Liquidity

What is Liquidity?

When you trade stocks, there are two ways to do it:

• You can place a limit order whereby you promise to sell (or buy) a stock at a given price to whomever wants (doesn't want) it. This price is called the limit price. Given a set of seller's (buyer's) limit prices in the exchange, the lowest (highest) limit price is called the ask (bid) price.
• You can place a market order whereby you look at the most favorable limit order and accept it, completing the trade

If two limit orders satisfy each other, they will immediately execute. For this reason, the bid price will always be lower than the ask price. The difference between them is called the bid-ask spread.

Suppose WMT is trading at $100 with a spread of $4. That means, someone has placed a limit order to sell WMT at $102 and someone else has placed a limit order to buy it at $98. Suppose Alice placed the limit order to sell at $102.

Now Bob decides to add $200 to his retirement account. He decides to place a market order for WMT. When this goes through, he buys a WMT stock from Alice for $102 and is left with $98 still in cash. Note: the price of WMT is only $100 but Alice made $102. In this way, Alice made a tidy profit atop the current price. This is her compensation for offering liquidity to Bob and the broader market: that is, Bob wanted the ability to buy WMT immediately and Alice provided that service.

So why doesn't everyone place limit orders?

Well, suppose news comes out that WMT is actually 10% more profitable. Between the time this news comes out and the time Alice hears of it and updates her limit order, she will be taken advantage of by active investors trying to buy on this news. In this case, Alice will be selling stocks worth $110 for just $102, losing out on $8 of profit. For this reason, using limit orders to make the bid-ask spread is only profitable in the long-run if you're constantly updating your orders in light of new knowledge - i.e, if you're a high frequency traders. Of course, nothing stops low frequency traders from (dumbly) placing limit orders, so the more general term for investors who place limit orders is "market maker".

While the bid-ask spread is a good measure of liquidity for small investors in most reasonable asset classes, others exist. Moreover, large institutional investors have to contend with the risk that their orders will change the market price, which means they also must care about market depth, an abstract idea encompassing how hard it is for large trades to move the market price Market depth, but that's beyond the scope of this post.

What Determines Liquidity?

From our discussion above, it should be clear that the main thing that market makers worry about is that the stock price moves significantly and people take advantage of their limit orders. From this follows the two main determiners of liquidity: price volatility and trading latency.

Other factors of particular importance include:

• transaction costs - since limit orders are more complicated than market orders, brokerage fees are typically higher. This (a) directly impacts the bid-ask spread and (b) causes lower volume which also impacts liquidity (see above)
• insider trading - insider trading allow people to take advantage of naive market makers and, therefore, discourages liquidity

I consider these four factors the primary determinants of liquidity. Lots of more detailed factors have been identified, but as far as I can tell, they all merely affect liquidity via the above four.

Finally, as with normal volatility - liquidity shouldn't be thought of in isolation. The liquidity of two stocks tend to positively covary - that is, there are periods where pretty much all stocks are more liquid and other periods where pretty much all stocks are less liquid - typically these are low-risk and high-risk periods, respectively.

As with traditional risk, if a stock's liquidity doesn't correlate with the liquidity of the overall market, you can make this downside negligible via diversification. It is this positive covariance that implies a "market liquidity risk", which functions similarly to beta. In an efficient market, securities with high market liquidity risk should have higher expected returns to compensate owners for this additional risk.

Why Liquidity Matter

In addition to its importance to liquidity spirals (see below) acknowledging liquidity is how many people "beat the market":

The idea that lack of liquidity and market liquidity risk are frequently accompanied by higher returns is generally backed up by a literature review, though contradictory studies do exist Naik Jones.

The simplest thing to do is to adjust our existing CAPM model to account for liquidity. This has been done Acharya and it results in the standard CAPM model with three additional "beta" parameters to represent three types of liquidity risk:

• The covariance between asset illiquidity cost with market illiquidity cost
• The covariance between asset returns and market illiquidity cost
• The covariance between asset illiquidity cost and market returns

The authors find this new model outperforms naive CAPM and that these three types of liquidity risk tend to to be positively associated (e.g. assets with lots of one type of liquidity tend to have lots of the other types of liquidity). They find stocks with low liquidity tend to have annual returns about 1.1pp higher than those with high liquidity.

Funding Risk

For traders using leverage, liquidity risk can greatly exacerbate another type of risk: funding risk: the risk that you will be forced to unwind a position before you want to.

For instance, suppose WMT is trading for $100 and has a 50-50 chance of going up by $11 today or down $10. Tomorrow, the probabilities are the same. Suppose you go long on WMT, investing $10 of your own money and $90 borrowed dollars (at 0% interest, for simplicity). There are four situations:

• Up Up: Make $22
• Up Down: Make $1
• Down Up: Lose $10 the first day; get forced to unwind and pay down your position
• Down Down: Same thing.

Note, that without leverage, your expected return would have been $1.00. With leverage, your expected return is only $0.75. Naively, this seems impossible: the investment has expected positive returns and the interest rate was 0%. In practice, though, there was a 50% chance of a forced unwind, which would prevent you from taking advantage of the hypothetical rally on day 2.

From this we can see that, unlike volatility, funding risk can actually reduce the expected return of a trade.

This same unwind risk also holds for shorting stocks.

Liquidity Spirals

Liquidity and funding risk work together to create financial crises: a price drop causes investors to unwind, which causes increased volatility, which makes market makers reluctant to place limit orders, which increases the bid-ask spread, which makes assets less attractive. Rinse and repeat. This is made all the worse by the fact that

1. the market makers and the unwinding investors are frequently one and the same (i.e. hedge funds)
2. some investors try to exploit or cause liquidity spirals (e.g. "short squeeze")

This is the root of the two different "epochs" of stock behavior: roughly log-normal random walks and crashes. While volatility is a reasonable measure of risk during the random-walk periods, it falls short at realistically evaluating the risk of dramatic crashes.

Aside on Banks

If you invest $100 in a bank, they are required to keep some of it in cash (a legally mandated "reserve requirement"), but they generally invest the rest - typically in low-risk bonds.

The highly leveraged nature of this investment throws liquidity in sharp relief. For instance, suppose the bank keeps $10 in cash and puts the other $90 in 30-year treasury bonds paying 4% interest. In 30 years, the bank is guaranteed to make a tidy return on those bonds.

However, if interest rates rise by just 0.6pp, then the market value of those bonds today will fall by about 10% and the bank will be insolvent. This risk would be dramatically mitigated if the bank bought shorter term bonds: if the bank bought 12-month bills interest rates would need to spike ~10pp for the bank to become insolvent.

This is one of the reasons interest rates are lower on shorter-term bonds: bond buyers tend to be leveraged (e.g. banks) and shorter-term bonds have less liquidity risk.