Liquidity-at-Risk

This article originally appeared in Risk.net, co-authored with my good friend Ken Akoundi, President of ASPN Solutions. Ken and I will be speaking at the RiskHedge conference in NYC on July 8 on the topic of Liquidity Risk.

Market liquidity, when not taken for granted, is a complex topic that has no quick and easy explanation, measure or analysis. Without liquidity, a market cannot really exist, so most economic, valuation and risk models assume a high level of liquidity. Any other assumption is just too messy: how exactly does one go about modelling a market when one of its required characteristics – liquidity – is in short supply or non-existent?

Both the Wall Street Journal and Investopedia define liquidity similarly: the degree to which a security can be easily bought or sold without materially changing its price. Liquidity is not just the ability to buy or sell – liquidity is about the ability to do so without moving the market. That last bit means that to be truly liquid, a security needs plentiful buyers and sellers so anyone can transact at nearby prices, leading to one of the most common measures of liquidity: volume. But high volume alone does not mean you can always transact without moving the market: what if all that volume is dominated by buyers when there are few sellers – a strategy used by some hedge funds in frontier markets. Without plentiful sellers, just one buyer can and will move the market. The mirror image is also true. Size matters: small quantities can often be easily bought or sold and therefore some would describe the security as ‘liquid’, but the same security at larger quantities may not find a market at all.

Liquidity, then, is not really a characteristic of a security or of a market. Liquidity is a situational attribute that is ephemeral: it depends on characteristics of the security, the position and the market. Increasing liquidity risk, and therefore decreasing level of liquidity, is associated with increasing position sizes/increasing market volatility and with decreasing market size, decreasing trading volume, decreasing number of market participants and decreasing time horizon. Liquidity is a bit slippery, like creativity: when you think you have it everything works the way it is supposed to, but when you know you do not have it, you can only wish for it. Warren Buffet, in his 2014 annual letter to Berkshire Hathaway investors, beautifully summarised his disdain for “substitutes for cash that are claimed to deliver liquidity and actually do so, except when it is truly needed”.

Measuring liquidity

Regulators around the world have become fond of requiring funds of all sorts, from hedge funds to mutual funds to money market funds, to measure the liquidity of their portfolio and ensure that they can match the liquidity needs of their investors. Refraining from specifying a preferred methodology for measuring liquidity, the regulators leave that task to the market. Two methods have gained prominence in liquidity measurement, but neither is widely regarded as authoritative or particularly useful on its own.

Wider bid-ask spreads are generally associated with lower liquidity. The New York Stock Exchange (NYSE) has demonstrably lower bid-ask spreads than the Bombay and Thai exchanges, and near-term futures contracts also have much narrower spreads than longer-dated and more thinly traded contracts on the same underlying security.

Both large and small equity exchanges experience a bid-ask spread widening during sharp downturns. Investor Analytics studied the Thai exchange’s December 19, 2006 drop of 15% and compared it with the NYSE’s February 27, 2007 drop of 4%. In both cases, relative spreads increased significantly. For the Thai Exchange, the proportion of issuances with the widest spreads – of more than 5% – jumped from 3% of all stocks traded to 11%, while the proportion of issuances with the narrowest spreads – less than 1% – shrank from 81% to 60%. The NYSE had a similar dynamic: the proportion of issuances with the widest spreads – of more than 0.5% – doubled from 2% to 4% of all traded stocks while the proportion of issuances with the narrowest spreads – less than 0.1% – fell from 78% to 66%. While both exchanges experienced similar directional effects, the smaller exchange with larger typical bid-ask spreads experienced a much larger effect than the more liquid market. As markets become increasingly interconnected, bid-ask spreads can play an important role – after all, Long Term Capital Management was supposed to be invested in uncorrelated markets.

Traded volume is a more typical way to assess liquidity: securities with larger trading volume are regarded as more liquid than those with smaller volume. Indeed, most regulators accept this approach to measuring and managing liquidity risk in a portfolio. The typical direct measure is the “number of days to liquidate” a given position, measured simply as the ratio of the quantity held divided by the average daily volume. For typical markets in which the quantity is well below the volume, this may well be a good measure as it gives an estimate of the fraction of the market the position makes up and therefore what small fraction of the daily volume is needed to liquidate the entire position.

