We generally measure the accuracy/quality of an alpha’s predictions by metrics such as information ratio (IR) and information coefficient (IC). The IR is the ratio of excess returns above a benchmark to the variability of those returns. It suggests that an alpha with high excess returns and low variability consistently predicts future returns over a given time period. The IC measures the relationship between the predicted and actual values using correlation, and a value of 1.0 suggests great forecasting ability.

While high IR and IC are great, we must not forget that they measure return prediction irrespective of real world constraints; they assume liquidity is endless, trading is free, and there are no other market participants but ourselves. But actual trading strategies must abide by certain constraints, and an alpha that makes predictions correctly and often, but does so with reasonable assumptions about market conditions, will be more easily leveraged.

WHAT IS TURNOVER?

Predictions change as new information becomes available. Whether a stock moved one tick, an analyst revised his recommendation, or a company released earnings, this change in information is a catalyst for trading activity. We measure this trading via turnover: the total value traded divided by the total value held. A company’s stock price changes much more often than does a company’s earnings per share, and so it follows that an alpha based on price movements (e.g. price reversion) will usually have a higher turnover than an alpha based solely on company fundamentals. As more trading opportunities provide more opportunities to capture return, we find IR or IC to be higher for price reversion alphas than those of fundamental alphas.

DOES THAT MEAN LOWERING TURNOVER WILL RESULT IN LOWER RETURN?

The tradeoff between return and turnover is certainly one that needs to be balanced. Reducing turnover need not always reduce the quality of the prediction, however. Using smoothing methods like linear decay may actually improve performance in sparse signals with very few events. Winsorizing (limiting extreme values) or decaying the data itself may also help in reducing the turnover in cases where high sensitivity to changes in information may be changing predictions unnecessarily. It will ultimately depend on the alpha. Regardless of the end result, understanding how the alpha behaves under various turnovers gives us a sense for its tradability. One would consider an alpha that maintains most of its return to be more easily leveraged compared to an alpha that loses all return after a slight turnover reduction.

HOW DOES LIQUIDITY FACTOR INTO THIS?

Every trade has a cost, both in terms of fees (i.e. commissions paid to the broker or exchange) and the spread cost. Trading cost is the cost incurred in making an economic exchange. When buying a stock, we not only pay a commission to the broker, but we also pay a spread cost. The highest price a buyer is offering for a stock (the bid) is usually below the lowest price a seller is willing to accept (the ask); this is the bid–ask spread. To realize a return, you must sell what you buy and, at any given time, we may buy a stock only at a price higher than what we could sell it for.

We expect this spread cost to be proportional to the liquidity of the universe or market in question. The top 500 most liquid stocks in the US equities market have an average spread of about 5 basis points (bps). In comparison, smaller markets like those in South East Asia may have average spreads as wide as 25–30 bps.¹ The cost of trading is much higher in these markets, increasing the importance of turnover.

As such, understanding the liquidity of the market is helpful when designing alphas, and testing the alpha idea on a variety of universes of instruments is an important step in understanding its potential tradability. A given level of turnover might be acceptable in the most liquid universes, but become untradable when extended to include less liquid instruments. Or, what works in one country might only work in the most developed markets. For example, an alpha that trades the top 500 most liquid stocks in US equities with X% turnover may be perfectly acceptable. However, when considering a similar alpha on a larger universe with less liquid instruments (e.g. top 3,000 most liquid stocks in the US), or an alpha trading a developing market, it would be wise to evaluate the performance at lower turnovers keeping the cost of trading in mind.

DOES THE ALPHA ITSELF PLAY A ROLE?

Consider two hypothetical alphas that use price and volume data to make a prediction on prices on the following day. Both alphas operate on the same set of instruments, and let us assume both alphas have the same return and IR. The first simply invests in instruments based on their recent volatility while the second invests based on their current market volume.

We see that the first alpha is investing in more volatile instruments, but as high volatility stocks tend to have lower volume, it makes it difficult for a strategy to allocate a large amount of capital to turn those returns into actual profits. The second alpha, on the other hand, is investing in more liquid, large cap instruments, and is likely to be easier to leverage. If we also pretend that volume data is more stable over time relative to volatility, we would expect turnover for the second alpha to be lower, further increasing its appeal.

SO WHAT IS THE RIGHT TURNOVER FOR AN ALPHA?

It’s a balancing act. The turnover margin measures how much the alpha actually earns relative to its trading; it is defined as profit divided by total trade value, which is the amount of money being traded. A good turnover is one that maximizes this ratio between the profit/IR and the turnover. But more importantly, the exercise of understanding how the alpha performs across different liquidity sets and under varying turnover levels should give you a certain confidence about the alpha’s robustness and tradability. In the end, it’s all relative.