Now consider a different situation. Assume that we have two buckets of systems from which to choose. The systems in bucket A have mutual correlations of 0.8 to each other but mutual correlations of 0 to all the systems in bucket B. Similarly, the systems in bucket B have mutual correlations of 0.8 to each other but mutual correlations of 0 to the bucket A strategies. What we are describing now is an idealized case in which one can choose half of the portfolio from long-term strategies and the other half from short-term strategies that are assumed to be decorrelated from trend-following.
In this case, we effectively can consider our portfolio to be constructed using C=0.4, which is the average mutual correlation value. Returning to our equation, we find that we can achieve a diversification factor of =1.58 if C=0.4. The implications of this are profound. Again assuming that each program independently can produce a Sharpe ratio of 0.75, we now find that our portfolio will produce an overall Sharpe ratio of 1.19, a substantial improvement from the previous range of 0.84 to 0.90. "Building a diverse team," (above) summarizes the effect of different diversification factors on the final portfolio Sharpe ratio SP. The diversification factor increases rapidly as the average correlation decreases.
In real portfolio construction, other factors also must be considered. But the most important ingredient in the recipe is still a set of diversified strategies with which to start, and short-term systems provide at least one way in which to acquire this all-important ingredient.
Challenges of short-term trading
As with most things, even this proverbial free lunch comes with costs. Primary among those is that short-term systems incur higher trading costs and are, hence, somewhat capacity-constrained. Consider a trend-following system that achieves about a 12% annualized volatility. This typically is measured by taking the standard deviation of monthly returns and multiplying by or directly computing the standard deviation of yearly returns. A 12% annualized volatility roughly corresponds to a one-sigma deviation of 0.75% in the daily returns, i.e., most of the time the daily return will lie between -0.75% and +0.75%. For such a system, a typical trading frequency is about 1,000 round-turn trades per year, per million dollars traded. The true cost of these trades must account both for explicit costs such as commissions, exchange fees, etc., but also must estimate the hidden slippage cost that trading incurs. The slippage cost commonly is taken to be proportional to the difference between a particular trade’s fill price and the volume-weighted average price of all trades during that period. If buying, this difference is typically positive, and if selling it is typically negative. Considering the most commonly traded futures markets, we estimate that the sum of explicit and hidden costs is about $20 per round-turn on average. This implies a yearly cost of $20,000 per million dollars traded for the trend-following example above, or 2% of the portfolio value. This is not an insignificant amount of frictional loss because of trading costs, but neither is it excessively onerous.
Now consider a short-term trading system that also achieves 12% annualized volatility. Owing to the shorter holding period, this system must trade more often to facilitate its frequent trade entries and exits. For this system, a typical trading frequency is about 3,000 round-turn trades per year per million dollars traded, or three times that of the trend-following system. A similar analysis to that above implies a yearly trading cost of $60,000 per million dollars traded, or 6% of the portfolio value. To achieve a net return equal to that of the trend-following system, the gross performance of this system must, therefore, be 4% larger to compensate for the additional trading costs.
If we subsequently migrate to an even shorter-term system that now trades twice as frequently, we would pay 12% per year in trading costs alone! At our 12% annualized volatility, in this case we are effectively "spending" a Sharpe ratio of 1 in trading costs (i.e., 12% in costs for a program with 12% annualized volatility), whereas the original trend-following system only had to "spend" a Sharpe ratio of 1/6 (2% in costs for a 12% annualized volatility) to achieve its returns. Some short-term systems will trade as many as 10,000 round turns per million.