, and an all-out exit from the silver standard, a process outlined in a 1988 paper by Kevin Chang (and referenced by Friedman). This self-fulfilling mechanism, very similar in nature to the recent run on Greece, may have encouraged the authorities to sever the currency's linkage to silver and put it on a managed fiat standard. The Chinese economy went on to perform very well in 1935 and 1936, although that all ended with the Japanese invasion in 1937.

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As I mentioned at the outset, these events and the way they were perceived by freshwater and non-freshwater economists seem to me to have some relevance to modern Chinese monetary policy. As in 1934, China is to some extent importing made-in-US monetary policy. The yuan is effectively pegged to the U.S. dollar, so any change in the purchasing power of the dollar leads to a concurrent change in the purchasing power of the yuan.

There's an asterisk to this. In 1934, China was a relatively open economy whereas today China makes use of capital controls. By immobilizing wealth, these controls make cross-border arbitrage more difficult, thus providing Chinese monetary authorities with a certain degree of latitude in establishing a made-in-China monetary policy.  But capital controls have become increasingly porous over the years, especially as the effort to internationalize the yuan—which requires more open capital markets—gains momentum. By maintaining the peg and becoming more open, China's monetary policy is getting ever more like it was in 1934.

As best I can tell, the monetary policy that Fed Chair Janet Yellen is exporting to China is getting tighter. One measure of this, albeit an imperfect one, is the incredible rise of the U.S. dollar over the last year. Given its peg, the yuan has gone along for the ride. Another indication of tightness in the U.S. is Scott Sumner's nominal GDP betting market which shows nominal growth expectations for 2015 falling from around 5% to 3.2%. That's quite a decline. On a longer time scale, consider that the Fed has been consistently missing its core PCE price target of 2% since 2009, or that the employment cost index just printed its lowest monthly increase on record.

If Chinese prices are as flexible as Brandt and Sargent claimed they were in 1934, then the tightening of U.S. dollar, like the rise in silver, is no cause for concern for China. But if Chinese prices are to some extent rigid, then we've got a Friedman & Schwartz explanation whereby the importation of Yellen's tight monetary policy could have very real repercussions for the Chinese economy, and for the rest of the world given China's size.

Interestingly, since 2014 Chinese monetary authorities have been widening the band in which the yuan is allowed to trade against the U.S. dollar. And the peg, which authorities had been gently pushing higher since 2005, has been brought to a standstill. The last time the Chinese allowed the peg to stop crawling higher was in 2008 during the credit crisis, a halt that Scott Sumner once went so far as to say saved the world from a depression.

Chinese GDP [edit: GDP growth] continues to fall to multi-decade lows while the monetary authorities consistently undershoot their stated inflation objectives. In pausing the yuan's appreciation, the Chinese authorities could very well be executing something like a Friedman & Schwartz-style exit from the silver standard in order to save their economy from tight U.S. monetary policy. This time it isn't an insane silver buying program that is at fault, but the Fed's odd reticence to reduce rates to anything below 0.25%. Further tightening from Yellen may only provoke more offsetting from the Chinese... unless, of course, the sort of thinking underlying Wallace and Brandt takes hold and Chinese authorities decide to allow domestic prices to take the full brunt of adjustment.