This PhD dissertation research primarily aims to empirically investigate into two financial topics using annual and monthly data sets of market-capitalization based size portfolio returns from the US stock market for the period 1925 to 2012. Using size-based portfolio returns is a pioneering effort for both topics. The first empirical research using annual data is on short and long horizon stock return predictability using three widely selected ratios in terms of price-output, price-earnings and price-dividend. Using univariate and multivariate predictive regressions for horizons from one year to fifteen years for the full sample and three different sub-samples for comparison reasons with the previous research using aggregate stock market data, it is reported that both short and long horizon return predictability exists albeit with different predictive ability for different horizons. Among the three selected ratios, overall the price-output ratio is empirically favoured as a superior predictor of stock returns. The empirical findings refer to that this is robust across the three sub-samples investigated. It is empirically shown that size significantly matters in terms of return predictability. The second empirical research using monthly data is on the analysis of impact of macroeconomic volatility in terms of inflation and industrial production growth on asymmetric time-varying volatility of stock returns. Using a two-stage econometric methodology, first, based on estimation of asymmetric conditional volatilities of stock returns and macroeconomic variables, and then employing a vector autoregression methodology; it is reported that volatility of size-based portfolio returns are, in general, not significantly dependent on macroeconomic volatility. It is also shown that stock return volatility is more responsive to its own previous shocks as shown by the variance decomposition. It is also found that size does not matter in this specific case.