The Rise of Carry and Macroeconomic Risk

REVIEW ESSAY
The Rise of Carry:
The Dangerous Consequences of Volatility Suppression and the New Financial Order of Decaying Growth and Recurring Crisis
by Tim Lee, Jamie Lee, and Kevin Coldiron
McGraw-Hill, 2019, 240 pages

For most of the twentieth century, the neoclassical synthesis in economics was generally believed to provide a solid basis for public policy. There were, nonetheless, significant dissenters. Hyman Minsky, for instance, wrote that “modern orthodox economics is not and cannot be a basis for a serious approach to economic policy.”¹ In the wake of the financial crisis and the great recession of 2008, such questioning became even more vociferous, and criticisms like Min­sky’s are now increasingly accepted.

The failure to incorporate finance is the most obvious lacuna of the neoclassical consensus. A greater understanding of how financial mar­kets impact the economy is needed, but financial macroeconomists who seek to address the deficiency are rare, even at the highest levels. A decade ago, I was invited by Andrew Haldane to give an address about asset valuation at the Bank of England, where he is now chief economist. Approximately thirty to forty people attended this semi­nar, and afterward I remarked to Haldane that I was surprised he had been able to find so many financial macroeconomists. “I couldn’t find any,” he replied, “so I hired some financial economists and some macroeconomists and put them together.” Thus a work like The Rise of Carry, in which experienced professionals with a sound understanding of the underlying issues assess an important aspect of finan­cial macroeconomics, is a welcome addition to the literature.

The “rise of carry” here refers primarily to the growth of the market in volatility, in which traders can hedge the stock market exposure of their individual portfolios by buying options on a volatility index. This strategy has grown dramatically in recent years and now has a significant potential to amplify systemic risks. Coupled with the misaligned compensation incentives of various financial mar­kets participants, the rise of carry could have profound implications for market behavior as well as for macroeconomic policy.

Hedging Volatility Risk

The prices of financial assets have two key characteristics: the long-term return they provide, and their volatility, which is the extent to which that return fluctuates. Carry traders deal in market volatility. The most significant example of this is the market in the Chicago Board Options Exchange’s Volatility Index (VIX) which, as the au­thors observe, provides the key indicator of financial markets’ assess­ment of risk not just for the S&P 500 index, on which the VIX is based, but more generally. The willingness to accept risk in the bond and currency markets appears to vary with that in equities, and in each case is probably associated with the extreme ease of U.S. mone­tary policy. In addition, the importance of the VIX as an indicator of risk applies worldwide as well as to the United States, as the swings in international stock markets are strongly correlated and the degree to which they move together has been growing. In the authors’ words, “The S&P 500 is both the key driver of world markets and increasingly the epicenter of global carry.”

Many owners of financial assets wish at times to take out insurance against a sudden drop in asset values, and those who are worried about the U.S. stock market can buy the VIX, as its price changes with the market’s expectations about volatility, which in practice are almost identical to changes in its actual volatility. If the fluctuations in the S&P 500 index are greater than anticipated, the price of the VIX will rise and it can then be sold at a profit, thus offsetting any losses incurred as a result or in association with an increase in the market’s volatility.

The VIX is based on the prices of put and call options, which give buyers the right to sell and buy at set prices. If investors wish to protect themselves against a falling stock market they can buy a put, which entitles them to sell at any time during the life of the option at a set price. Investors can also hold cash and insure themselves against missing out should the market rise significantly by buying a call option, which allows the holder to buy a security at a set price. According to the Black-Scholes formula for option valuation, changes in the short-term value of puts and calls depends almost entirely on changes in the volatility of the return on the underlying asset.²

Unlike the stock market, which gives a positive return to long-term holders, the VIX gives a long-term negative return, as it is priced above the actual volatility of the market over the long term. This difference in price is the premium paid by those who take out insur­ance against a rise in volatility. In other words, the VIX’s implied volatility is greater than the actual volatility of the stock market, as it is based on option prices in which an insurance premium is embedded.

