Diversification and risk
Here is a question for you. You are creating a portfolio containing two assets, choosing from three potential stocks: a company making umbrellas, a raincoat company, and an ice-cream company. Which two securities would you choose for your portfolio?
You have seen how we measure the risk of a security by the standard deviation of returns, if the security is held in isolation.
When we look at portfolios, the appropriate measure of risk of a security must express how it contributes to the risk of the overall portfolio. This is given by the covariance between the returns on the security and the returns on the portfolio. Covariance measures how the returns on two assets covary, or vary together.
Positive covariance between two assets means, on average, when the returns on one asset are greater than their expected value, the returns on the second asset are also greater than their expected value. When one asset overperforms relative to its mean, the second asset also usually overperforms. Conversely, when the returns on one asset underperform, the returns on the second asset also underperform. The returns on the two assets tend to move in the same direction.
Negative covariance between two assets means, on average, when one asset overperforms the second asset underperforms, and vice versa. The returns on the two assets tend to move in opposite directions.
How would you build the ideal portfolio?
Let’s get back to umbrellas and raincoats.
First consider profits of the umbrella firm and the raincoat firm. If the weather is wet, sales of both umbrellas and raincoats will increase. When the weather is sunny, the demand for umbrellas and for raincoats will decrease. The profits of the two firms tend to be positively associated: they have a positive covariance.
Did someone mention ice-cream?
Now consider profits of the umbrella firm and the ice-cream firm. When the weather is wet, sales of umbrellas will increase, but sales of ice-cream will decrease. When the weather is sunny, the demand for umbrellas will fall, but sales of ice-cream will increase. The profits of the two firms tend to be negatively associated: they have a negative covariance.
To establish how a security contributes to the risk of a portfolio, we look at the covariance between the returns on the asset and the average return on the portfolio. If the covariance is negative, the asset tends to offset the returns on the other assets in the portfolio, and reduces overall portfolio risk. However, if the covariance is positive, the asset tends to reinforce the effect of fluctuations in the returns on the other assets, and increases the risk of the portfolio.
Covariance can take any negative or positive value, and in principle could range from minus infinity to plus infinity. The correlation coefficient is easier to interpret, and takes values between -1 and +1. When the covariance is positive, the correlation coefficient is positive; when the covariance is negative, the correlation coefficient is negative. A correlation coefficient close to 1 or +1 indicates returns on the two assets are very strongly related. A correlation coefficient close to 0 indicates returns on the two assets are weakly related.
We are considering a portfolio of two assets, but in a portfolio which includes many assets the standard deviations of the returns on individual assets are largely irrelevant: what really matters is the average covariance between the assets.
This is important. If we want to form a relatively safe portfolio, we should select assets with a low or negative covariance. Such a portfolio will be well diversified, and will have lower risk.
Did you double up on shares in the ice-cream company? You clearly have ‘ice-cream bias’.