Skewness: The fallacy of the expected return
<p>In this post we will take a closer look at the expected return that is often stated for investments like stocks and other financial assets, or for certain outcomes in gambling. The point we want to convey is that the expected return is only valid for one period or a single “iteration” (say, one year, or one round of a game such as Blackjack), but that the expected return can be highly misleading for more long-term investments that involve continuous re-investing, i.e. compound interest. We will see that compounding introduces substantial positive skewness in the long-term return distribution. While this skewness certainly represents a beautiful property for building wealth in the long-term, it also renders the expected long-term return misleading as there is a high probability that one will not achieve the long-term expected return! We will learn that to correct for skewness, we need to use the geometric mean instead of the arithmetic mean that is used to compute the expected return — which will lead us to the Compound Annual Growth Rate (CAGR).</p>
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