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Inter-Strategy Correlation Risk

In managing the risk of a macro fund employing multiple strategies, it is essential to not only understand the distribution of returns and probabilities of various events, but also the correlation of each strategy to each other. When adding strategies to our fund, we are looking for non and negatively correlated strategies to existing strategies employed. The remainder of this post will show the extraordinary benefits. Let's start with a one-strategy fund, perhaps employing an equity value strategy or even tactical momentum-breakout setups... it doesn't matter much. Each singular strategy has a specific distribution of returns and risk (I will leave my definition of risk aside for another post and stick with Variance squared or Standard Deviation for now). Let's say the strategy A averages 0.41% per month (an annual 5%) with a standard deviation of 3 times that per month leaving us with a return-to-risk ratio of 1:3. A random sample of returns from this strategy are shown in Table A. The average monthly return of this sample is 0.5% per month with a standard deviation of 1.17%. This gives us a return-to-risk of ratio of 0.43. Now with this data, we know that only 1 out of 100 times will our drawdown be more than 2.71% [normsinv(.99)*1.17% ].

Strategy A

Now this is good for a long-term strategy, but we can actually make this better. By taking another strategy that has the same distribution of returns, but correlated by a factor of less than one (less than perfect correlation), we can see that the return-to-risk ratio rises while improving our drawdown probabilities and sizes. Let's take another random sample, this time from strategy B. That sample is shown in Table B and has an average monthly return of 0.59% with a slightly increased standard deviation of 1.18%. This leaves strategy B with a return-to-risk ratio of 0.50, slightly better than strategy A, although not statistically different. However, the difference with Strategy B is that the correlation to strategy A is low with 0.18. Using a Cholseky Decomposition, I solved the correlation matrix such that matrix A* = LU, and then used L to factor a correlated data series. When we view these two strategy series, we see the similar distribution of returns shown by similar line patterns (or returns).

Strategy A & B Indexed Price

However, this difference in correlation allows us to reduce variance of returns, which our lowers our chance and magnitude of a losing month, while maintaining the same average return of the portfolio (as correlation only affects variance, not returns). The combined portfolio, assuming an evenly weighted distribution of funds to each strategy yields the following statistics:
  • Mean Monthly Return: 0.54%
  • Standard Deviation: 0.90%
  • Return-to-Risk: 0.6%
The reason the return is simply the average returns is because there is no correlation adjustment in its calculation. However, when calculating variance, the co-variance (or the absolute squared movements of the two assets together) affects the total portfolio variance. Think of it this way, if the assets move the same distance in opposite directions, the variance of the portfolio will be 0 as there was not actual movement when viewed together. So the extent to which assets move together matters... or in this case, strategies.

Return-to-Risk benefits

The main benefit to our fund with this simple math is that the more non-correlated strategies (with diminishing marginal benefit) we add to our fund, the higher we can raise our Return-to-Risk ratio. So we can lower risk as defined by standard deviation by employing multiple alpha strategies with non-correlated return streams. The lower their correlation...the higher Return-to-Risk we can achieve. While the initial benefit may be obvious, our main reason for employing this taking it one step further.

The Compounding Effect of Low Drawdown

Drawdown RecoverOne of the main types of risk we avoid at the fund is drawdown. We measure return in relation to drawdown not standard deviation for the most part. How much we can lose is the price we are willing to pay for a return in our eyes. The key to diversifying strategies is that drawdown is lower, and the benefit to that can be seen above. With the same average returns across all the above portfolios, why does the combined end at a higher overall rate of return? The answer lies in smaller drawdowns. By keeping them small, we have less lost ground to make up. This less ground is covered more quickly with the still constant average return that is the same as the other portfolios. Look at the graph to the left. The lower your drawdown, the less return you need to get into new high ground. So while we may never make ground breaking returns, our low-drawdown focus keeps us consistently moving our equity line up, and we believe higher than other assets over a longer-time frame. The last key here is that exposure and leverage can be employed to control returns once drawdown is measured and controlled. So let us assume you have set a goal for the risk to be 99 out of 100 months contain drawdowns of 2.71% or less. Well due to our lowered standard deviation of the combined portfolio, we are seeing that drawdowns are contained to 2.1% or less (with 99% degree accuracy). So we can employ slight leverage of 1.27 for our combined portfolio. We now match the drawdown risk (in theory using covariance mathematics, we use historical and monte carlo adaptations in actuality) of strategies A and B; however, now we have a far superior return. This is benefit of focusing on Return-to-Drawdown. We maintain the same improved Return-to-Risk ratio as before.

Leveraged Combined Strategy

So this writing shows our focus on Inter-Strategy Correlation Risk. What we have done is to take a strategy, add something to it, and dramatically increase its Return-to-Risk ratio (by adding non-correlated strategies then leveraging back up to the previous chance of drawdown or variance). We believe that by strictly focusing on measuring, managing, and moving between risks, returns will naturally accumulate.

Table ATable B