Volatility insurance differs in one important respect from other common forms of insurance (such as life, home, and vehicle insurance), which allow the specific risk of events to be pooled. In these forms of insurance, the aggregate risks taken by insurers are significantly less than the sum of the individual risks. Homeowners who buy fire insurance, for instance, pay regular premiums and are pro­tected thereby against loss. The number of houses destroyed by fire annually does not vary much from year to year, and so the insurance industry’s total income is sufficient each year to pay for the individual costs without being at risk of significant overall loss, although profits will fluctuate as fire damage varies from year to year. But this common sort of risk pooling is not characteristic of the carry trade, in which the aggregate risk is systemic rather than specific.

Increases and decreases in the value of the Volatility Index are similar to the annual changes in total losses from fire damage, not to the specific risk that an individual house will burn down. Those who own many houses spread over different locations would find no bene­fit from insurance as the premiums would cost at least as much as the losses. But insurance provides a real benefit to those who own one house. Shares are different: they go up and down together. Investors reduce their risks by owning diversified portfolios of shares, but they cannot thereby avoid the systemic risk of a market crash. They can, however, do this by buying the VIX. Volatility insurance is therefore more like the reinsurance market than that for insuring individual houses, but even here the scale of the aggregate risk overshadows any similarities. Short of war, 89 percent of houses will not burn down over any given four-year period, whereas the stock market lost 89 percent of its value from its peak in 1928 to its trough in 1932. As Henry Kaufman wrote in his autobiography, “financial options create risks that cannot be hedged perfectly without, in effect, undoing the transactions altogether.”³

Investors who insure against volatility usually want protection from sharp drops in share prices, which are closely correlated with increases in market volatility. As shown in figure 1, the actual pattern of equity returns is not quite a normal distribution, in which rises and falls are symmetrical. There are more years in which returns are above average than years in which they are below average, and there are more bad years with extreme results than good years. This pattern of returns can be closely represented by two normal distributions in which the market gives an above-average return 90 percent of the time but a negative return in the remaining 10 percent.⁴

These characteristics are reflected in the options market on which the VIX is based. As both put and call options provide the same cover against market volatility, the prices of the two exhibit a phenomenon known as “put-call parity,” diverging little from each other.

Buying puts and calls is possible only because investment banks and others are prepared, for a consideration, to take on the risk of selling options. They in turn wish to avoid the losses that result from market fluctuations. In the case of small changes in the market, this is achieved through a process known as “delta hedging.” This involves dealing in the cash market (buying and selling the underlying equities) with its associated costs, as The Rise of Carry explains in detail. If the price of the underlying security changes, the price of the option will also change (by an amount usually represented by the Greek letter Δ). The relationship between the change in the option price and the change in the stock price is stable for small fluctuations. Sellers of options can thus hedge against loss by taking a position in the stock opposite to the risk they have assumed on the option. For instance, if they will lose money on a call option in the event that the stock price increases, then they buy the amount of the stock which will give them an equal profit from that same increase. This amount must equal Δ times their exposure on the option. But losses cannot be avoided in this way when price changes are too large.

Stephen Wright and I provided an example of how the process of delta hedging works in a 1997 report.⁵ The example we gave was for prices on July 10, 1997, but the same basic arithmetic applies today. At the end of 2020, when the S&P was at 3,695, one-month put and call options with a 3,695 exercise price had almost exactly the same exposure to the risk of small changes (the same delta), in opposite directions, and very similar prices of around $80. A dealer selling a thousand of each would have had liabilities of around $16 million (2,000 × 80 × 100 options per contract) and would be more or less perfectly delta hedged. If the market had fallen by 1 percent, the price of the put would have risen and that of the call would have fallen by around $18, leaving total liabilities little changed. In the case of larger movements, the situation would have been very different, however. If, for example, the market had fallen by 10 percent, the call would have become essentially worthless, while the put would have been worth around $360, roughly the difference between the exercise price and the new stock price. The liabilities of the option dealer would therefore have increased from $16 million to $36 million (1,000 × 360 × 100).

