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Liquidity Signals

Incorporating market-liquidity levels in a dynamic asset-allocation policy improves portfolios.

James X. Xiong, 04/16/2013

A longer version of this article will be published in the 2013 summer issue of the Journal of Portfolio Management.

At the micro-level, liquidity relates to the speed and ease with which an investor can trade an asset. Amihud and Mendelson (1986) used the bid-ask spread as a measure of liquidity to test the relationship between security returns and liquidity. They found evidence that investors demanded a premium for illiquid securities. Datar, Naik, and Radcliffe (1998) used the turnover rate (number of shares traded as a fraction of the number of shares outstanding) as a proxy for liquidity and found that firm-level stock returns are strongly negatively related to their turnover rates. Using autocorrelation in returns as a proxy for illiquidity, Khandani and Lo (2011) showed that illiquidity premiums are generally positive and significant, ranging from 2.74% to 9.91% per year among hedge funds and fixed-income mutual funds. These results all support the notion of an illiquidity premium: Lower levels of liquidity relate to higher average returns.

At the macro-level, liquidity has also been shown to be an important variable in the pricing of assets. Stock prices relate cross-sectionally to fluctuations in aggregate liquidity [Amihud (2002), Pastor and Stambaugh (2003), Kamara, Lou, and Sadka (2008)]. This research further shows that common measures of liquidity risk move together and that liquidity influences the market return, not just the return of a single asset, cross-sectionally.

Altogether, research suggests that the market’s aggregate liquidity relates to real economic activity. Indeed, Naes, Skjeltorp, and Ødegaard (2011) show that when aggregated to the market level, cross-sectional liquidity contains useful information about the current and future state of the economy. This is where our study comes in. Our results extend these efforts by shedding light on how changes in market-liquidity risk premiums have an impact on a portfolio’s performance.

Market Liquidity and Dynamic Portfolio Allocation
To accomplish this task, we propose a model of portfolio selection that adjusts an investor’s portfolio allocation to changing market-liquidity premiums and market conditions. We find that changes in market liquidity provide a useful “leading indicator” in dynamic asset allocation.

We apply the Amihud (2002) illiquidity measure, which is calculated for each stock for each month and then aggregated to a market level. The Amihud measure is a priceimpact measure of illiquidity and reflects the degree to which prices move in response to trading volume changes. A higher value of Amihud signifies higher illiquidity (lower liquidity) because a particular dollar volume traded is associated with a relatively high price movement. We calculate the Amihud liquidity measures using data consisting of all the stocks on the New York Stock Exchange that met our criteria over our study period of January 1980 to September 2010.

To illustrate the effectiveness of liquidity as an information signal, we employ a simple two-asset portfolio choice model composed of stocks and bonds. The benchmark and the constructions of the dynamic liquidity premium portfolios are shown in the first table. The specific asset classes we employed are shown in the second table. Each one of the six equity assets separately comprises the equity component, while the bond component is always the BarCap US Gov/Credit 1–3 Year Total Return Index. We use this simple two-asset construction to generate the performance of a dynamic asset-allocation (DAA) portfolio. We use a simple high-liquidity premium/no-liquidity premium signal to adjust the asset-allocation risk posture. We then compare the DAA performance results to the strategic, or benchmark, portfolio (SAA) allocation. In all cases, we use total returns and rebalance monthly.

In choosing which of the two portfolios to use in forming our DAA portfolio each month, we first calculate the market environment based on the degree of liquidity risk and use this to inform our asset-allocation decision. Here, our portfolio decision is determined by one of two possible states of the world: low or no expected liquidity premium or high expected liquidity premium. The two market states are governed by the level of liquidity risk in accordance with the thresholds shown in Exhibit 1. In calculating our liquidity time-series measurements, we use a six-month average value.

The liquidity-risk-regime thresholds were chosen in a straightforward way in order to equalize the portfolio asset-allocation risk postures over time between the dynamic portfolio and the static benchmark portfolio. That is, the average monthly weightings for both the SAA and DAA portfolios over the full study period equal 50% stocks/50% bonds.

First, we determine the threshold triggers using the entire sample period, 1980–2010, which allows our regime changes to reflect the reality of market-liquidity conditions. Exhibit 2 relates the Amihud measure over time versus the fixed threshold trigger. The model chooses high liquidity premium (or no liquidity premium) when Amihud is greater (or less) than the horizontal line, or negative 0.065. At first glance, it may appear counterintuitive to hold a greater allocation to stocks when market liquidity is low. However, this idea makes sense when placed in the context of a market-liquidity premium. That is, investors want to extract potential excess market returns in the form of a liquidity premium by offering market liquidity when it’s needed most and, in turn, be compensated for doing so.

