- Standard Deviation and Probability
Standard Deviation and Probability make us better risk managers because they cause us to consider lower probability outcomes in our financial decision making process.
What is Standard Deviation?
Standard deviation is a standard measure of investment risk. It is a historical statistic measuring volatility and the dispersion of a set of data from the mean. In other words, the concept of standard deviation is to understand the probability of outcomes that are not the mean.
An investor does not need to know the exact definition or formula to understand the concept of standard deviation. The purpose of this article is to understand the concept of standard deviation and probability and how they relate to risk and financial decision making.
We understand we must accept risk to achieve investment returns above the risk-free rate of return. But accepting risk blindly is not sound investing. The mean is almost never the real return. By definition one-half of the outcomes will be below the mean and one-half of the outcomes will be above the mean. Standard deviation is a measure of the volatility, or how far away from the mean the outcomes will be, based on probability. I want to focus on the negative outcomes that are far away from the mean.
Investment Risk Example
A small-cap stock will typically have a high standard deviation compared to a stable blue chip dividend stock. The small-cap stock may have a higher expected rate of return but that is to compensate the owner for a greater amount of risk. In other words, the probability of the return on the small-cap stock being farther away from the mean or expected rate of return is greater than the stable blue chip dividend stock.
The importance of the set of data determines how critical the outer or smaller probabilities are to the investor. If we consider a 1% position in a high risk stock an investor may choose to accept a large dispersion of possible outcomes. The investor recognizes that regardless of the expected rate of return the risky stock may have returns from negative 100% to positive 100% or even greater. Because it is only 1% of the portfolio the investor may be willing to accept the large amount of risk.
Portfolio Investment Loss Example
In a recent post, “Probable Maximum Investment Loss and Asset Allocation” we looked at the importance of an investor determining maximum probable loss as the first step toward developing a risk management plan and a target asset allocation.
This process is an exercise in considering negative outcomes that are far from the mean and their effect on investment returns. The article demonstrates the importance of not losing a large percentage of a portfolio because of the difficulty of getting back to breakeven. Because of the devastation a large loss inflicts on a portfolio, the analysis of the probability of large negative returns is critical to long term investment planning.
Retirement Withdrawal Rate Example
Let’s consider a retiree making a decision on how much they want to withdraw from their retirement plan to live on in retirement. Would we not want to be more conservative about such a decision than we would about buying a 1% stock position?
As an example, if we determined that a 5% per year withdrawal rate would give us an 80% chance of not running out of money in our lifetime; would that be a risk we would be willing to take? Most people would probably desire to have the odds higher than that. Therefore they might have to choose a lower withdrawal rate.
Financial Decision Making
These are examples of the importance of understanding the concept of standard deviation and probability. The importance of the decision would have a large influence on how much risk we are willing to take. A crucial decision such as a retirement withdrawal rate would require greater consideration of lower probability negative outcomes than a decision on a 1% stock position.
The concepts of standard deviation and probability are risk management tools that allow us to consider lower probability outcomes in our financial decision making process.
| AAAMP Blog by Ken Faulkenberry | |
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Ken Faulkenberry earned an MBA from the University of Southern California (USC) Marshall School of Business with an emphasis in investments. Ken has 25 years of investment experience and is dedicated to helping people with self-directed investment management through the Arbor Investment Planner. His asset allocation strategies have an outstanding performance record. |
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Really good topic. I was explaining counting cards to someone the other day and how even though you can switch a 1.5% house edge to a 1% player edge, the standard deviation in blackjack is so great that it doesn’t make sense for most people unless you have hundreds of hours and an enormous bankroll. They didn’t get the concept. In essence, even though you have a statistical advantage, there’s no guarantee you’ll walk out ahead; you may end up down 50% in fact. It’s all about standard deviation!
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