Thus options traders have “gamma exposure,” which is the risk that volatility will increase. But the VIX market provides a counterbalance: individual traders who buy the VIX profit from rises in the market’s volatility and can therefore hedge against the gamma risk. Delta and gamma do not comprise all the risks which options dealers incur; for example, they cannot collectively hedge their exposure to the market’s own estimate of volatility, known as “vega exposure.” Likewise, the Black-Scholes formula does not account for all risks, so traders use highly complex and proprietary computer programs to maximise profits and reduce their risks. As Henry Kaufman has noted, “dynamic hedging is an inexact science, one that relies on extraordinarily complex computerized models, which themselves are far from infallible (because they are built on historical data).”⁶

With fire insurance, the risk that any one house will burn down is specific to each owner and the companies who provide insurance to many householders do not bear this specific risk but, if they charge enough to cover the average risk of houses being destroyed, they are only at risk if that average is volatile. If it is, they incur some systemic risk, but for houses this is very low except in wartime, which is therefore usually excluded in insurance policies. The stock market differs from fire and motor insurance in that its volatility, against which the VIX provides insurance, is itself very volatile, as illustrated in figure 2. Moreover, the pattern is one of long-term rather than short-term fluctuations. As a result, there is, in practice, no market for insuring against long-term falls in share prices. The VIX is for one month and the risk of sharp falls over this period are systemic rather than specific. Thus, as Henry Kaufman remarks, the risks of the option market cannot in practice be hedged away; they must be borne by somebody.

Have Markets Become More Vulnerable
to Swings in Volatility?

Financial instability has thus risen as the carry trade has grown. The Rise of Carry does not estimate the size of the market, for which reliable data do not seem to be available, but the authors argue convincingly that it is very large and has expanded greatly in recent years. They also point to the risk that volatility in different financial assets may be contagious: “There is also evidence of a growing correlation between currency and equity market carry, suggesting that a single global volatility risk factor may be a driver of all forms of carry in the future. If this is true, future carry crashes may impact on all asset classes at the same time.”⁷

Because volatility risk cannot be hedged in aggregate and the total amount insured seems to have grown so much, there is broad agree­ment that a future increase in volatility will produce big winners and big losers. There is, however, no consensus on whether this will simply involve a large-scale exchange of wealth between otherwise equivalent players in the market—the Pauls receiving large sums from the Peters—or if it will have serious economic, political, or social consequences.

It is for example a matter of dispute whether derivatives increase or decrease the volatility of their underlying financial assets. Some hold that speculation is generally stabilizing; and since it has become easier with the rise of derivative trading, asset markets should have become less volatile.

The majority view, however, is that derivatives “introduce phe­nomenal leverage into the system . . . which can make greater volatil­ity in the system.”⁸ The Rise of Carry not only argues that leverage has been encouraged by monetary policy but that central banks are directly involved in the market. “The Fed’s increasing carry trade will eventually depress the returns to be earned from carry as a whole,” but “in the short-term, as that extra supply is put to work in the markets, the realized return to carry increases.”⁹ I do not find this part of their argument wholly convincing, as quantitative easing does not involve the Fed directly in the options or VIX markets, nor does its provision of credit lines to other central banks involve it directly in currency markets. It is nonetheless likely that both policies have eased the provision of credit, the expansion of which is necessary for the growth of derivative markets.

It is almost universally agreed that quantitative easing has pushed up asset prices. But the corollary—that the markets have become more volatile—seems generally ignored, often on the shaky assumption that low interest rates will be with us for many years (“the foreseeable future,” in the phrase favored by those who see the future as foreseeable). The Rise of Carry argues convincingly that we should expect to see greater volatility in asset prices in the future. This is likely not only because of the general rise in asset prices, but also because of the expansion of the carry trade, which is accompanied by—in aggregate—an unavoidable increase in risk.

Figure 2 shows that the volatility of equity returns measured at constant prices has probably been mean-reverting over the long term, but volatility is itself volatile. There have been previous prolonged periods when volatility was high. Over the past decade, it has been nearly at its lowest ever level since the data series starts in 1871. If volatility is in fact mean-reverting, its recent, prolonged low level makes another bout of high volatility likely, and because it has been at times very high in the past, such a sustained rise would not necessarily change its trend level, even if we suffered a repeat of the market’s behavior in the 1930s.

