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PostModern Portfolio Theory: SemiDeviation & SemiCorrelation 2 comments
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, PostMPT, 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.
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 “fattailed,” 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 (fattailed) pattern of returns – and more normallydistributed returns, such as stock returns.
Downside Risk, SemiDeviation, and SemiCorrelation
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 twothirds 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 semideviation) and “upside” risk, the downside risk for stocks will be about twothirds of the total standard deviation! On the other hand, the newer strategies that more actively manage risk will often have semideviations that are closer to onehalf of the standard deviation.
“Semideviation” 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 semideviation, what about correlation? Institutional investors and other large investors are always seeking diversification and additional asset classes. My research has shown that similar to semideviation (which makes a lot of sense theoretically and pragmatically, in the real world), a semicorrelation approach also makes sense.
Summary
It is important to study and measure true downside risk and the interrelationships amongst various asset classes. More specifically, determine which particular asset classes may help when certain assets are declining in value. Semicorrelation as well as semideviation 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 PostMPT. On top of a “riskmanagement 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
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