Portfolio Returns

As a first step, we analyze if the four illiquidity measures described in section 2.2 are qualitatively similar. For this reason, we calculate the cross-sectional correlation, which is provided in table 2.4. Trading quantity exhibits a relatively strong correlation to the other illiquidity measures. The correlation is negative because a higher trading quantity reflects a higher degree of liquidity, whereas a high value for the other measures indicates a low degree of liquidity. The correlation is highest to trading speed (-0.77). Between the other three measures there also exists high average cross-sectional correlation. Correlation between trading speed and trading costs is 0.69, between trading speed and price impact 0.52, and between trading costs and price impact 0.62.

Further, we have a look at the cross-sectional correlations between the four illiquidity measures and the size of the firm. We find a negative correlation between size and trading

Table 2.4: Cross-Sectional Correlation Variable Correlations TQ TS TC PI Size TQ 1.00 -0.77 -0.56 -0.40 0.13 TS 1.00 0.69 0.52 -0.43 TC 1.00 0.62 -0.40 PI 1.00 -0.39 Size 1.00

This table shows the average cross-sectional correlations between the four illiquidity measures and size.

Sizeis the logarithm of the market capitalization. T Qrepresents the logarithm of the trading quantity,

T Strading speed,T Ctrading costs, andP Iprice impact. The sample period runs from 1975:01-2006:12. speed (-0.43), between size and trading costs (-0.40), and between size and price impact (-0.39). By contrast, trading quantity is hardly correlated with firm size (0.13), which is not very surprising given that trading quantity has been constructed to be relatively uncorrelated to firm size. The results so far suggest that our illiquidity measures partly capture a size effect.

In the following, we evaluate if more illiquid or less illiquid stocks earn higher returns. We categorize stocks into five portfolios based on the degree of illiquidity and calculate the average return of each portfolio. Following Liu (2006), we use equally-weighted port- folios.9 We rebalance portfolios every month. Table 2.5 documents the results for the four illiquidity measures described in section 2.2. Portfolio ”Low” includes the least illiq- uid stocks or the most liquid stocks whereas portfolio ”High” contains the most illiquid stocks. All measures detect that more illiquid stocks tend to earn higher returns than less illiquid stocks, even though, the difference between ”High” and ”Low” is insignificant. The difference is highest for the trading speed and price impact dimension, 0.35% per month, followed by trading quantity and costs, 0.27% per month. We also report the results of theM Rtest. The hypothesis of a flat pattern in expected returns when moving from portfolio 1 to portfolio 5 is not rejected at a 10% level for all measures except in the case of trading speed. Table 2.5 also provides information about the standard deviation of the portfolio returns and the average market capitalization of the stocks included in the portfolios. The liquid portfolios have a higher standard deviation than the illiquid portfolios. This effect is very pronounced for trading quantity and trading speed. More- over, the results suggest that illiquid stocks tend to be stocks from small firms across all

Empirical Results 55

measures and vice versa. To control for size, we also conduct a double sort. Each month, we sort stocks based on size into five portfolios. Within each of the five size portfolios, stocks are again sorted into five portfolios based on one of the four illiquidity measures. The returns of the five illiquidity portfolios are then averaged over the five size portfolios such that we receive five illiquidity portfolios controlling for size. However, we still find that the most illiquid portfolio includes the smallest firms. Thus, the use of a double sort cannot completely seperate between the size and illiquidity effect. Results are not reported.

Additionally, we differentiate between two subperiods. The first one runs from 1975:01 to 1991:12 and the second one from 1992:01 to 2006:12. Subperiods are characterized by two main differences. First of all, the number of observations in the cross-section is about twice as high in the second subperiod. This is primarily due to the dotcom bubble and the resultant rise of newly listed firms. The increase in the number of cross-sectional observations creates a greater diversity in the level of illiquidity in the second period and enables us to differentiate between liquid and illiquid stocks in a more precise way. Furthermore, relative to the first subperiod, the second subperiod is characterized by a distinctly higher volatility of stock returns.

Results are summarized in table 2.6. In the first subperiod liquid and illiquid stocks earn similar returns independent of the illiquidity measure. The only exception is price impact, for which we detect a monotonically increasing relation. In the second subperiod, portfolio 5 has higher average returns than portfolio 1 independent of the measure chosen, though, the difference does not significantly deviate from zero. We only find a monotonically increasing relation between expected returns and illiquidity in the case of trading speed. In comparison to the other measures, the difference be- tween the average returns of portfolio 5 and 1 is highest, 0.81%. Using trading costs and price impact, we find that the most illiquid stocks perform best but followed by portfolio 1.