The Consequences of Higher Asset Prices

A significant rise in the volatility of the stock market will almost certainly be accompanied by a large fall in share prices, and similar falls will probably occur in credit markets and other financial asset prices. One significant result of such market behavior is a general contraction of economic activity: people will feel poorer and cut back on consumer spending, and companies will cut back on capital expenditures because the demand for their products has fallen and they find it more difficult and costly to borrow. Reductions in savings and investment will cause a recession, and the response needed to prevent it from becoming severe will be some combination of fiscal and monetary easing. But the prospects of using either of these policy levers effectively seem increasingly grim. Unless interest rates rise significantly from present levels, there will be little scope for them to be cut. If they have risen enough to provide scope for meaningful declines, it will probably be in response to an increase in inflationary expectations. Paul Volcker showed, after the oil crises, that such expectations could be brought down, but only at the cost of a pro­longed period of high unemployment and by sharply higher interest rates, which today would surely be accompanied by a stock market crash. Meanwhile, the size of the Biden administration’s fiscal stimu­lus is so great that it has met heavy criticism even from Democratic economists like Larry Summers, so a further increase in the government’s deficit will be difficult. Thus, neither fiscal nor monetary policy will be ready at hand to cope with a severe recession, and the outcome of such a recession will be even more uncertain than usual.

Higher volatility will also result in large insurance payouts to those who have bought the VIX or have a long position in volatility by other means. Notably, market makers who provide liquidity will reap the long-delayed benefit from their insurance. For instance, Jane Street, one of the world’s largest, traded “more than $17tn worth of securities in 2020” and “spends $50m–$75m a year on put options.”¹⁰

Holding a short position in volatility, by contrast, produces steady profits at the expense of occasional large losses. In the event of higher volatility, those who provide insurance against such an increase have a high risk of going bankrupt—a risk that is amplified if, as seems most often to be the case, they are leveraged. Thus a rise in volatility has the potential to set off a vicious cycle: when volatility rises, the cost of insuring against both gamma and vega risks will likewise rise; as a result of this increased cost, the market will become less liquid, and the decline in liquidity is itself likely to enhance volatility.

When short positions were largely confined to investment banks who sold put and call options, these institutions were the only ones seriously exposed to this risk and the ones most likely to suffer bankruptcy. But as the authors of The Rise of Carry note, since the implementation of the Volcker Rule in 2014, “the scale of investment bank proprietary trading has been reduced. Anecdotal evidence sug­gests that many proprietary trading groups have simply joined hedge funds.”¹¹ Hedge funds, which take a percentage of profits in good years, but which do not pay back fees in bad ones, also have a strong incentive to be short volatility and are often highly leveraged. The Rise of Carry rightly points out the moral hazard this involves: “While their liability profile argues against carry, their compensation structure creates a strong incentive in the opposite direction.”¹²

It is therefore likely that the risk of large losses arising from a rise in market volatility has shifted from loan losses for banks and insur­ance companies to the stock market as hedge funds are forced to unwind their positions. In the 2008 financial crisis, taxpayers under­wrote much of the losses which successfully cushioned the economy, but a collapse in the carry trade is likely to exacerbate stock market falls. This might induce central banks to follow Japan’s example and buy shares.

Momentum and Serial Correlation

One of the assumptions of the Black-Scholes formula is that prices follow a “random walk”: price changes are independent of one another, and it is no more likely that a fall will be followed by a rise than that it will be followed by a further decline. But The Rise of Carry argues that since 1987 this has not been the case for daily price changes. Instead, these have shown a negative serial correlation: a rise is more likely to be followed by a fall than by a further rise. This is a surprising claim, as it is generally accepted that the real equity returns show mild positive short-term serial correlation over a one-year period, and then negative serial correlation of increasing strength thereafter (see the tiny initial rise followed by the subsequent large decline in figure 3).¹³ The positive serial correlation of returns is also shown by the success of “momentum investing”; this investment strategy, which assumes that shares which have recently performed well are more likely than others to continue to perform well, seems to have become increasingly popular among fund managers. I therefore questioned the authors about the validity of their claim, and they helpfully sent me their data on daily prices for the S&P 500 since the end of 1927; I show the results in figure 4.

