Testing arbitrage pricing theory for the Indian market

Abstract

This is the first large scale direct validation of the Arbitrage Pricing Theory for Indian markets. The number of stocks considered is approximately four times the number of stocks considered in the Sood [1995] study. While more work is required to confirm and further our knowledge of the validity of the APT in the Indian context, we can make a few cautious conclusions. 1. The percentage of groups in which the single - factor APT pricing relationship linearity hypothesis is rejected is around 42% significance level and is around 21% for 10% significance level. These percentages are higher for APT models with higher number of factors. In a similar context, Cho and Taylor [1987] and Gultekin and Gultekin[1987] conclude that the APT does not hold. Following their footsteps, we conclude that the APT does not hold. Following their footsteps, we conclude that the APT does not hold for the Indian market. 2. The percentage of groups for which the APT pricing relationship linearity hypothesis is rejected, increases with increase in the dimensionality of the APT model under consideration. This, implies that lower dimensional APT models are more valid than higher dimension models. Our results are in clear contrast with the results of the Sood [1995] study, which are in favour of the APT for the Indian market. We hence point out that 1. Our sample size is much larger than his thereby lending more credence to our results. 2. He chose 98 liquid stocks with high market capitalisation. We applied liberal liquidity related criteria for selection of our sample but we did not impose any selection criteria related to market capitalisation. In the Indian market, large stocks are highly liquid. For relatively illiquid stocks, a no-arbitrage equilibrium is rarely reached since lack of trading opportunities prevents arbitrageurs from exploiting arbitrage opportunities. So his sample may be biased in favour of finding positive support for the APT. 3. The period analysed by him and the period analysed by us are two significantly different periods in the history of the Indian stock markets. In our opinion, the period considered by us is a much better benchmark period for further studies, because it lies completely in the post-liberalisation period. Limitations This study was severely limited by the data. The minimum size of groups in the literature seen was 30. But we had only 60 data points to estimate the Covariance matrix, so we had to make groups of 20 only, to ensure the reliability of the estimate. 5.3 implications Work by. Shivaprasad[1996] shows that market wide movements are more dominant than sectoral movements in the Indian stock markets. Similarly Ravikumar and Chandrasekhar [1996] show that the market factor explains a large amount of variance of stock returns in India. Our results show that APT models of lower dimension work better than APT models of higher dimension. CAPM is very similar in its empirical content to a single factor APT model where the only factor is the market factor. Hence our study, especially in the context of the other two studies, implies that CAPM is a more useful asset pricing theory in the Indian context. Suggestions for further work a. Grinblatt and Titman[1983] derive an upper bound for the pricing errors for APT in finite economies. We found that this bound is unignorably high for market capitalisation wise skewed economics like the Indian economy. The form that APT takes for such economies needs to be explored theoretically and empirically. b. There is lot of debate about the factor structure of stock returns in the Indian market. Some people believe that it has changed due to liberalisation, while others disagree. Factor structure changes affect APT testing significantly. APT testing in face of factor structure instability is one of the long standing problems in the APT literature and till it is resolved, studies like our study will make the naive assumption that the factor structure has not changed. Some work needs to be done to identify whether the factor structure has changed in the sample period and then APT needs to be tested in view of the results of this work. c. The Sood[1995] study showed positive support for the APT, while our study does not support the APT. Sood’ s sample had a size bias, due to his using large stocks (mostly a group BSE stocks). Whether the size bias is responsible for the difference between our results and his results, needs to be verified. One other possibility is that, since size and liquidity are highly correlated, the more important reason for the difference in results may be the difference in the liquidity of the samples analysed by him and us. Thus there is a need to investigate the impact of liquidity and stock market anomalies on APT asset pricing tests in the Indian market, like Gultekin and Gultekin[1987] have done for the American market.