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You can feel a bit better about the rand

A retort to Magnus Heystek … 20 cappuccinos for R1 000, anyone?

 

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?

Wrong.

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.

COMMENTS   17

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Are you not describing, in a similar fashion, the Big Mac Index?

Interesting article. I agree with you, except that the error in logic is not caused by confusing the numerator and denominator, but rather due to the fact that to calculate the decline in the value of the ZAR, you need to compare the buying power of 1 ZAR (in Sterling) over a period of time and not the ZAR value of 1 Pound. 1/13 VS 1/19.5 gives the same 33% decline answer. Likewise with the Sterling, comparing the buying power of the Pound (in ZAR), the increase from 13 to 19.5 equates to 50%.

But your solution of switching the ‘beginning’ and ‘ending’ level gives the same answer though in the case of the ZAR.

Sorry for sounding smirky.

Well put. It is the buying power of each currency that must be compared.

Valid point, my reference to numerator/denominator was a bit of a clumsy one. Your smirk is justified 😉

What if your property’s value had gone from R100k to R200k in 3 years – would you say it had appreciated in value 100% or 50%? You would say 100% wouldn’t you?

Also very much time frame dependent. If your start date is 20/10/2008, we have lost 1.5% against the Euro, 12.05% against the Pound and 23.24% against the USD – HOWEVER the JSE has returned 196% since that start date.

Very easy to write an emotive article with your start date as the most recent low point January 2011.

Thanks for your comment. My intention was not to write an article with any emotion (or one that is guilty of selection bias from a date point of view), but simply to try & explain a basic point of mathematics which appears to be somewhat misunderstood.

I actually meant Magnus’ article in terms of the emotion and selection bias. I quite enjoyed your article, get people thinking from a different point of view.

I know the article is about the decline in the value of ZAR, but when you are used to ZAR10 to One pound with 10% VAT and an espresso in Harrods @ Pound2.50 in 2007/8 and now has to pay Pound4.75 + VAT at 17.5% and nearly ZAR20 for One Pound – then you feel the pinch!

However, thank you for a good analysis

this morning i had a very good illy cappucino for £1.45, far better than the £2.40 cappucino marketed by the coffee specialists next door.

In a weakening ZAR environment shopping more wisely will realise far more real savings than the hocus-pocus described here. besides, focussing on the numbers in MH’s article is surely missing the general gist.

Just to clarify, in respect of the article by Magnus that you refer to: I think that is a very good article and I personally agree fully with its general gist.

thanks for responding to my somewhat irreverant coment ! i thought you did a good job …. Magnus’ article is on point and in my opinion dififcult to argue with.

But, i agree with your view – in this day of soundbytes and headline grabbing, its important that stats are 100% accurate.

thanks for taking the time

It’s sad that people can’t grasp simple arithmetic. There was a letter in the local rag about a year ago from someone who insisted that you can add the percentage fullness of two reservoirs and divide by two to arrive at the overall percentage. But it’s not just in SA that there’s a problem. A couple on “Who wants to be a millionaire” in Britain could not translate four-fifths into a percentage, despite using all their “lifelines”, so they chickened out and took the 1000 quid.

http://www.numbeo.com (for real time info)

Indices Difference
Consumer Prices in London are 112.20% higher than in Johannesburg
Consumer Prices Including Rent in London are 180.30% higher than in Johannesburg
Rent Prices in London are 347.82% higher than in Johannesburg
Restaurant Prices in London are 132.63% higher than in Johannesburg
Groceries Prices in London are 96.52% higher than in Johannesburg
Local Purchasing Power in London is 29.82% lower than in Johannesburg

The rain, cold and wet are not factored in…

I can see the logic, but it becomes tricky to contextualise into the real world.

For example
A can of Coke cost me R5 in 2010 but costs R10 today.
In a conversation with my buddies, I would therefore say that:
A can of Coke cost me 50% less in 2010 (R10-R5) but,
I am paying 100 % more for a Can of Coke today than I did in 2010 because the price has increased by a 100 % since 2010.

Fascinating indeed…

Can someone please tell me where the article by Magnus on the 20 cappuccinos can be found?

fwiw i realised my other concern with the approach set out in this article …. if you take an approach of “bottom up” calculation, the top tax rate in SA is actually 41/59, ie 69.5% !

End of comments.

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