There are few topics that stir the emotions of the typical well-to-do South African more than the decline in the value of the rand.
This is understandable, as many of us see ourselves as global citizens: we all like overseas holidays and we use iPhones and we run in Nike trainers and we drive BMWs… the list goes on. And all those things are ultimately priced in other currencies (at least in part).
Real financial freedom means that one has enough money to settle anywhere in the world if you chose to. But if the rand halves in value, it clearly becomes a bit more difficult to follow your kids to Sydney or San Diego, no?
Which brings me to the point of this article: what does it actually mean that the rand has halved in value?
Unfortunately, the basic mathematics of such a seemingly simple statistic are poorly understood.
To illustrate, consider the rand/pound exchange rate from three years ago, at approximately R13 to the pound. Today, the same exchange rate is near enough to R19.50 to the pound (perhaps slightly worse if you look at tourist rates; it also fluctuates on a daily basis so it may be a little different when you read this).
The reason I chose these dates (and hence, levels) is that this is exactly the kind of example that most people would focus on to say that the rand has halved in value over the period. A quick calculation seems to prove the point: the change in exchange rate in this instance is 6.50 (i.e. 19.50 minus 13), and the decline in value is therefore 50% (i.e. 6.50 divided by the starting level of 13). Right?
It is easy to illustrate why this algebra is spurious: imagine for a moment the rand went from the same starting level of 13 to 26. Doing the calculation in exactly the same way results in a decline in the value of the rand of… 100%? In other words, the rand has no value left? Can one not buy anything, anywhere in the world, even if you have thousands of rands to convert?
The correct way is to divide the difference in exchange rate (the same 6.50 over the past three years, as calculated earlier) and divide it by the ending level (i.e. 6.50/19.50)… translating into a decline of 33%.
Seeing the value of your global balance sheet drop by 33% over three years is hardly good news, but it is still a less dramatic number than the 50% that a lot of people may tend to focus on.
Go test the logic: convert R1 000 into pounds at both the starting rate (13 in July 2012) as well as the ending rate (around 19.50 currently), and work out how many cappuccinos you can buy in London at £2.50 each (assume constant prices) at both points in time.
I won’t bore you with the detailed calculations, but if you are that way inclined, you can work it out for yourself. You will see that the answer is as follows: for R1 000 (converted into pounds at a 19.50 exchange rate) you would have been able to buy a total of 30 London cappuccinos in 2012 (and have £1.92 left for a tip), whereas you will be able to buy only 20 of those for the same rand equivalent today (and you will have £1.28 left for a slightly less generous tip)…. This represents a 33% decline in cappuccino consumption (not to mention a tip that is also exactly 33% smaller).
What probably confuses the issue even more, is that a 33% decline in the value of the rand compared with the pound (as per the above) does in fact equate to a 50% increase in the value of the pound compared with the rand over the same period (i.e. the two numbers are not the same… which might simply not appear logical at first).
You can test the veracity of the previous paragraph in a similar way, i.e. calculate how many times you can go to your favourite Seattle Coffee shop and indulge in your regular beverage with the rand equivalent of £1 000 in your pocket at different points in time… you will see the number increases by 50% over the same three-year period referred to above.
Ultimately, this just boils down to confusing your numerator and your denominator. Play around with it, use different examples, and you will never make the same mistake again. And spread the word… you will have many dinner party opportunities to help educate your fellow global citizens.
Please forgive the slightly geeky theme of this piece. But, if we’re going to quote numbers and statistics and use them in order to inform investment decisions and other important discussions, I believe it’s important to get them right.
The decline in value of the rand has been bad enough. We definitely do not have to exaggerate it.
Deon Gouws is Chief Investment Officer at Credo Wealth in London. His Twitter handle is @deongouws_credo.