These data show that daily price changes of U.S. equities followed a random walk when measured over the whole span from 1927 to 2020. The actual variance over periods of one to thirty-two days is almost exactly the same as that implied by the daily variance (vari­ance, the square of the standard deviation, is a measure of volatility). Price changes do not, however, show a consistent pattern when measured over shorter time periods: since 1945 there has been a sharp positive serial correlation for one-day changes measured over periods of one to eleven years, but steady negative serial correlation there­after. Yet the authors are correct in claiming that daily price changes have shown a negative serial correlation since 1987.

A market that exhibits negative serial correlation is less risky than one that follows a random walk. The risk of providing short-term insurance against market volatility has thus been less since 1987 than it was over the longer term. The Rise of Carry demonstrates that selling volatility has therefore been more profitable over the past thir­ty-three years than over the past ninety-three years, and this profit­ability has likely contributed to its growing popularity. Negative serial correlation also encourages investors to “buy the dip,” because the market is more likely to rise after a fall than to fall further.

The longer-term historic instability illustrated in figure 4 indicates that it would be unwise to expect the recent pattern of negative serial correlation in daily price changes to continue. The Rise of Carry, however, seems to suggest that it will: “The evidence . . . suggests a persistent positive return for a strategy that bets on mean reversion of the S&P 500 since October 1987. It is unclear whether the modern mean-reverting behavior of the S&P 500 truly began in 1982 with the advent of index futures trading or in 1987 following the stock market crash of that year.”¹⁴

My own view is that the more likely explanation for the reduction in volatility since 1987 is the change in corporate payout policy. Over time, the trend return on shares (i.e., the return which excludes short-term price volatility) is the sum of the next year’s dividend yield and the growth of the dividend, as set out in the Gordon Growth Model. The dividend-to-payout ratio has fallen since 1987, as a result of the simultaneous rise in corporate leverage. Dividends are much more stable than share prices; thus, the higher the proportion of a return that comes from dividends, the greater must be the volatility of share prices. Before 1987, companies were net issuers of shares, but since then they have been net buyers. Buybacks and debt-financed take­overs have assumed greater importance than dividends as a means of distributing cash to shareholders. This has had a nontrivial impact on the volatility of share prices, which as a consequence has been lower since 1987 than in earlier years. This analysis is confirmed by a posi­tive correlation (r² = 0.368) between the variance of one-day price changes measured over ten years and the dividend payout ratio of the S&P 500 Index.¹⁵

The negative serial correlation of daily price changes has boosted returns on selling volatility; for it to continue, though, there will have to be further falls in payout ratios. This is possible, but without a significant increase in the growth rate of the U.S. economy, it will require a continued rise in corporate leverage.¹⁶ Financial instability is thus likely to be amplified either by an end to the negative serial cor­relation of price changes or by a rise in companies’ debt ratios—which, as The Rise of Carry observes, are already high.

Risks Ahead

Equity valuations are extremely high, and the volatility of equity returns has been exceptionally low over the past decade. Each of these trends is likely to be mean-reverting, and thus the risks of rising vol­atility and negative returns to shareholders are high. The economy as a whole does not always tank when the stock market falls; as Paul Samuelson famously joked, “the stock market has predicted nine out of the past five recessions.”¹⁷ But the severity of recessions is asso­ciated with large drops in share prices.

Both the extremely high level of the equity market, which cur­rently matches the previous peaks of 1929 and 2000,¹⁸ and the low level of volatility over the past decade, indicate that we face a high risk of a major bear market. The Rise of Carry provides a timely des­cription of how this situation has arisen and an urgent warning of dangers ahead.

This article originally appeared in American Affairs Volume V, Number 2 (Summer 2021): 46–59.

Notes