Imagine you are creating a portfolio. For simplicity, we are considering that you are only considering two asset classes in your portfolio. You have three options to choose from - A, B, C and you want to create a portfolio with two of them in equal proportions.
Note: This is a very simplified example. In real life, the proportion in which you allocate to two asset classes also needs to be decided.
Now, you have the three options – AB, BC and CA. Which one should you choose?
We can start with the aggregate returns, but calculating the weighted averages.
Consider, the average annual return of A is 10%, B is 15% and C is 7%.
So, the aggregate return of AB = 0.5 x 10% + 0.5 x 15% = 12.5%
the aggregate return of BC = 0.5 x 15% + 0.5 x 7% = 11%
the aggregate return of CA = 0.5 x 7% + 0.5 x 10% = 8.5%
As the aggregate return of AB is the highest, we go with AB, right? Wait, but what about Risk?
The above calculations do not take into account the volatility of A, B, C and more importantly the aggregate volatility. Keep in mind that the whole purpose of creating a portfolio is managing risk through diversification. We could have invested in asset class B if it is only about getting the maximum return.
Now, consider the annual volatility ( standard deviation of return ) for A is 15%, B is 35% and C is 10%. Now, how would we calculate the aggregate volatility?
We cannot just calculate the weighted average as we did in case of the return. Apart from the proportions and the volatility, we have to also consider the correlation between the returns.
WHAT IS CORRELATION COEFFICIENT?
Correlation Coefficient is the measure of the relationship between two variables. The coefficient varies between '-1' and '1'. The correlation coefficient of ‘0’ means there is no relationship between the variables. A positive correlation coefficient means that an increase in one variable is statistically tied with an increase in the other one. A negative correlation coefficient means that an increase in one variable is statistically tied with decrease with the other.
EFFECT OF CORRELATION COEFFICIENT
In case of returns from asset classes, a negative correlation is preferred because this means when an asset class underperforms, the other asset class overperforms and makes up for the underperformance. So, the volatility of the overall portfolio is lower than the volatility of each of the asset classes.
Let us see that with some numbers
Let us assume the correlation coefficients between A and B, r(ab) = 0.50, the correlation coefficient between B and C, r(bc) = -0.50 and correlation coefficient between C and A, r(ca) = 0.12.
Let us calculate the expected return volatility of the portfolio which the assumed returns using the following formula
(((% of first asset class) X (volatility of the first asset class) )^2 )
(((% of second asset class) X (volatility of the second asset class) )^2 )
2 x (% of first asset class) X (% of second asset class) X (volatility of the first asset class) X (volatility of the second asset class) X (return correlation between the two asset classes)
Also, let us calculate the risk-adjusted expected return of the portfolio as Sharpe Ratio.
Note. The assumption for Risk-Free Rate = 6.9%
Note: The higher the Sharpe Ratio the better.
We can see that the Sharpe Ratio for BC portfolio is the highest even though BC return is lower than AB portfolio.
Now, let us tweak the correlation coefficients a little bit.
r(ab) = 0.8
r(bc) = 0.1
r(ca) = -0.5
Now, we see that portfolio CA, even with the lowest expected return gives us the higher Risk-Adjusted Return.
While creating a portfolio based on past return, the investors should always keep in mind that past return does not guarantee future returns. This is why a risk-adjusted return is a much more useful measure for portfolio creation than expected return.
Now, we can see that it is not only the returns from the asset classes but the correlation between the returns have a profound effect on the risk-adjusted returns.
So, how exactly correlation affects the portfolio return
1. The positive correlation between asset classes increases the portfolio volatility reducing the risk-adjusted return.
2. A negative correlation between asset classes decreases the portfolio volatility increasing the risk-adjusted return.
So, while creating of a portfolio is not only about the returns but the correlation between the returns plays a major role.