Volatility Management

On the Theory of Asset Allocation Part 2

In this post, I would like to show some research I have done on the front of utilizing portfolio theory to efficiently and optimally allocate capital to a pair of systems.

Traditional theory applied outright can be problematic. As I mentioned in the previous post, the assumptions that go in are not consistent in the long run, ie expected return, therefore the optimized portfolio performance will deviate significantly from backtest results. This is similar to developing a system on data that no longer reflect the current market state which will ultimately bankrupt you.

In my opinion, there are ideas within the traditional framework that are useful. Expected return of individual assets may not be reliable, but expected return of a well designed system should be, in a probabilistic sense.

For the past year, I started to view everything as a return streams. By this I mean rather than differentiating between assets and trading systems applied on assets, one should look at them equally. Although this may sound obvious, I will come back to this subject later and expand on it. But this way of thinking has helped me go against traditional methods of system design to built more robust systems that are model free and parameter insensitive.

In portfolio theory, the lower the correlation between instruments the better. In this experiments, I will be referring to two trading systems that are different in nature; Mean Reversion and Trend Following. Both of these trading systems will be applied to the same asset, SPY. System details:

Their daily return correlation is 0.04. The following is their equity curve.

Both of them are profitable and aren’t optimized as all. Test date is 1995-2012. Daily data are used from yahoo finance and no commissions or slippage was taken in to account. Next is their risk reward chart as popularized by traditional theory.

MR = Mean reversion, TF = Trend following, SPY = etf. From an asset allocation point of view, MR seems to be the most desirable of the three. Up next I show the efficient frontier of the two systems from 2000-2004 and then based on the minimum variance (MV) allocation in that period, I will forward test it. More concretely, I will compare the portfolio level equity curve from trading the two systems together.

The MV allocation is the left most point on the curve. It’s the allocation that minimizes portfolio variance. The following is the equity curves from 2005-2012 with different allocations.

Apologies for not plotting the legend! The red curve is the buy and hold of the SPY, the blue is a equal weight allocation between the two systems, and the orange curve is the MV allocation (~19% TF and ~81% MR). From a pure return perspective, trading the MV allocation produced the most return but from a risk reward standpoint, the equal weight allocation is better. In my optimization process, I found that the allocation that maximizes sharpe ratio would be allocation 100% to MR system. Now the numbers…

If I were to choose, I would go with the equal weight allocation as it has in my opinion the features that I will be able to sleep at night. I am not going to discuss the results in more depth as its well passed midnight, maybe another time I will come back and do something different.

Note: the portfolio level testing was simulated using tradingblox while the optimization and plotting were done in R. If you have any questions or comments, please leave a comment below! Email me if you want the TB system files.

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Volatility Parity

When I first started out in system research a year ago, I was told that in this business, if you can achieve return with lower volatility, you will definitely attract a lot of people’s attention. Since then, I’ve found myself to leaning towards strategies with lower volatility, usually achieved through proper volatility management.

In this post, I’d like to take a look at portfolio volatility by using some tools from portfolio theory. I’d like to show that through peeling into volatility one can better manage their portfolio.

There exists a fine line between academic finance and practitioners of finance. The opposing ideas are  whether the markets are efficient or not. I am not going to dive in to the discussion of this, but I stand to reason that there are no rules or equation to the markets. They are ever changing, therefore, I believe that one should treat every concept as tools.

A bit of equations…portfolio variance is defined by the following equation. I am only going to use a two asset class example to avoid bringing in the use of covariance matrix.

        

    

 

The variance contribution of each asset is thus…

In my opinion, the above equations capture a lot of information that can be used to manage volatility. At any given time multi market strategies will have more than one position. If you are able to position size each position so that each one contributes equally to overall portfolio volatility, you will have much smoother balanced and diversified portfolio.

In the following graphs, I calculated according to the above equations how Bonds and Stock contribute to aggregate portfolio variance. For stocks, I used SPY and for bonds, I used IEF, both are exchange traded funds. This is a rolling 252 day graph with traditional 60/40 allocation.

 From the above graph one can infer that the volatility contribution is not equal and at times, you will see that stocks will contribution more than 100% while bonds contributed negatively.

The above graph also gives a pretty good market timing signal. When bonds contributed negatively, it seems that the market is in turmoil and vice versa for stocks when it contributed more than 100%.

I hope through this, the reader will be able to understand volatility more and look and just how it affects your portfolio.