Wealthy Maths: Getting back to where you started

Kristia van Heerden

Watching your portfolio value fall during a market collapse is a sickening experience. If you started 2020 with some investments, you probably already know this.

Unfortunately we have more bad news. To get back to where you were in January, your portfolio has to work much harder than it fell. In this post, we are going to show you by how much the share price of your investment has to grow to get back to where you started. This is called the drawdown recovery rule.

To illustrate this, we are going to assume that your portfolio of R500 lost 20% in value. 20% of R500 is R100. That means, following the market collapse, your portfolio is now worth only R400. When you add 20% back to R400, however, you don’t get R500. You get R480. Did your head just fall off? Ours too.

Want to recap how to work out percentages? Learn that simple formula from this post.

What the hell?

Good question. The answer lies not in what you lost, but what you’re left with. So what if we reframed the question like this: By how much does R400 need to grow to become R500? Now you can start putting your Wealthy Math brain to work. Follow these steps:

1. Subtract how much you have left from how much you had. This is the rand value by which your portfolio has to grow to get back to where you were. Now we need to work out what percentage that value is of what you have left.
2. Divide the result of step one by how much you have left.
3. Times by 100 to get the percentage.

Like this:

1. 500-400 = 100
2. 100/400 = 0.25
3. 0.25*100 = 25%

Now you know R400 needs to grow by 25% to become R500. That already hurts a little, but as you can see from the table below, the more value your portfolio loses, the harder the money you have left has to work to get back to where you started.

What if you don’t know how much you had

I don’t keep a record of the rand value of my portfolio over time. Most of the time when I log in, I only pay attention to the percentage I lost. That means right now I know how much money I have in my account and what by what percentage my portfolio fell. Here’s how to work out how much money you had at the start.

1. Subtract the percentage you lost from 100.
2. Times what you have left in your portfolio by 100
3. Divide the answer you got in step two by the answer you got in step one.

Like so:

1. 100-20 = 80
2. 400*100 = 40,000
3. 40,000/80 = 500

What can I learn from this?

One of the rules I drum into every new trader is the drawdown recovery rule.

If you lose 50% of your capital you need to now grow it by 100% to get back to where you started. Worse, a whopping 90% loss requires 1,000% growth to get back to your initial starting capital (see below for detailed table).

For traders this is especially important and helps focus the mind on one’s stop loss.

For investors holding individual shares this rule is why you don’t hang onto those busted stocks like African Bank in August 2014 and Steinhoff in December 2017. When an individual stock you own is fundamentally broken, exiting sooner rather than later is hugely important to your capital.

It is also why one diversifies. If you held Steinhoff as your only stock, your portfolio is now broken. But if it was one of many stocks you held, then it has a nasty hole but the other stocks can help you recover.

ETFs are by their nature diverse and no index, and hence no ETF, has ever gone to zero. So while the collapse in prices we’re currently seeing leaves a sickening feeling in one’s stomach, most locally listed broad diverse ETFs are down in the 25% – 35% range, they’ll recover but it’ll take some time.

Time is the issue here and why stock market investing is for the long-term. Investing is not a short-term smash and grab.

Another important point is that with a fundamentally broken stock buying on the way down does indeed reduce your average price. It also increases the total capital you have invested and lost. You’re increasing your position into a broken stock. It’s never a good idea.

Again ETFs are different in that they will recover. That’s why I continue my monthly ETF debit order. Prices are cheaper than a month ago and indices recover. No smashing and grabbing, but a simple carrying on of my long-term plan.

 Loss Required recovery to get actual growth 10% 11% 20% 25% 30% 43% 40% 67% 50% 100% 60% 150% 70% 233% 80% 400% 90% 1,000% 100% Game over

Wealthy Maths blog

Many of us avoid making financial decisions because we worry that we can’t do the maths. Luckily, there are only a few formulas you need to understand to make a good financial choices. This series of articles is dedicated to helping you understand how to do the calculations for yourself. Once you grasp these simple formulas, you can make better financial choices on the fly.