The correlation hedge is a simplified version of Keller and Butler’s EAA-formula (see paper or primer). For GPM we only use return and correlation information as momentum metric. We do so with two variations:

- GPM
**x**M: the correlation multiplied return metric**ri * ( 1 – ci )** - GPM
**x**F: the correlation fractioned return metric**ri / ( 1 + ci )**

**x**is the degree of crash protection,

**ri**is the average return of asset i over 1, 3, 6 and 12 months, and

**ci**the 12-month correlation of asset i with the equal weighted “risky” investment universe. The correlation multiplier

**( 1 – ci )**is based on the EAA-model, the correlation fraction

**1 / ( 1 + ci )**was recently suggested by Wouter Keller. For the mechanics of the crash protection algorithm, see the PAA-post.

In the graph below, the two correlation hedge variations are painted.

Notice how

**ri**is downplayed by the multiplier variation

**( 1 – ci )**(blue curve) for assets with positive correlations more and more (the hedge multiplier approaches 0 when

**ci**approaches 1), while

**ri**is amplified in a near linear fashion for assets with negative correlations (the hedge multiplier increases to a maximum value of 2 when

**ci**approaches -1).

For the fraction variation

**1 / ( 1 + ci )**(red curve) the hedge effect is inverted: for assets with positive correlations ri is downplayed by half (the maximum hedge fraction is 2 when

**ci**approaches 1), while

**ri**is increasingly amplified for assets with negative correlations (the hedge fraction approaches 0 when

**ci**approaches -1).

We will illustrate the two hedge variations for the “risky” N12 globally diversified universe as demonstrated in our PAA-paper (SPY, QQQ, IWM, EEM, VGK, EWJ, IYR, GSG, GLD, TLT, HYG and LQD). As safety asset we deploy the best out of two treasury ETFs: SHY and IEF, using the same correlation hedged momentum measure for selection. 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. The backtests cover the 45+ year period December 1970 until May 2016.

Contrary to our SA-contribution where high protection is applied, we will now backtest GPM with low protection. Quick re-cap: with low protection (so x = pf = 0, see PAA-post) for each “risky” asset with non-positive momentum a capital fraction of 1/N is allocated to the safety asset. With low protection GPM leaves more room to the “risky” assets for harvesting risk premia. This also allows for a good look at the absolute and relative changes in average capital allocation for the risky assets.

The table below holds some key performance indicators for three variations of GPM:

- GPM0R: unhedged “raw” 1/3/6/12m return and low protection (green)
- GPM0M: correlation multiplied return and low protection (blue)
- GPM0F: correlation fractioned return and low protection (red)

*NB! All results in this post 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.*

None of the low protection scenarios of GPM meet our positive performance requirements: rolling 1-year return win rates of above 95% and 99%, but the mark is barely missed (with medium or high protection enabled GPM does satisfy the requirements for both correlation hedge variations. See our SA-contribution). Regarding risk-adjusted performance, both hedged correlation variations beat GPM’s unhedged “raw” return baseline scenario, see for example the lower drawdown (D), the higher Sharpe (SR) and MAR ratios.

The table below shows the effect of the correlation hedge on the average capital allocation for both the hedge multiplier and the hedge fraction compared to the unhedged “raw” averaged return version of GMP, all with the PAA-like capital protection set to “low” (0). The capital allocations for the safety assets SHY and IEF are excluded from the table.

Notice that for

**ri * ( 1 – ci )**compared to

**ri**emphasize is added to EWJ, GSG, GLD, TLT, HYG and LQD, while SPY, QQQ, IWM, EEM, VGK and IYR are de-emphasized.

Compared to

**ri**, for

**ri / ( 1 + ci )**the capital allocations for SPY, QQQ, IWM, EEM and VGK are downplayed again, but less strongly than with

**ri * ( 1 – ci )**, EWJ and IYR both get about the same allocations, while GSG, GLD, TLT, HYG and LQD are again emphasized, but to a lesser extent.

