Soul in the Game

One thing that puzzles many in quantitative finance is when log return is appropriate and when simple return should be used. Simple Return Formula:                    Log Return Formula:                           While there are several benefits of using log returns like log-normality, time additiveness, approximate raw-log equality and mathematical ease, a common fallacy is to use is at places where it is not appropriate. The most important difference between simple and log returns is the features of time-additivity and asset-Additivity. Simple returns are asset-additive : Portfolio return is the weighted average of the stocks in the portfolio.  where weights are the proportion of an individual stock in the portfolio and the sum of the weights is 1. Therefore, if an investor puts an equal amount of money in each stock it will be called “equally-weighted” portfolio. The return of an equally-weighted portfolio is just the average return of all stocks in t

The empirical regularity that stocks provide a higher return than government bonds is known as “equity premium” puzzle, a term first coined by Mehra and Prescott (1985). The most intuitive answer that stocks are riskier than Bonds is not a sufficient explanation for this observed puzzle. Moreover, this equity risk premium (ERP) epitomizes the investor risk aversion. A person if given a choice between a low but sure payoff and a high but uncertain payoff would choose the guaranteed payoff if he is risk-averse. Given the expected utility of both the scenarios are same, a risk-neutral person would be indifferent between the choices. However, the presence of equity risk premium (ERP) exemplifies that investors are largely risk-averse. Because arbitrage by investors should have eliminated (or reduced) the return difference between these two investment opportunities which is not the case in the present case. Table-Equity Risk Premium in India 2000-2016 Year BSE500