But if the position makes up a sizable portion of the daily volume, there is virtually no way to liquidate in that suggested time frame without either moving the market or signaling the trade intention, which can have disastrous effects like getting crowded out. Indeed, Nick Maounis, CEO of Amaranth, explained the demise of his fund this way: “A series of unusual and unpredictable market events caused the funds’ natural gas positions (including spreads) to incur dramatic losses while the markets provided no economically viable means of exiting those positions… as news of our losses began to sweep through the markets, our already limited access to market liquidity dissipated.” Long Term Capital Management’s founder John Meriwether told his shareholders in a September 3, 1998 letter: ”We expected that sooner or later… we as a firm would be tested. I did not anticipate, however, how severe the test would be.”

Liquidity-at-risk

We recently examined two stocks with vastly different trading volumestable using Bloomberg and Yahoo! Finance: Apple (AAPL) and WD-40 Company (WDFC), the makers of the eponymous lubricant. AAPL’s average daily trading volume over the last 10 years is about 160 million shares, while WDFC’s average daily trading volume is about 70,000 shares. We calculated the number of days to liquidate a particular holding by dividing the set quantity by the daily volume for each day over that time period. The quantities of each stock were chosen so that the median ‘days to liquidate’ is one day: 134,550,000 shares of AAPL and 55,000 shares of WDFC.

distributions

Click the graph to enlarge

The measured probability distributions of these two stocks’ days to liquidate are shown in figures 2 and 3. The first point we noted is the similarity these both exhibit to a Poisson distribution: very few events with extremely short times to liquidate, a pronounced peak followed by a long tail. The figures are drawn with the same axes – zero to nine days – for easier comparison, even though the Apple graph has no events past 5.5 days and the WDFC graph’s last point is at nine days. Inspired by the simplicity of the definition of value-at-risk as a chosen point on the return distribution, we examined the 95%, 99% and 99.5% points along the measured distributions for liquidity of these two stocks, summarised in figure 1.

distribution2

Click the graph to enlarge

Interestingly, the companies’ liquidity profiles are remarkably similar over the past 10 years, suggesting that similar underlying dynamics govern the trading volumes of these very different companies over this period, which includes high and low equity volatility regimes and, of course, includes the global financial crisis. It is only in the very extreme that these stocks show even a marginal difference in their liquidity profiles: at 99.5%, it would take an insignificant 10% more time to sell off the holding of WDFC than Apple.

While the similarity between these two stocks’ liquidity profiles is intriguing, our intention is to examine a significantly larger sample with special focus on times of liquidity crisis.

Intra-day liquidity concerns

The Wall Street Journal recently ran front-page articles about intra-day liquidity issues surrounding exchange-traded fund and index fund dynamics, noting that for many stocks, such as WDFC, a significant portion of the trading occurs at the opening and just before the closing bells. They noted that 6% of all trading occurred in the last five minutes of the day, and that figure has risen every year since 2010. Due to lower liquidity in the mid-day hours, transaction costs near lunchtime can be as much as twice as high as at the end of the day, driving even more traders to transact toward the close. In 2014, the last half hour of trading accounted for one in six trades on the S&P500. Since index funds benefit from closely matching the indexes they follow, and those indexes use the day’s closing price to calculate their values, there is a natural tendency for them to trade near the day’s end. Edge effects matter.

The exchange’s solution to this is to hold mid-day auctions in those stocks that are most affected by this phenomenon, injecting liquidity when it would otherwise dry up. The question is, how many will participate in this artificial liquidity stimulant?

Portfolio liquidity strata

The US Securities and Exchange Commission has recently modified its regulations for money market funds, requiring them to take a more mature approach to liquidity risk management with a series of analyses that are useful for all funds. Portfolio managers are required to take a stratified view of their portfolio, bucketing their investments into liquidity categories, from most to least liquid, and then analyse the impact on portfolio value as the managers are required to sell off securities to meet investor redemption demands. Similar to ubiquitous ‘top 10 exposure’ or ‘top 10 volatility’ reports, they are required to report on the liquidity characteristics of the portfolio strata to ensure that they can continue to provide market liquidity in times of crises.

Such analyses, to be useful, should not only be done assuming normal market liquidity conditions, but also under extreme conditions when all others are trying to sell the same securities. Like most things we take for granted, liquidity doesn’t matter except when it’s not there.

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