Module 6

What is a portfolio?


As a concept, diversification is easy to understand – you simply need to own a range of investments and not put all of your eggs into one basket.

The idea of diversification is well known, however, diversifying well is often not so obvious.

True diversification is about picking investments that do not behave in the same way to the same situation. This essentially means that you don’t want to have investments that are strongly correlated.

If investments are strongly positively correlated, they will move in the same direction all of the time. Therefore, you will always either make significant profits or losses, depending on the situation.

Likewise, if investments are strongly negatively correlated, they will move in the opposite direction. The downside of this is that you will never make a profit or a loss – when one stock increases in value, the other stock will decrease in value by the same amount.

So, making sure that investments in your portfolio are not too strongly correlated is important.

Calculating diversification

In order to assess the correlation of your investments, you need to use the following formula formula.

r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}

Where r is the correlation co-efficient, are the individual percentage changes of stock prices over a 5 year period and x̄, ȳ are the average percentage return of each stock.

The top half of the formula is called covariance, while the bottom half is simply the standard deviation of each stock. You should only complete this formula with two stocks at a time, over a period of 5 years. You should include monthly stock market returns (as a percentage).

For example, imagine that Stock A delivers returns of 2%, 4% and 6%, while Stock B delivers returns 8%, 2% and -3%. Of course, you should do this for the last 5 years, while we will only do it for 3 months for demonstration purposes.

First, we need to calculate the average return of each stock, which would be 4% for Stock A (2% + 4% + 6%/3 = 4%) and 2.34% for Stock B (8% + 2% – 3%/3 = 2.34%).

Next, we need to calculate the value of each datapoint when the average is subtracted.

So for Stock A, it would be -2% (2% – 4%), 0 (4% – 4%) and 2% (6% – 4%), while for Stock B, it would be 5.66% (8% – 2.34%), -0.34% (2% – 2.34%) and -5.34% (- 3% – 2.34%). 

Then, we can use these numbers in the formula to calculate the correlation coefficient.

The top half of the formula is basically all of the numbers that we previously calculated, multiplied together in their pairs, with each outcome being added together: (-2% x 5.66%) + (0 x -0.34%) + (2% x -5.34%) = -0.22%

The bottom half of the formula is the standard deviation of Stock A and Stock B added together. So, it would be 7.51%.

Therefore, the correlation coefficient would be -0.22% ÷ 7.51% = -0.0293.

Interpreting the coefficient

The correlation coefficient will tell you give you an idea of the relationship between 2 different investments. The coefficient will range between +1 and -1.

If two investments move in exactly the same way, then they will have a correlation coefficient of +1. Meanwhile, if two investments move in exactly the opposite direction, then they will have a correlation coefficient of -1.

When it comes to building a portfolio, it is better to avoid having too many investments that are strongly correlated as it will result in constantly losses or frequent gains.

If two investments have a correlation coefficient of 0, it means that there is no relationship between them at all.

The aim when building an investment portfolio is to achieve a slightly positive correlation between the investments held (just above 0).

This is the case because investments will not behave in similar ways and will react differently to different situations, meaning that if one stock crashes the others will not. This is important to protect the portfolio from downside risk.

The slight positive correlation ensures that the stocks behave in a similar enough way to increase in value over time. So, when one stocks increases in value dramatically, the other stocks should also increase in value, to some extent.

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