A semiparametric capital asset pricing model with liquidity and its application

In this paper, I propose a model that flexibly accounts for liquidity. Extending conventional asset pricing equations, I construct a semiparametric model that depends on an unknown liquidity function. This function depends on the standard set of liquidity proxies such as bid-ask spread, turnover rate, number of transactions and number of non-trading days. This approach neither imposes any restriction on the structure of liquidity nor limits the number of proxies which can be associated with liquidity function. The model is estimated by using semiparametric least squares in a time series context and the estimator is shown to be consistent and asymptotically normal.;In applying this model to stock data we find that the estimated coefficients of bid-ask spread, turnover rate and number of non-trading days are similar in magnitude and are statistically significant. That is, bid-ask spread, turnover rate and number of non-trading days have similar weights in affecting asset returns. Such an outcome implies that missing any of these three variables may significantly change the estimated value of liquidity thus distort the relationship between asset returns and liquidity. The signs of the estimates also support the common belief that bid-ask spread and number of non-trading days are related with the illiquidity cost thus increasing required returns while the other two capture the flexibility in trading. Liquidity impact parameters in construction, manufacturing, wholesale trade and retail industries are statistically significant. The two industries which have the largest liquidity impacts are agriculture, forestry and fishing, and public administration. The companies in these two industries are deemed to have little incentive to smooth out the liquidity level, which induces the second order impacts of the liquidity to be high.