Another way to measure turnover, is called the factor rank autocorrelation. The factor rank autocorrelation is close to one, when the ranking of stocks doesn’t change much from day to day. To give you an illustration, let’s imagine our universe consists of just two stocks, apple and alphabet. If over several days, the rank of apple, based on its alpha signal is always two, and the rank of alphabet is always one, then the previous ranks of each stock are perfectly correlated with the current day’s ranks. In other words, the ranks are highly correlated or the factor rank autocorrelation is close to one. When the ranks of stocks don’t change much from day to day, this also means that the weights of our theoretical portfolio don’t change much either, which means less trading, and therefore less turnover. To calculate the factor rank autocorrelation for a single time period, we’ll get the ranked alpha vector for the previous day, and also the ranked alpha vector for the current day. Then we calculate the Spearman rank correlation between the prior days and current days ranked alpha vectors. We can repeat this for multiple days and a time window, so that we have a time series of factor rank autocorrelations. A high factor rank autocorrelation is a proxy to indicate that the turnover is lower. A low, or even negative factor rank autocorrelation, would then indicate high turnover. Let’s look at how we would use a turnover measure, such as factor rank autocorrelation in the context of other evaluation metrics. If two alpha factors have similar sharpe ratios, similar quintile performance, and similar factor returns, we’ll always prefer the one with lower turnover. If an alpha factor has high sharpe ratio, but very high turnover, we may need to consider whether the alpha factor would survive backtesting, paper trading, and real trading. As a reminder of why lower turnover helps us, it makes it more possible for us to execute trades if the stocks are liquid and can reduce our transaction costs. Managing turnover is a delicate balance. On one hand, we want high turnover because that means alpha factor is taking advantage of new information, and making more trades which likely implies higher breath. However, on the other hand, trading costs money and excessive turnover could mean the alpha is simply capturing noise. Over time, the more you work in alpha research, the more you will develop intuition about this. Evaluating alpha factors is both an art and a science. Keep in mind that factor rank autocorrelation is different than rank IC. Even though these metrics both use ranking and correlation, rank IC is measuring whether an alpha factor is correlated with forward returns, while factor rank autocorrelation is measuring how stable the ranked alpha vectors are from day to day.