- If you started with R100 and lost R50, what return do you need to get back to R100?
- Misunderstanding gains and losses can lead to bad decision-making, says Joao Frasco.
- Remaining invested is usually a good idea.
If you lose 50% of your money, what return will you need to subsequently make, to get back up to your original investment?
Your gut reaction may be to say 50%, seeing as that is how much you lost, but with a little consideration you will probably get to the right answer of 100%.
Consider the simple example that you began with R100, and lost 50%, or R50. What return would you need to turn the R50 investment back into R100?
Clearly 50% of R50 is R25, and would only get you back to R75, so you would need 100% or another R50 to get back to R100.
Now, if you consider this for all possible losses and the subsequent gains needed to recover fully from those losses, you will realise that the gains required become exponentially higher (not just higher). The chart below shows this relationship, and at the extreme of a loss of 90%, the subsequent gain would need to be 900% (or 10x money back).
The way this is normally positioned is that because this is the case, you should avoid losses (especially large ones) as they are increasingly difficult to overcome.
Now, although the above is mathematically true, it is not the whole story, and it in fact misses the “true” story. By providing the wrong impression, it can lead to bad decision-making. We will address this by considering the above from three different perspectives, for completeness; mathematically, theoretically, and empirically.
Mathematically speaking
Let us begin by understanding that a return is a rate. When we quote a value like 12%, it is important to state that it is per annum (p.a.) or per month (p.m.). Including this time element is what makes it a rate.
If we consider the continuous rates related to losses and subsequent gains needed as per the chart above, we get the chart below. Note how the chart has become completely symmetrical i.e. the losses and subsequent gains are now equal in absolute terms (just the signs differ). This is not a coincidence, but a mathematical truism. These continuous rates can be thought of as forces.
This is a very important result. The same force of return that leads to a loss of a given amount, is required to get back to the starting point (no more or less). You should now not be feeling that the gains required to undo losses appear insurmountable.
Theoretically
Now imagine a specific piece of information that causes the price of a share to change substantially (say drop by 50%). What information would be required to bring the share price back to its price before the fall? You may imagine that lots of good news would need to follow to cause it to appreciate by 100%, and you may conclude that this is very unlikely. However, a single piece of information is all that is needed, and that is a reversal of the information that caused it to fall in the first place.
Empirically – what does the data show?
Let’s have a look at data from a single share as an example (Carvana – an American car sales company), and an index (the JSE All Share Index).
Carvana sells cars in the US, and it fell substantially with the drop in car sales related to the lockdown in the US (80% in a couple of weeks from over $115 per share to about $22 per share on an intra-day basis). You can easily calculate that to recover from an 80% loss requires a 400% gain, and this may appear impossible, especially over shorter time frames. However, as you will see from the share price chart below, the share price for Carvana has all but bounced back from the 80% fall.
All that was required for the bounce back, was a reconsideration of the impact of Covid-19 and the lockdown on Carvana. Forget about whether this revaluation is right or wrong, as that is not the point here. The point is that if you think about the return profile of being down 80% requiring a subsequent gain of 400%, you may miss the non-mathematical explanation that this simply requires a reversal of the impact of Covid-19.
Let’s explore what happens if we consider the annual returns of the All Share Index over the past 95 years (since 1925).
The chart below provides a histogram (count) of the number of annual returns that fall into specified return buckets of 10% p.a., ranging from -30% to +60% i.e. the bucket on the far left represents -30% to -20%, and the bucket on the right represents 60% to 70% (all p.a.).
You will note that we don’t have a return worse than -30% p.a. (even though this could, and probably will happen in future). Yet, we do have a return above 60% p.a. All that is required to recover from a 25% loss, would be a 33% gain, and we have many returns that equal and exceed this value (11 to be precise).
Empirically, theoretical losses of 90%, that would require subsequent gains of 900%, don’t really appear to be a real problem. If anything, they seem to misinform and create misunderstanding around how markets actually work.
The above analysis should provide clarity around how markets actually work, and why fears of losses should be understood in their proper context.
Not only do markets tend to go up over time, they also combat losses, making losses transitory. Remaining invested is still one of the most powerful messages in investing for the long term.
Joao Frasco is Chief Investment Officer, STANLIB Multi-Manager. Views expressed are the author’s own.
