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Most of the prior research in the area of monthly regularities has been based on the Gregorian calendar; by contrast, little attention has been given to other calendars based on different religions or cultures. This thesis examines monthly calendar anomalies in the Pakistani stock market for both the Gregorian calendar and its Islamic counterpart. This is one of the first studies to investigate both calendars for monthly seasonality in one investigation on the same dataset. Empirical studies of the Pakistani stock market that have examined monthly calendar anomalies are relatively sparse when compared with investigations from other emerging markets throughout the world. Even the findings from the small number of Pakistani investigations that have examined for the presence of monthly calendar anomalies have arrived at different conclusions about the predictability of equity returns at different times within a year. Since the conclusions of these findings have been mixed, the current study undertakes further work on this topic to offer some clarity in this area; this thesis arrives at a firm conclusion about the monthly calendar anomaly. For the purpose of this thesis, both qualitative and quantitative research methods were employed. Firstly, 19 face-to-face interviews were conducted with brokers, regulators and individual investors to ascertain their views about share price regularities with regards to monthly calendar anomalies and to gain some insights about the role of investor sentiment in the Pakistani stock markets. Secondly, share returns for a sample of 106 companies listed on the KSE over the 17 year period from 1995 to 2011 were analysed to determine whether Pakistani stock markets are weak-form efficient or whether security price changes can be predicted from knowledge of the month when the return is earned; it also investigates whether there is a change in the risk (volatility) of shares in different months which might explain any pattern in returns. To answer these questions various research methods were employed. The results of the interviews suggest that most respondents believed that share prices exhibit patterns in certain months of the year. The most common pattern highlighted by the interviewees related to the month of January for the Gregorian calendar and Ramadan for the Islamic calendar. Interviewees also argued that volatility declined during the religious month of Ramadan; they attributed these changes to investor sentiment and religious duties. Overall, the results suggested that monthly calendar anomalies may be present in the market and that these are studied by investors in an attempt to earn profit. The results from the quantitative analyses supported the findings from the interviews. Initial analyses suggested that returns varied significantly during certain months which indicate that the market might not be efficient. Further, investigations for seasonality in both the mean and volatility of returns offered conflicting evidence; very little statistical evidence of monthly seasonal anomalies was identified in average returns. However, monthly patterns were present in the variance of equity price changes in Pakistan. Overall, the results confirm that whatever monthly seasonality may be present in the equity prices of Pakistani companies, it is more pronounced in the volatility data than in the mean return numbers. These findings may have useful implications for trading strategies and investment decisions; investors may look to gain from managing the risk of their portfolios due to time varying volatility documented in the findings of this thesis. Further, the results of this thesis have interesting implications for our understanding of the dynamics of equity volatility in the Pakistani stock market.

The thesis evaluates the benefit of allowing for long memory volatility dynamics in forecasts of the variance-covariance matrix for asset allocation. First, I compare the forecast performance of multivariate long memory conditional volatility models (the long memory EWMA, long memory EWMA-DCC, FIGARCH-DCC and Component GARCH-DCC models) with that of short memory conditional volatility models (the short memory EWMA and GARCH-DCC models), using the asset allocation framework of Engle and Colacito (2006). The research reports two main findings. First, for longer horizon forecasts, long memory volatility models generally produce forecasts of the covariance matrix that are statistically more accurate and informative, and economically more useful than those produced by short memory volatility models. Second, the two parsimonious long memory EWMA models outperform the other models – both short memory and long memory – in a majority of cases across all forecast horizons. These results apply to both low and high dimensional covariance matrices with both low and high correlation assets, and are robust to the choice of estimation window. The research then evaluates the application of multivariate long memory conditional volatility models in dynamic asset allocation, applying the volatility timing procedure of Fleming et al. (2001). The research consistently identifies the economic gains from incorporating long memory volatility dynamics in investment decisions. Investors are willing to pay to switch from the static to the dynamic strategies, and especially from the short memory volatility timing to the long memory volatility timing strategies across both short and long investment horizons. Among the long memory conditional volatility models, the two parsimonious long memory EWMA models, again, generally produce the most superior portfolios. When transaction costs are taken into account, the gains from the daily rebalanced dynamic portfolios deteriorate; however, it is still worth implementing the dynamic strategies at lower rebalancing frequencies. The results are robust to estimation error in expected returns, the choice of risk aversion coefficients and the use of a long-only constraint. To control for estimation error in forecasts of the long memory high dimensional covariance matrix, the research develops a dynamic long memory factor (the Orthogonal Factor Long Memory, or OFLM) model by embedding the univariate long memory EWMA model of Zumbach (2006) into an orthogonal factor structure. The factor-structured OFLM model is evaluated against the six above multivariate conditional volatility models in terms of forecast performance and economic benefits. The results suggest that the OFLM model generally produces impressive forecasts over both short and long forecast horizons. In the volatility timing framework, portfolios constructed with the OFLM model consistently dominate the static and other dynamic volatility timing portfolios in all rebalancing frequencies. Particularly, the outperformance of the factor-structured OFLM model to the fully estimated LM-EWMA model confirms the advantage of the factor structure in reducing estimation error. The factor structure also significantly reduces transaction costs, making the dynamic strategies more feasible in practice. The dynamic factor long memory volatility model also consistently produces more superior portfolios than those produced by the traditional unconditional factor and the dynamic factor short memory volatility models.