Generalized Protective Momentum

by: TrendXplorer

As demonstrated in a previous post Protective Asset Allocation has the capacity to obtain positive returns consistently over 45+ years.

Generalized Protective Momentum combines the protective momentum approach with correlation hedged returns.

GPM’s chosen hedge approach may boost return or reduce left tail risk while preserving consistent positive return performance.


In our SSRN-paper "Protective Asset Allocation" (PAA) we presented a multi-market breadth approach to quantify market meltdown risk (see our SA-contribution too). The crash protection algorithm was demonstrated with a simple momentum metric: the ratio of current price to its 1-year SMA minus one for both absolute and relative momentum. As stated in our paper, the crash protection algorithm can easily be combined with other quantitative methods for portfolio allocation. In this contribution we combine the multi-market breadth approach with a generalized momentum metric based on correlation hedged returns. We call the resulting model: Generalized Protective Momentum (GPM).

Generalized Protective Momentum

In their SSRN-paper about "Elastic Asset Allocation (EAA)" Keller and Butler merged momentum, volatility and correlation into one generalized measure for timing, selection and capital allocation. Based on the EAA-formula (explained here) we use a simplified formula for GPM: only return and correlation information are combined for measuring absolute and relative momentum. By mitigating the return information with a correlation hedge, risk-adjusted performance can be improved in two separate ways: a boost of portfolio return is possible without compromising left tail risk (drawdowns) or, alternatively, risk can be reduced while preserving portfolio return. For these two variations we combine return and correlation into a generalized momentum measure as follows:

  • GPMxR: the (traditional) non-hedged return metric ri
  • GPMxM: the correlation multiplied return metric ri * ( 1 - ci )
  • GPMxF: the correlation fractioned return metric ri / ( 1 + ci )

Where x is the degree of crash protection, ri is the average return of asset i over 1, 3, 6 and 12 months (denoted: 1/3/6/12), and ci the 12-month correlation of asset i with the monthly rebalanced equal weighted "risky" investment universe. The correlation multiplier ( 1 - ci ) is based on the EAA framework, the correlation fraction with 1 / ( 1 + ci ) was recently suggested by Dr. Keller. See "Deciphering Correlation Hedged Momentum" for the mechanics of the two correlation hedge variations.

Backtesting GPM

The highlighted backtests of GPM are performed with the same diversified "risky" universe we used in our PAA-paper, representing 12 global markets:

  • PowerShares QQQ Trust ETF (NASDAQ:QQQ)
  • iShares Russell 2000 ETF (NYSEARCA:IWM)
  • iShares MSCI Emerging Markets ETF (NYSEARCA:EEM)
  • Vanguard FTSE Europe ETF (NYSEARCA:VGK)
  • iShares MSCI Japan ETF (NYSEARCA:EWJ)
  • iShares U.S. Real Estate ETF (NYSEARCA:IYR)
  • iShares S&P GSCI Commodity-Indexed Trust ETF (NYSEARCA:GSG)
  • iShares 20+ Year Treasury Bond ETF (NASDAQ:TLT)
  • iShares iBoxx $ High Yield Corporate Bond ETF (NYSEARCA:HYG)
  • iShares iBoxx $ Investment Grade Corporate Bond ETF (NYSEARCA:LQD)

As safety asset we again deploy the best out of two treasury ETFs, using the same correlation hedged momentum measure for selection:

  • iShares 1-3 Year Treasury Bond ETF (NASDAQ:SHY)
  • iShares 7-10 Year Treasury Bond ETF (NASDAQ:IEF)

Each month 3 out of 12 assets with the highest correlation hedged return readings are eligible for capital allocation next to the safety asset's allocation. For crash protection we will use the same "high protection" level as introduced in our PAA-contribution. With the protection level set to "high (2)" the capital fraction of the safety assets equals twice the fraction of assets with non-positive momentum in the risky universe. The backtests cover the 45+ year period December 1970 until May 2016.

On the chart below our previously introduced PAA strategy with high protection (black) is compared with the two mentioned variations of GPM and also with GPM's "raw" return baseline strategy:

  • GPM2R: unhedged "raw" 1/3/6/12 return ri and high protection (green)
  • GPM2M: correlation multiplied return ri * ( 1 - ci ) and high protection ((blue))
  • GPM2F: correlation fractioned return ri / ( 1 + ci ) and high protection (red)

Notice that PAA2 is based on the -unhedged- ratio of current price to its 1-year SMA minus and high protection.

The equity curves, charted in semi-log scale, are depicted in "wet paint fashion" to emphasize the magnitude and duration of drawdowns. The table below the chart holds some key performance statistics.

Equity Comparison Chart
Table with key performance indicators
NB! All results in this contribution are derived from synthetic monthly total return data constructed by us based on indices net of costs. Furthermore trading costs, slippage and taxes are disregarded. Results are therefore purely hypothetical.

Compared to PAA2 every GPM scenario shows improved risk-adjusted performance reflected in higher Sharpe and MAR-ratios. Return is 0.2-1.5% higher, volatility levels are nearly similar, drawdown is 0.5-4.1% better. Just like PAA, GPM obtains positive performance consistently as is shown by the rolling 1-year return win rates of above 97% and 99%.

As stated, in correlation fractioned return mode this slightly riskier GPM variation boosts portfolio return to 16.46% yet preserves left tail risk, with a maximum drawdown of -10.48%. When GPM's hedge mode is set to correlation multiplied return, left tail risk is considerably reduced with a maximum drawdown better than -7% while the compounded portfolio return of above 15% meets the PAA performance.

The low-risk profile of the hedge multiplier ( 1 - ci ) is manifest in the following chart with drawdowns painted for ri * ( 1 - ci ): GPM2M in blue, and ri / ( 1 + ci ): GPM2F in red. Notice the frequent longer red tails of hedge fraction variation.

Comparison chart of drawdowns


The following charts provide a detailed view of GPM2M's performance, so with correlation multiplied momentum approach ri * ( 1 - ci ), and high protection with the earlier mentioned top selection of 3 out of 12 "risky" assets along with the best out SHY and IEF as "safety" asset.

Portfolio equity graph:

Annual return distribution:

Monthly return distribution:

Rolling 1-year returns:

Histogram of monthly returns:

Profit contribution:


For the GPM approach we join together our multi-market breadth algorithm for crash protection with a simple, generalized metric combining returns and correlations for measuring momentum. Compared to PAA, risk-adjusted performance improves for both GPM correlation hedge approaches. Risk wise the correlation multiplied return approach ri * ( 1 - ci ) is best, closely followed by the correlation fractioned return approach ri / ( 1 + ci ). With high protection enabled, both of GPM's correlation hedged momentum approaches obtain positive performance consistently, which is even true for GMP's unhedged "raw" return approach.

Google Spreadsheet

A "live" updating Google Spreadsheet for the correlation multiplied momentum variation ri * ( 1 - ci ) and high protection with a top selection of 3 out of 12 "risky" asset (denoted: GPM2MT3) is available for reviewing performance over time:

Disclosure: I am/we are long GLD, IYR, IEF. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.