We rebalance both the strategic and dynamic portfolios monthly. Transaction costs for our dynamic asset-allocation portfolio are assumed to equal 0.1% and applied to the amount of portfolio turnover. Performance results are summarized in Exhibit 1, reported on an annualized basis. Risky Assets Each row in Exhibit 3 represents performance associated with one of our six underlying risky assets used in portfolio construction. As mentioned, the BarCap US Gov/Credit 1–3 Year is used for the bond portfolio in constructing all portfolios. For example, the first row reports performance for our dynamic (DAA) and strategic (SAA) portfolios whereby largegrowth stocks are the risky asset. The second through fifth columns report total annualized portfolio return and standard deviation of return for the DAA and SAA portfolios, respectively. As can be seen from Exhibit 1, in comparing the SAA and DAA portfolios, the DAA portfolios consistently generate higher returns with roughly the same level of risk. Recall that the risk levels between SAA and DAA are roughly the same by design because the allocations are required to be the same, on average. The outperformance of DAA portfolios results in slightly higher Sharpe ratios for DAA across the board.

We next regress the monthly returns of the DAA against the SAA portfolio for the full sample period in order to calculate the monthly alpha for the DAA portfolio. The reported risk-adjusted alpha is simply the resulting intercept of the regression of the DAA total returns against the SAA total returns. The alpha for each of our DAA portfolios is statistically significant at the 5% level as indicated by the t-stats in the far right column. Finally, we calculated monthly turnover of about 5.9% per month or 71% annually for each of the DAA portfolios and incorporated the turnover costs into the performance results. These results support our thesis that changes in market liquidity can be used to improve portfolio construction over time.

Next, we study how well the DAA model performs in rising and falling markets relative to the SAA portfolio. We use an up-market capture measure and down-market capture measure. The up-market capture is calculated as the average return of DAA divided by the average return of SAA when SAA returns are positive. The down-market capture is calculated as the average return of DAA divided by the average return of SAA when SAA returns are negative. Numbers greater than 100% indicate greater portfolio sensitivity of the DAA versus that of the SAA portfolio. Exhibit 3 reports the results. Consistent with our earlier findings, market liquidity leads to useful adjustments to the DAA portfolio by effectively applying higher-risk asset allocations in up markets and lower allocations to risky assets in down markets.

Because portfolio drawdown is an important measure of portfolio performance, we further explore relative performance of our DAA portfolios during three recent financial crises: Black Monday in October 1987, the tech crash of 2000–2001, and the global financial crisis of 2008–2009. In Exhibit 3, we find that the DAA portfolios compare favorably with the SAA portfolios during these turbulent periods for all asset classes.

In combination, these results support our thesis that changes in market liquidity can be used to improve portfolio construction over time as liquidity cycles between high- and low-liquidity premium environments. We further note that although the standard deviation of returns between the DAA and SAA portfolios are roughly equivalent, the drawdowns during market turbulence present much different results between the two portfolios. Consider that the downside capture for each of the DAA portfolios is roughly 90%. This suggests that liquidity-based DAA portfolios offer improved risk characteristics when using alternative measure of risk, such as maximum drawdown.

Better Portfolios
We show that changes in market liquidity can be used as a good “leading indicator” to inform dynamic asset-allocation portfolio decisions. Using data from 1980 to 2010, we document that measures of stock market liquidity contain useful information about the state of financial markets. We determine how market-liquidity dynamics anticipate changes in prices of risky assets and the extent to which portfolio managers are able to opportunistically rebalance portfolios to enhance their performance.

 

References
Amihud, Yakov (2002), “Illiquidity and Stock Returns,” Journal of Financial Markets, vol. 5, pp. 31–56.
Amihud, Yakov and Haim Mendelson (1986), “Asset Pricing and the Bid-Ask Spread,” Journal of Financial Economics, vol. 17, pp. 223–249.
Datar, Vinay T., Narayan Y. Naik, and Robert Radcliffe (1998), “Liquidity and Stock Returns: An Alternative Test,” Journal of Financial Markets, vol. 1, pp. 203–219.
Kamara, Avraham, Xiaoxia Lou, and Ronnie Sadka (2008), “The Divergence of Liquidity Commonality in the Cross-Section of Stocks,” Journal of Financial Economics, vol. 89, no. 3 (September), pp. 444–466.
Khandani, Amir E. and Andrew W. Lo. (2011), “Illiquidity Premia in Asset Returns: An Empirical Analysis of Hedge Funds, Mutual Funds, and U.S. Equity Portfolios,” The Quarterly Journal of Finance, vol. 1, pp. 205–264.
Naes, Randi, Johannes A. Skjeltorp, and Bernt Arne Ødegaard (2011), “Stock Market Liquidity and the Business Cycle,” Journal of Finance, vol. 66, issue 1, pp. 139–176.
Pastor, Lubos, and Robert Stambaugh (2003), “Liquidity Risk and Expected Stock Returns,” Journal of Political Economy, vol. 111, pp. 642–685.

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