The standard deviation associated with the return on an asset decreases with the square root of time. Therefore, the longer the analysis horizon is, the lower the standard deviation of the annualized returns over the horizon will be. Extending the time horizon decreases the risk of a stock investment in relation to a riskless asset. A minor forecasting mistake can have an important impact on the final portfolio value if the analysis horizon is long. For example, assume that investment has an expected annual return of 10% with a standard deviation of ± 20%. This means that the return on the investment can vary from -10% to 30% in any given year. However, if the investment is held for 10 years, the standard deviation drops to ± 6.32%; after 25 years, the standard deviation is ± 4.0%; and after 45 years, the standard deviation drops to ± 3.98%.
The Relationship between Investment Horizon and Risk

Where:
= standard deviation of average return over n years
= standard deviation of rate of return in 1 year
n = time in years
Another important measure used in portfolio analysis is correlation. Correlation describes how well two assets move relative to one another. The correlation coefficient describes the pattern of two asset's returns relative to one another. A correlation coefficient can range between -1.0 and + 1.0. Assets are said to be perfectly positively correlated if the correlation coefficient equals 1.0 and the assets are said to be perfectly negatively correlated, if the correlation coefficient is -1.0. A correlation coefficient of 0.0 indicates that the returns of two assets are uncorrelated. In portfolio management, the intent is to locate and combine assets with low or negative correlations. For diversification purposes, a perfectly negative correlation is most attractive, since this indicates that the securities vary in opposite directions and fluctuations will tend to cancel one other. Correlation of -1.0 (perfect negative correlation) allows the risk of the portfolio as measured by the standard deviation to equal zero.
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