# Active Strategy (A) Returns Analysis

The quest for the perfect trading strategy is never ending; trading strategists are constantly examining all sorts of information that can give them any predictive power. In this study, we employ econometric techniques to explore whether the returns themselves have any predictive information.

Trader A agreed to share his strategy realized returns to conduct our analysis and post it on this forum. The data and the analysis are available in the attached spreadsheet.

### Data

The data series, available in our attached example, covers strategy daily returns between May 2008 and March 20th, 2009. We have a total of 223 data points.

### Preliminary

First, we examine the data visually. The returns distribution looks positively skewed and probably exhibits fat positive tail. Furthermore, the returns are clustered in some periods and not others. To smooth en the daily returns, we plot the 20-days (1 calendar month) moving average and EWMA for volatility to see how stable they are throughout our sample life span.

Examine the descriptive statistics of the sample data and conduct tests for serial correlation (versus white-noise), normality distribution and ARCH effect.

As we suspected above, the returns' probability distribution is not Normal, is positively skewed and has significant excess-kurtosis (fat tail). The returns are not serially correlated, nor do they possess ARCH effect.

The log returns is not white noise, and its probabilistic distribution exhibits more fat tails than normal distribution.

### Comments

Note that in the second graph above, the returns are highest when volatility is growing, and one may suspect they are positively correlated. In other words, the returns can be explained as a **risk premium** for undertaking the risky strategy.

A GARCH-M model may be in order to explain the returns and hopefully to predict future ones. $$ X_t=\mu + c.\sigma_t+\epsilon_{t} $$ $$ \epsilon_{t} = \sigma_{t}z_{t} $$ $$ z_t\sim i.i.d N(0,1)$$ $$ \sigma_t^2=\alpha_0 + \alpha_1 \epsilon_{t-1}^2 + \cdots + \alpha_p \epsilon_{t-p}^2 + \beta_1 \sigma_{t-1}^2 + \cdots + \beta_q\sigma_{t-q}^2 $$

### Next

We will build a GARCH-M model next and estimate the risk premium coefficient and forecast volatility (and expected returns). Finally, we alter the strategy to leverage forecast and estimate the new returns.

Visit us again in few days.