Correlation, Alpha & Beta

Measures of performance relative to a specified benchmark.


Correlation, alpha and beta are terms that are used frequently in investment analysis but are often misunderstood. All three terms are interrelated and measure an investment’s performance relative to a specified benchmark.

Risk return Table

Correlation measures the extent of linear association between the investment performance and the benchmark performance. A high correlation (positive or negative) means that some of the investment’s performance can be explained by the performance of the benchmark. Positive correlation means that the investment is generally up when the market is up and down when the market is down. It measures only direction of movement over time and not whether the returns are similar. Negative correlation means the investment performance is generally opposite the performance of the benchmark.

Beta describes the sensitivity of the investment to movements in its specified benchmark. Alpha is a measurement of the value added by the investment manager. Each of these statistics is determined using regression analysis in which one determines the best-fitting line (the regression line) to explain the investment’s performance relative to the benchmark. The formula for the regression line is y = a + Bx where y = the investment’s performance, x = the benchmark, a = alpha and B = beta.

Example Let us assume that we have an investment with the following characteristics compared to a market index:

Alpha = 1%
Beta = 2
Correlation = .95

In this case, if the market were up 10%, you would expect the investment to be up 21%:

(1% + 2 x 10%) = 21%.

If the market were down 10%, the expected return for the investment would -19%:

(1% + 2 x -10%) = -19%

Because the correlation is 0.95 in this example we have a fairly high degree of confidence that there is significant relationship between the underlying market benchmark and the investment in question. If the correlation were 0.2 instead of 0.95, we would likely not be able to accurately predict the performance of the investment based upon the performance of the benchmark.

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