What Does Platykurtic Mean?
Let me explain what platykurtic means in statistics. It's a term for a distribution where the excess kurtosis is negative. This means the distribution has thinner tails than a normal distribution, so you'll see fewer extreme positive or negative events. The opposite is a leptokurtic distribution, which has positive excess kurtosis.
When you're deciding where to invest, consider the statistical distributions tied to different investments. If you're more risk-averse, you might lean toward assets and markets with platykurtic distributions, as they're less likely to deliver those extreme results.
Key Takeaways
Platykurtic distributions come with negative excess kurtosis. They offer a lower chance of extreme events than a normal distribution. If you want to cut down on the risk of big negative events, focus on investments with returns that follow a platykurtic distribution.
Understanding Platykurtic Distributions
There are three main types of statistical distributions: leptokurtic, mesokurtic, and platykurtic. They vary based on their excess kurtosis, which affects the odds of extreme positive or negative events. The normal distribution is mesokurtic with a kurtosis of three. So, distributions with kurtosis over three have positive excess kurtosis, and those under three have negative excess kurtosis.
Mesokurtic distributions stick to a kurtosis of three, but leptokurtic ones have positive excess kurtosis and platykurtic have negative. This means leptokurtic distributions carry a higher probability of extreme events, while platykurtic distributions do the opposite.
You can see this in charts of these distributions, all sharing the same standard deviation. The differences in tails might not jump out in a basic plot, but a quantile-quantile plot, or Q-Q plot, makes it clearer by comparing their quantiles.
Special Considerations
Most investors think equity market returns look more like leptokurtic distributions than platykurtic ones. That means while most returns hover around the market average, you'll occasionally get wild deviations from the mean. These unpredictable events, often called black swans, are less common in platykurtic markets.
If you're a cautious investor, you might steer clear of leptokurtic markets and go for investments with platykurtic returns. But some investors chase leptokurtic returns on purpose, figuring the big positive extremes will outweigh the negatives.
Real-World Example of a Platykurtic Distribution
Morningstar put out a research paper with data on excess kurtosis for various assets from February 1994 to June 2011. It covered everything from U.S. and international equities to real estate, commodities, cash, and bonds.
Excess kurtosis levels ranged widely. Cash and international bonds were on the low end at -1.43 and 0.58. On the high end, U.S. high-yield bonds and hedge-fund arbitrage strategies hit 9.33 and 22.59.
In the middle, you had international real estate at 2.61, equities from emerging economies at 1.98, and commodities at 2.29.
Looking at this data, you can figure out which assets fit your tolerance for potential black swan events. If you're risk-averse and want to minimize extreme events, go for low-kurtosis investments; if you're okay with extremes, aim for high-kurtosis ones.
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