Index Funds: The 12-Step Recovery Program for Active Investors by Mark T. Hebner

Author:Mark T. Hebner
Language: eng
Format: epub
Tags: Prudent Investing
ISBN: 9780976802358
Publisher: Bookmasters Group
Published: 2014-04-16T04:00:00+00:00

Blaise Pascal

Modern finance began with the realization that risk needed to be measured and managed. In 1654, French mathematicians Blaise Pascal and Pierre de Fermat tried to predict the future outcome of a game of chance. Their questions led to Pascal’s Theory of Probability, which quantifies the numerical likelihood of future events. Pascal’s Triangle was the foundation for learning how to manage the uncertainty of future outcomes, such as investment returns.

Every investment carries an expected return. The risk of an investment is quantified by the degree to which the returns of the investment deviate from the average return during specific periods of time. Higher risk investments carry a wider range of short-term outcomes but also carry higher expected returns, compensating investors for withstanding short-term volatility. In contrast, investments that have had a narrow range of outcomes over long periods of time are expected to provide more consistent returns with the trade-off of lower returns. For example, an all-bond index portfolio has provided a small but consistent return, while an all-equity index portfolio has provided a larger but more erratic return. Higher expected returns are the reward for an investor’s willingness to accept this volatility. In other words, risk is the source of returns and, therefore, should be embraced in appropriate doses.

STANDARD DEVIATION OF RETURNS

An effective and common method to measure the deviation of investment returns from the average is the standard deviation of returns. Standard deviation provides a statistical measure of historical volatility and sets forth a distribution of the ranges of probable outcomes. In investing, measuring standard deviation of returns shows the extent to which returns (daily, monthly or annual) are distributed around the average return, estimating a range of probable outcomes and establishing a likely framework of risk and return trade-offs.

The normal distribution in the form of a bell-shaped curve shown in Figure 8-1 illustrates the concept of standard deviation. The curve represents a set of outcomes. In this case, let’s say the outcomes are the monthly returns of an investment. The yellow area covered in one standard deviation away from the average in both directions accounts for approximately 68% of the outcomes in a period. The area within two standard deviations from the average, the yellow and green shaded areas, accounts for 95.6% of outcomes, and the area up to three standard deviations away from the mean, illustrated by the yellow, green and orange shaded areas, accounts for 99.7% of all outcomes. The higher an investment’s standard deviation, the greater the chance that future returns will lie farther away from the average return.

Figure 8-1

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