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Understanding Standard Deviation
By Julia O’Neal; MA, CPA
The risk of a single asset is measured by its standard deviation of return and by its co-movement with the expected return of the assets in the market in which it is traded.
Defining Standard Deviation
The standard deviation is a measure of the variation around the average or mean. It is the statistical measure of the degree to which an individual value in a probability distribution tends to vary from the arithmetic mean of the distribution.
The standard deviation of a portfolio is affected by the correlation of the returns of the various asset classes in the portfolio.
A Measure of Volatility
For a series of asset returns, the standard deviation is a measure of the volatility, or risk of the asset.
As applied to modern portfolio theory, SD is where the past performance of securities is used to determine the range of possible future performances, as a probability is attached to each performance with the following constraints:
- The standard deviation of performance can be calculated for a security, or for a portfolio as a whole – and the greater the degree of dispersion – the greater the risk.
- For a probability distribution with a small standard deviation, there is little chance that a return will be significantly different from expectations.
- If the standard deviation of a probability distribution is large, there is significant probability that the return will be much different from what is expected.
Assessment
The risk of a portfolio is complicated because the assets in the portfolio are not likely to move together perfectly. If they do not move together perfectly, the risk of the combined set of assets cannot be estimated by the simple average of their individual risks:
- The extent to which pairs of assets move together is measured by their covariance. Alternatively, the co-movement of assets is picked up by the correlation of returns to two assets.
- Perfect positive correlation refers to two assets whose expected rates of return move together exactly.
- Perfect negative correlation means that if the return of one asset is expected to go down, the other is expected to go up.
- Zero correlation means that no association of returns exists between the assets. If the return of one increases; there is no way to predict what will happen to the other; it may increase just as much as decline or remain unchanged.
- Combining assets with perfect positive correlation results in no risk reduction. However, when assets are combined with perfect negative correlation, the potential to totally eliminate risk exists.
Finally – the less correlation between assets – the greater the gain in efficiency.
Conclusion
Stocks move together but not perfectly, and rarely are negative correlations between asset classes found. In reality, perfect correlation, either positive or negative, is not likely to exist.
Nevertheless, historical correlations of returns are measurable and can be helpful to the physician-investor in portfolio construction if appreciated and used correctly; do you?
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