An investigation into aggregation bias: the case of stocks and treasury bill returns in Ghana

The paper investigates aggregation bias by comparing the risk and returns characteristics of stock exchange-traded shares and Treasury bills (T'bills) in Ghana. The study uses end of period annualized data on T'bills and stocks returns, and inflation from 1990 to 2020. We mainly consider four separate investment periods: 1990-2000, 2001-2010, 2011-2020, and 1990-2020 (i.e. the aggregated period) in order to determine possible aggregation bias occurring from lumping the years together. We measure average annual returns, standard deviations, co-efficient of variations, Sharpe ratio, ANOVA, Jarque-Bera test, maximum drawdowns (MDD), and correlation analysis to determine risk and return characteristics of the two instruments. The study finds that T'bills compared to stocks shows higher returns yet lower risk, thereby indicating an inverted yield curve. Levene's Test for Equality of Variances indicates stocks significantly outperformed T'bills over the 31-year aggregated period. The study reveals the presence of aggregation bias as stock and T'bill risk and return characteristics of two segregated periods (i.e. 1990-2000 and 2011-2020) contradict the general expectation of risk-return trade-off theory contrary to that of the aggregated period. The MDD, ANOVA results, Anova F-test and Welch F-test reveal aggregation bias for T'bills but not for stocks. We recommend future studies to ensure that analysis and conclusions made do not suffer aggregation bias by disaggregating aggregated units. The problem of aggregation bias is one of the neglected issues in most research in finance and economics. There is perceived reliability and generalizations provided by studies with larger sample sizes without recourse to changes in political and macroeconomic conditions that potentially impact investment performance. Hence, investment decisions and policies could be affected by misleading conclusions drawn from aggregated data. By segregating the aggregated periods into three separate decades, we show that risk and return characteristics (as measured by risk-return trade-off theory, co-efficient of variation, Sharpe ratio, maximum drawdowns, and likelihood of loss) of stocks and treasury bills differ among the segregated periods suggesting the presence of aggregation bias. The study potentially enhances the effectiveness of investment and policy decisions among investors. As investor value increases through prudent investment decisions, it would attract more investors, thereb