## Summary

- Hedged Convexity Capture is not dependent upon bull markets.
- It is not a perfect strategy.
- Hedged Convexity Capture is merely superior to the publicly available alternatives.
- The strategy represents an actuarial approach which is revolutionary.

Previously, we explored Long-Biased Hedged Convexity Captures, a strategy which seeks to capture the negative convexity associated with leveraged ETPs. The idea behind Hedged Convexity Capture, as I outline in my book, is to capture the potential returns from shorting leveraged inverse equity ETPs with lower drawdowns and far higher Sharpe ratios than by just shorting them outright. The strategy seeks to accomplish this by shorting leveraged inverse equity ETPs like SPXU (NYSEARCA:SPXU), and pairing that short with a short position in TMV (NYSEARCA:TMV), an inverse-leveraged long bond ETP.

Not only does shorting TMV often provide a hedge for the equity portion of the strategy, but TMV itself suffers from negative convexity, further increasing the effectiveness of the long bond hedge.

However, what most investors do not understand is that a portfolio constructed in a manner which is non-correlated to the S&P 500, not only enjoys the moderate benefit of the often inverse performance of equities and long duration bonds, but also is far more efficient at capturing the far larger and more dominant phenomenon of the negative convexity of the inverse leveraged instruments themselves in a more pure fashion which is independent of long term S&P 500 performance.

Investors considering a Non-Correlated Hedged Convexity Capture Strategy make a huge mistake when they believe that such a strategy depends upon bull markets in equities or bonds. While I totally concede that discontinuous drops (flash crashes, surprise crises, etc) in markets can have devastating effects on a Hedged Convexity Capture Strategy (which is why the non-public version we have created does not use shorting), the notion that secular bull markets in equities and bonds are required for the strategy to enjoy a positive return is incorrect. Most of the performance of Non-Correlated Hedged Convexity Capture comes from the negative convexity often associated with the daily reset of the leveraged inverse exchange traded products themselves.

Let us examine the actual performance of Non-Correlated Hedged Convexity Capture. As before, we will use some simple rules, but this time, will focus on creating a Hedged Convexity Capture strategy which is non-correlated to the S&P 500, but still captures excellent negative convexity. We shall efficiently capture this negative convexity in a hedged manner with the following rules:

I. Short SPXU with 40% of the dollar value of the portfolio.

II. Short TMV with 60% of the dollar value of the portfolio.

III. Rebalance weekly to maintain the 40%/60% dollar value weighting between the two instruments.

Here are some graphs of the results:

We can see that Non-Correlated Hedged Convexity Capture has an extremely low 0.13 correlated to the SPY (NYSEARCA:SPY) S&P 500 ETF over the entire period. I believe that even this tiny correlation will prove to be a spurious result of the fact that the performance of both strategies drifts upwards during the period.

To really drive home the point that the strategy is non-correlated to the SPY, let's look at some periods of drawdown in the S&P 500. I think the following graphs will totally destroy the false notion that the strategy needs strong bull markets. To the contrary, Non-Correlated Hedged Convexity Capture should tend to underperform during strong bull markets in equities and massively outperform during sideways and down markets. Indeed, as we can see above, YTD the strategy is beating the SPY ETF by 15.9 percentage points, and outperformed the SPY ETF by 90.8 percentage points in 2011.

Let's focus in on 2011 in the graphs below:

In intuitive terms, it is as if the equity curve for the strategy does not even "know" that the drawdown in the SPY exists. And now we see in times of market stress, a correlated of 0.02 to the SPY. Remember when I argued above that I thought the 0.13 correlated over the strategy's whole history was spuriously high due to the phenomenon of both equity curves drifting upwards during the entire test period?

Now let's zoom in more closely on the period of intense drawdown for the S&P 500 in 2011:

There is no effect from a 17.5% drop in the SPY over the period. To the contrary, the strategy actually gains 41.5% during that drop. The notion that some critics have that Hedged Convexity Capture needs bull markets in equities is totally wrong. The whole point of the strategy is that it captures negative convexity. Literally, by shorting instruments which have negative convexity, the strategy enjoys positive convexity. Hence the "Convexity Capture"! We are capturing the available convexity in these instruments, and moreover, doing it in a hedged manner which is non-correlated to the S&P 500. Pretty neat, eh?

That's the power of math. It is really an actuarial approach to trading. We are making the same shrewd bet on convexity again and again, by focusing on a repeatable phenomenon (remember that concept from science?) called negative convexity. We are not making a bunch of individual predictions every day like most investors or traders. And when the phenomenon observed is especially strong, the results of that phenomenon become proportionally more predictable.

Literally, we are capturing a glaring market inefficiency -- the willingness of people to hedge with instruments which suffer from negative convexity -- quite literally, the willingness of people to be convexity insensitive while hedging. Hedgers may think that they are being risk adverse by buying leveraged inverse instruments, but they are actually taking on a new risk. They are attempting to lay off market risk, but are taking on negative convexity risk. And that decision is grossly inefficient, because the negative convexity risk turns out to be, on average (remember, on average!), a far larger risk than the market risk they were seeking to avoid.

As I often say, no strategy is even close to perfect. There are only strategies which are preferable to all other possible alternatives. We have created an advanced non-public version of the strategy for clients, which does not use shorting. I think the public version presented here has the ability to stimulate thinking on the part of investors by clearly illustrating that even seemingly simple strategies using powerful mathematical principles can dramatically outperform strategies presented in popular bestsellers, while using fewer instruments with less hassle to implement.

Investors are constantly bombarded with intuitive strategies. And intuitive strategies may be excellent marketing vehicles, but they are often far worse performers than non-intuitive strategies. Strategies which rely upon an understanding of pure mathematics have a higher probability of sustained outperformance, because most people are not wired to feel emotionally comfortable with mathematical strategies.

It is this emotional discomfort which not only hinders the popular adoptions of such strategies, but also creates the potential for sustained outperformance for those unique investors who do appreciate their logic.

The bottom line for investors is that technology is evolving quickly. Professional traders like myself have invested heavily in cutting-edge R&D. We have objectively proven that the results of this R&D far exceed the performance of everything else publicly available up to this point. Therefore, the public should stop being impressed going forward with any method which does not have the ability to outperform equity indices by huge margins.

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