## Amazing correlations

When I did a Masters in Applied Finance the very first lecture was a recap in basic mathematics and by the afternoon we were into standard deviation, variance, covariance and correlations. It is pretty simple stuff although I imagine a lot of investors go through the whole of their investment life not knowing what any of them mean. It would only take about an hour to explain.

I recently wrote an article about volatility in which I explained standard deviation in layman’s terms. **Here it is again. This is a share price snaking up and down with the** ‘average’ shown by the straight regression line. If you measure the average deviation of the snaking share price from this regression line (from the average), add them all up and average them you get a measure of volatility. With this stock you get deviations averaging “x”.

x = the standard deviation of the stock from its average. Hence the expression ‘standard deviation’.

You can read the full article here:

Correlation on the other hand is well understood. The Mathematical representation of a correlation coefficient (**ρX,Y** ) between two random variables **X** and **Y** with expected values **μX** and **μY** and standard deviations **σX **and **σY** where **E** is the expected value operator, **cov** means covariance, and **corr** is a the correlation coefficient is defined as:

This may look complicated but its actually quite easy on Excel because Excel has a **CORREL **function that finds the correlation coefficient between two variables. - A correlation coefficient of +1 indicates a perfect positive correlation. A correlation coefficient of minus 1 indicates a perfect inverse correlation.

A positive correlation means that as variable X increases, variable Y increases. As variable X decreases, variable Y decreases. An inverse (negative) correlation means that as variable X increases, variable Y decreases. As variable X increases, variable Y decreases.

To make it more palatable, let’s say that is two variables (X and Y) are perfectly positively correlated then let’s say they are 100% correlated. And if they are perfectly inverse or negatively correlated they are minus 100% correlated.

**THE VALUE OF LOOKING AT CORRELATIONS**

All stocks have drivers. Take FMG. In 2016 FMG sold $6.923bn worth of iron ore out of total sales of $7.083bn. In other words 97.7% of their sales were in iron ore. In which case the iron ore price is critical to sales and profit.

Of course there are other factors before you get to FMG’s EBITDA (which is a better factor with which to value the stock) like forex gains (or losses), royalties, shipping costs, production costs etc. but the point being is that FMG earnings are almost 100% dependent on the iron ore price which moves daily.

So let’s look at the correlation on a chart:

*It is important when looking at these charts that you don’t worry about the exact fit of the lines. It is not about ‘magnitude’ of the move it is about the correlation. I could fiddle with the scales on each chart to overlap the lines more closely so the size of the moves look exactly the same, but that is not the point. The point is that they trend in the same direction and peak and trough at the same time*.

Clearly FMG is highly correlated to the iron ore price. If you do the mathematical correlation it turns out that **FMG has an 86% correlation with the iron ore price**. If 100% means they match each other perfectly then this is a very high number and what it tells you is that whilst you could do a lot of research on FMG, visit its operations, calculate its resources, estimate its production, make assumptions about costs, the truth is that day to day **the fundamental analysis is rendered almost completely redundant**, because the iron ore price is the main driver and it moves the FMG share price daily.

So what we are doing here is realising that **you don’t really need to know anything about FMG**. The share price is a proxy for the iron ore price and because FMG will move 10% when the iron ore price moves 5%, it is a highly leveraged proxy or trade on the iron ore price. A great trading stock if you can get the iron ore price trend right.

Sure the company may do things, like significantly cut their costs of production which they have done, that is as good as an iron ore price rise, and yes, they may have some ‘event’ that upsets production and damages the share price, or be bid for, or have management changes, all things that could impact the price. But day to day, because of the correlation, this share price is simple - “Get the iron ore price right and you’ll get the FMG share price right. Simples.

Now lets look at some others. **BHP** for instance. They make more money when the iron ore price, the coal price, the copper price and the oil price go up. These are the main share price drivers day in day out. Iron ore is the main one. BHP and iron ore – 71% correlation. Very close in mathematical terms considering zero means no correlation.

Now lets do a few others:

- BSL and the iron ore price = 81% correlation (huge – don’t bother analyzing them either)
- RIO and the iron ore price = 80% correlation.
- AGO and the iron ore price = 53% correlation.
- BHP and the copper price = 82% correlation.
- OZL and the copper price = 72% correlation.
- SFR and the copper price = 69% correlation.
- CDU and the copper price = minus 48% correlation.
- NCM and the copper price (NCM produce a lot of copper) = 29% correlation.
- WSA and the nickel price = 82% correlation.
- IGO and the nickel price = 79% correlation.
- NCM and the Gold price = 88% correlation.
- RRL and the Gold price = 84% correlation.
- NST and the Gold price = 87% correlation.
- EVN and the Gold price = 87% correlation.
- WHC and the coal price = 95% correlation (Wow!)
- WPL and the oil price = 56% correlation.
- STO and the oil price = 27% correlation (only).
- ORG and the oil price = 63% correlation.
- BHP and the oil price = 78% correlation.
- The oil price and the iron ore price = 72% correlation.
- The Gold price and the copper price = 4% correlation.
- The ASX 200 with the financials sector = 92% correlation.
*The ASX 200 with the S&P 500 = 92% correlation*.

**Correlations with the Australian dollar** - here is a list of the stocks most commonly accepted as benefiting from a falling Australian dollar. The slight surprise here is that a lot of them have a really very positive correlation with the Australian dollar which goes to say that the currency is only a small factor with many of these stocks despite them being highlighted as beneficiaries or victims of the currency. On this basis you can pretty much stop worrying about the currency when choosing whether to buy or sell these stocks. The most inversely correlated are the companies that have their primary share prices listed overseas so the Australian share prices are playing follow the leader and directly reflect the overseas share price converted by the currency. The most obvious ones are NWS and JHG both of which have their primary listings in the US and the UK.

Hope that was interesting, and I hope it saves you a heck of a lot of research. All you need really do is make a guess about a commodity price and trade the stock that has the closest correlation. Plenty of Australian stocks offer that.