Embedding Diversification in Momentum Analysis

Portfolio engineering is certainly a place where the whole can be greater than the sum of the parts.  Historically, momentum has been a study of the parts with no real concern for how those parts are ultimately combined.  If we consider the most academic of methodologies – taking 1000 securities, ranking by trailing returns, and selecting a portfolio of the top N – we may ultimately end up with considerable concentration risk in our construction.

While investors may not be able to eat risk-adjusted returns, risk-aversion certainly means they care about them.  Once we begin to consider how to construct a momentum portfolio based on risk-adjusted return profiles, we run up against an interesting dilemma: does a portfolio of the top N (risk-adjusted / total) returning asset classes necessarily construct the top risk-adjusted returning portfolio?  The answer is certainly not.

So how can we consider diversification within our momentum construction?  A naive solution is to actually explicitly construct the portfolios we would consider investing in and run our momentum model over those portfolios.

So consider the following simple example: a strategy (the “Either/Or” strategy) that invests either in the S&P 500 or 20+ Year Bonds and another strategy (the “Diversified” strategy) that can invest in a 100/0, 80/20, 60/40, 40/60, 20/80 or 0/100 combination.  The strategies each rebalance opportunistically, always investing in the opportunity that exhibits the greatest trailing 252-day risk-adjusted return.

diversified-momentum-growth-of-1-dollar

The Diversification strategy has an annualized return of 9.46%, an annualized volatility of 10.73% and a max drawdown of 26.58%.  The Either/Or strategy has an annualized return of 7.90%, an annualized volatility of 12.98%, and a maximum drawdown of 30.73%.

We see that since mid-2010, using trailing 252-day risk-adjusted returns as a switching mechanism has, for the most part, out-right failed to be predictive between SPY and TLT.  It would appear that the relationship between the two securities was mean-reversionary, making selecting the previous winner a losing proposition.  Looking within the allocations of the Diversification strategy, we see that the portfolio ultimately allocates to the 40/60 and 60/40 portfolios over this period, which resulted in a steady return profile.  While the relationship between SPY and TLT may have been mainly mean-reversionary over the period, by combining the assets into a single portfolio, their negative correlations dampened volatility and enabled a trend to emerge, creating a portfoliothat seemed to exhibit momentum characteristics.

By including portfolios as if they are their own asset class, we are able to capture the effects (and, hopefully, benefits) of diversification within our momentum selection process in a completely implicit manner: we don’t really have to make any extra assumptions beyond the ones we are already making.

 

People often ask us why we focus so much on momentum and other factors that can be derived from price (like volatility and correlation).  Why don’t we consider economic, fundamental, or other market data?  As we can see here, one of the benefits of using models that only rely on price data is that they give you a massive amount of flexibility.  Trying to do the same process above by aggregating fundamental or economic data would be near impossible when you start to include fixed income, commodities, currencies, and international asset classes.  By focusing solely on the behavior of the time series, we can become agnostic as to what those time series represent and begin to include factors – whether they be valuation, diversification, or something else entirely – in an implicit manner.

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