The table below holds the relative changes in average capital allocations for each asset compared to the ones for

**ri**.

Especially the change for SPY stands out: compared to the unhedged ri baseline the correlation hedged multiplier

**ri * ( 1 – ci )**causes a reduction in capital allocation of 85% (5.5% to 0.8%) On the opposite end of the spectrum LQD is to be found with an amplification from 2.5% to 7.2%, a gain of nearly 290%, followed by TLT and HYG with a gain of 255% and 229% respectively.

The impact on average capital allocation demonstrates the provident characteristic of the hedge multiplier

**( 1 – ci )**through the strong emphasis foremost on bonds and secondly on “physical” assets to the detriment of stocks. The hedge fraction

**1 / ( 1 + ci )**shows a similar, but less distinct effect, leaving more room for stocks to prospect risk premia.

The effect of the correlation hedge is noticeable on the following two screenshots of monthly rankings for a 3 out of 12 asset selection. Based on “raw” return ri, the top three assets are: IYR, QQQ, EWJ. However, due to the correlation multiplied hedge

**ri * ( 1 – ci )**the generalized momentum top three becomes: EWJ (3), GLD (7), VGK (5). Because of its negative correlation reading, GLD climbs from 7th to 2nd place. The opposite happens for IYR: as a result of its high correlation IYR drops from 1st to 4th place, out of reach for capital allocation. This occurs also for QQQ, which drops from 2nd to 6th place.

The second screenshot shows the monthly rankings for the correlation fractioned hedge

**ri / ( 1 + ci )**. Due to the strong amplication of its negative correlation reading, GLD (7) even climbs to 1st place, followed by IYR (1) and EWJ (3, so unchanged). High/positive correlations are downplayed too, but to a lesser extrent. IYR declines from 1st to 2nd place, still eligible for capital allocation. QQQ drops from 2nd to 5ft place and gets no capital allocated.

The observed characteristics of the two hedge approaches present themselves in the following cumulative profit contribution table too.

The difference in hedge effect are most clear when we review the relative changes in cumulative profit contributions as shown in the table below.

For the hedge multiplier

**( 1 – ci )**, EEM (18%), IWM (32%) and SPY (35%) form the lower-end extremes, while LQD (439%) and GSG (527%) are the higher-end extremes.

The impact of the hedge is controlled by the (non-stationary) correlations of the respective “risky” assets. To illustrate the differences in correlations and their non-stationary nature, the following chart has in the upper price pane the equity curve of the monthly rebalanced risky N12 equal weighted (1/N per asset) portfolio (black) as well as the equity curves of three buy-and-hold investments: for SPY (blue), TLT (green) and GLD (orange “gold”) respectively. In the three subpanes the 12-month correlation coverage is plotted for the equal weighted N12 with SPY, TLT and GLD respectively.

The chart above shows that an asset like SPY, which on average reflects a high correlation with the N12 risky universe (see the correlation graph in blue), generally will be substantially downplayed through the correlation hedge term. Hence SPY has a slim chance on selection for capital allocation. On the other hand, assets like TLT and GLD benefit especially during the periods when their correlations are negative, resulting in a hedge induced boost of their momentum rankings and thereby fatter chances on capital allocations.

To wrap-up: Highly correlated assets are downplayed most pronounced by the correlation multiplier hedge

**( 1 – ci )**and to a lesser extent by the correlation fraction hedge

**1 / ( 1 + ci )**. For low correlated assets the effect is inverted. Both correlation hedges have about the same impact for assets with correlations in the -0.25 until +0.25 range. Joining the generalized momentum measure based on correlations and returns together with our multi-market breadth crash protection algorithm, leads to conservative capital allocations resulting in higher risk-adjusted performance.

Special thanks to Wouter Keller for his support and contributions to this post.

The monthly asset selections for GPM's correlation multiplied momentum approach

**ri * ( 1 - ci )**with high protection are shown below. For interpretation of the signals please refer to the explanation on the Strategy Signals page. GPM can be tracked through AllocateSmartly too (affiliation).

*NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the signals. Please do your own due diligence and use at your peril. The*

**Important Notice**in the footer applies as well as the Disclaimer.**Disclosure**: long GLD, IYR, IEF.

The full AmiBroker code for GPM is available upon request. Interested parties are encouraged to support this blog with a donation.