Covariance and Correlation
The below table compares the correlations of stock returns to different asset classes:
| Correlation Coefficient | Corporate Bonds | Commodities | Real Estate |
|------------|----------|-------|--------|
| Stocks | -0.3 | 0 | 0.5 |
Based on the correlation coefficient, which asset class would provide the most diversification if added to a portfolio of stocks?
Covariance and correlation are useful statistics for evaluating if assets historically move together or inversely. __Covariance__ measures how two variables, such as stock and bond returns, move in the same or opposite direction. A positive covariance indicates that two assets move in the same direction, but does not quantify the magnitude of the movement.
The below table compares the covariance of stock returns to different asset classes.
| Covariance | Corporate Bonds | Commodities | Real Estate |
|------------|-----------------|-------------|-------------|
| Stocks | -0.598 | 0.251 | 0.688 |
Based on the covariance, which asset class do you think had the best chance for a positive return if stocks returned a -2% last year?
Incorrect.
Commodities have positive covariance, which indicates variables move in the same direction.
What do you think is a limitation of covariance when comparing different asset classes?
Incorrect.
Real estate has a positive covariance, which indicates variables move in the same direction.
Correct.
The limitation to covariance is that it does not measure the degree to which variables move together or apart.
Incorrect.
It is true that covariance does not make investment decisions, but that is not what it measures.
Covariance measures how two variables, such as stock and bond returns, move in the same or opposite direction. The limitation to covariance is it does not measure the degree to which variables move together or apart.
Incorrect.
A correlation coefficient of .5 does offer diversification since the asset classes do not move perfectly together, but another option provides more diversification.
In summary:
[[summary]]
Incorrect.
A correlation coefficient of zero indicates the two asset classes are uncorrelated and have no meaningful relationship, in terms of movement, to each other.
To measure the degree to movement of two variables you would need to evaluate the correlation coefficient. A __correlation coefficient__ standardizes the degree to movement of variables with a range of value from minus one to one. A correlation coefficient of one indicates two assets would perfectly move together and a minus one shows perfectly inverse movement.
Correct.
Corporate bonds and stocks have a negative covariance. A negative covariance indicates the two asset classes returns move in opposite directions.
Correct.
Corporate bonds would provide the most diversification due to the negative correlation coefficient. If the correlation coefficient is plus one, the two asset classes would move perfectly together. A coefficient of minus one indicates the two asset classes always move in different directions. Risk in a portfolio can be reduced by combining assets that are not perfectly correlated.
Real estate
Commodities
Corporate bonds
Commodities
Real estate
Corporate bonds
Covariance does not measure the strength of movement between two asset classes
Covariance does not indicate which asset an investor should select
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