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Post-Modern Portfolio Theory: Semi-Deviation & Semi-Correlation

The popular mean-variance approaches are well-documented methods of improving a portfolio’s risk-reward characteristics.  The fact that Markowitz’s contributions to Modern Portfolio Theory have stood the test of time – more than fifty years later – shows the power of these methods.  Over the years, additional models have been developed, that, for example, help investors establish reasonable assumptions and optimizer inputs such as expected returns, volatility (standard deviation), and correlations amongst asset classes.

In general, I use best practices from institutional investing and hedge fund strategies -- and apply risk management concepts -- to maximize the available diversification potential.  Theoretical approaches are applied in a sensible manner to ensure practical and robust results in our pragmatic world.  The result is a more complete model that combines Monte Carlo analyses, Post-MPT, and more meaningful risk measures.  Below, are a few thoughts on these meaningful statistical measures and approaches.

Modern Portfolio Theory, Normal Distributions, and Downside Risk

If you scan the two charts below, you will note that stocks have more data points in the -20% range.  Stocks have more downside risk than the alternative asset, which has a more positively skewed return distribution.

Click to enlarge

Over the years, it has been shown that asset class returns are not normally distributed as assumed by classical MPT and Capital Asset Pricing Models.  Indeed, while the traditional asset classes such as stocks and bonds (or buying and holding of other hard/real assets) might approximate a normal distribution, the same cannot be said of newer asset classes, certain types of hedge funds – and especially many quantitative investment strategies. 

More specifically, the pattern of returns for some of these newer strategies are positively skewed and are “fat-tailed,” meaning that portfolio managers control risk and minimize losses, while letting gains accumulate.  The most common measure of risk (standard deviation) does not differentiate between this (fat-tailed) pattern of returns – and more normally-distributed returns, such as stock returns. 

Downside Risk, Semi-Deviation, and Semi-Correlation

Market watchers will tell you that stocks tend to fall harder and faster, than they rise.  Indeed, historical data shows this to be true, with about two-thirds of the risk (or standard deviation) for many traditional asset classes to be on the downside.  Note that standard deviation is a function of the difference of each data point (in this case, returns) from its mean.  However, if you break the standard deviation down into two components: “downside” risk (often called semi-deviation) and “upside” risk, the downside risk for stocks will be about two-thirds of the total standard deviation!  On the other hand, the newer strategies that more actively manage risk will often have semi-deviations that are closer to one-half of the standard deviation. 

“Semi-deviation” is a better overall risk measure than standard deviation.  The implications for portfolio optimization can be significant, and the actual measure is logical.  And speaking of downside risk and semi-deviation, what about correlation?  Institutional investors and other large investors are always seeking diversification and additional asset classes.  My research has shown that similar to semi-deviation (which makes a lot of sense theoretically and pragmatically, in the real world), a semi-correlation approach also makes sense. 


It is important to study and measure true downside risk and the inter-relationships amongst various asset classes.  More specifically, determine which particular asset classes may help when certain assets are declining in value.  Semi-correlation as well as semi-deviation have proven to provide a more accurate picture – when applying portfolio diversification models. 

In addition to improved risk measures and correlation studies, a variety of tools (such as Monte Carlo analysis) form a strong foundation for enhanced portfolio optimization and Post-MPT.  On top of a “risk-management portfolio optimization engine,” robust alternative investment strategies add meaningful diversification and greatly improve expected risk/return characteristics to a portfolio.   

Carlton Chin, CFA, is a specialist in strategic asset allocation, quantitative investment strategies, and alternative assets.  Carlton has worked with institutional investors on asset allocation and is a fund manager.  He holds both undergraduate and graduate degrees from MIT. 

Disclosure: No positions