Can Strategy use Dictate Required Model Accuracy?

At Newfound, we are big believers that strategy benchmarks should serve both as a yardstick for measuring performance as well as an indicator for how a strategy should be used in an overall portfolio.

Up for internal debate, recently, has been how to benchmark a simplified strategy that makes a monthly decision to be either 100% long equities or 100% cash. Traditionally, this strategy would be benchmarked against a long equity index, like the S&P 500.  At Newfound, however, we believe that benchmarking this way implicitly tells investors that the strategy should be used to replace S&P 500 exposure.

We believe a more nuanced approach to using the strategy is to replace a piece of existing S&P 500 exposure and a piece of cash-like holdings (e.g. short-duration fixed-income).  Therefore, we believe the appropriate benchmark is more akin to a 50/50 portfolio.

One of the reasons we prefer this approach is because in the former positioning, the strategy can only add value when the S&P 500 is losing value.  Put another way: even if the model is 100% accurate in identifying up markets, it can only achieve benchmark returns.  In the latter positioning, the strategy can take advantage of upside accuracy because it will end up tilting the investor's entire portfolio towards equities.

This positioning argument has an interesting effect upon the required accuracy of the underlying model to add value.  If we define active returns as returns in excess of the benchmark, we can create a table of active returns based upon what the benchmark is doing and whether our model is right or wrong (let R be the return of the S&P 500):

 

S&P 500 Up

S&P 500 Down

Model Accurate

0

-R

Model Inaccurate

-R

0

Now consider the active return profile when the benchmark is a 50/50 portfolio:

 

S&P 500 Up

S&P 500 Down

Model Accurate

R/2

-R/2

Model Inaccurate

-R/2

R/2

In the first table, the only place the strategy can add value is when the S&P 500 is down and the model is accurate.  In the extreme, if the market is up 100% of the time, to retain a positive expected active return profile, the model has to be 100% accurate.  On the other side, if the market is down 100% of the time, the model only has to be accurate once in a blue moon to create positive expected active returns.  If the market is up 50% of the time and down 50% of the time, the model has to be at least 50% accurate to have positive expected active returns.  What we find is that since the model can only add value when the market is down, the accuracy will be a function of the percentage of time the market is down.  For the S&P 500, we find that monthly accuracy needs to be ~58%.

In the second table, the strategy can add value regardless of whether the market is up or down.  Therefore, so long as the model has an accuracy greater than 50%, the strategy will have positive expected active returns, regardless of the percentage of time the market is up or down.

What if we considered this strategy as a replacement for a 0/100 portfolio?

 

S&P 500 Up

S&P 500 Down

Model Accurate

R

0

Model Inaccurate

0

R

This is the exact opposite scenario of the first case: we can now only add value in up markets.  Since, long term, the market is up more than it is down, our required accuracy is actually less than 50%!

Now, the expectancy of active returns says nothing about the variance of active returns, and a stated benchmark frequently has just as much to do with risk as it does return expectations.  In other words, replacing a cash position with a strategy that can be 100% long the S&P 500 may not fit from a risk allocation stand-point.  Nevertheless, the interesting takeaway here is that how we position a strategy in our overall portfolio may dictate the requirements we put on model accuracy to add value.