Investment performance: the maths you need

It’s often a matter of love or hate when it comes to maths. Whichever camp you belong to, there are a three key concepts you need to master to manage your money well: percentages, attribution and absolute growth. Understanding investment performance is what makes you a better investors. Here’s what you need to know.


The reason we invest is to make money. The more you make the better, right?

Perhaps, so, but lets face it: if you put in £1,000 pounds and double that, your gain of £1,000 would still be half of what you would get from a 20% rise on an investment of £10,000.

Rule 1: Focus on the percentage increase/decrease

Doubling your investment takes either great mastery or incredible luck. More so than to increase it by 20%. Measuring success should therefore be in relative terms, i.e. by what percentage did you increase your wealth?

Consider this:

Scenario A: You start off with a £1,000 investment. You buy 100 shares priced £10 each. The price drops by 10%. So each of your shares is now worth £9, or your investment is down to £900 (£9 x 100 shares). You’ve lost £100.

Scenario B: You start off with a £10,000 investment. You buy 100 shares prices £100 each. The price drops by 1%. So each of your shares is £99, or your investment is down to £9,900 (£99 x 100 shares). You’ve lost £100.

A £100 is a £100. But I’d take the 1% loss any day. In fact, as a rule of thumb, sell if the value of your investment goes beyond 10% … to limit the losses. A 1% loss on paper or realised, is not worth to worrying about – prices move all the time.

The other benefit of percentages is that they allow comparisons across different investments, different time horizons, different investors.

Rule 2: High percentage changes mean greater risk

Achieving greater returns means exposing yourself to greater risk. To double your money over a short period of time you need to be looking at something new (e.g. R&D company), a penny stock where even small absolute changes translate to big percentage changes because the base is low or a company that has fallen on hard times.

Contrarians, for example, specifically look for stocks or industries that have fallen out of favour and a trading cheaply. An example right now would be oil companies, some of which are 75% lower than in the summer of 2014. There’s money to be made in the sector as prices recover, but the risk is that prices may fall further or stagnate for a prolonged period of time. Or maybe the company itself has taken on too much debt or over-expanded and its costs have spiralled out of control compared to revenues.

If the price moves around a lot or it barely moves until financial results are announced and then it jumps or drops by a mile, then you’ve got a volatile investment. How do you know? Look at a chart or do a percentage calculation.

Do you want to risk it? Perhaps you do with part of your money, but you can also grow a small pot big by giving it time, sticking with winners and reinvesting any income the portfolio generates from dividends or bond coupons.

Rule 3. Don’t put your eggs in one basket

You really should consider each investment within the context of your wider portfolio. So if my whole portfolio is £10,000 and it’s all invested in the one stock, I’d be much more likely to suffer a loss if something goes wrong with that company than if I had £1,000 investments in 10 companies. A 10% loss on the £1,000 investment is really just 1% in my £10,000 portfolio and if everything else is doing OK, I’ve done a great job.

Rule 4. Do the maths – KEY LESSON

Let’s say your £1,000 investment in XYZ rises 20% of the back of great corporate news. Then overjoyed investors start cashing in on the gain, some bad news emerges and the stock falls 20%. Is it back to the price you paid?

The correct answer is “no” and here’s why.

  • A 20% rise will mean a gain of £200 = 20% x £1000
  • So your investment is now £1,200 = £1,000 + £200
  • A drop of 20% means £240 = 20% x £1,200
  • So you’re down to £960 = £1,200-£240
  • Oops! You started off with £1,000 but it’s now £960. You lost £40 or 4%!

Let’s look at the reverse scenario. Take oil. It’s fallen 75%. How much does it need to rise to get back to the price of $110-115 it enjoyed in the summer of 2014?

  • Say you started with $1,000 invested in oil. It’s now down to $250 after that 75% drop.
  • So to get back to $1,000 you need your $250 to quadruple!

That’s why contrarian investors look for beaten down sectors and stocks. Get in at the bottom and enjoy the ride up. Provided you have picked a winner. Some companies and sectors “die” for a reason.


There are two aspects to growing your wealth. On the one hand your investment can go up in value. On the other, you can earn coupons or dividends while you hold an investment. Understanding what’s driving your returns is called attribution.

  • If your investment pays no coupon or dividends, then all of your returns (or losses) come from capital gains.
  • If you invest in a blue-chip company that awards you for being an investor by paying a coupon on debt or a dividend on its shares, then you have to sources of returns: ongoing income and capital gains.

Growing companies, i.e. ones that reinvest their profit in research and development or in new production capacity, do not usually pay dividends, but more established ones do. And UK companies pay some of the highest dividends.

If you have a long investment horizon – i.e. you are young – you’re better off investing primarily for capital gains. If you are relying on your investments to generate a healthy cash flow – e.g. you’re retired – you need to be in bonds or high dividend stocks to generate yield. Most investors want a combination of the two.


So how do you figure out what to invest in if you want yield? Simple. You compare yields. Here’s how:

  1. Figure out how much you get in dividends or bond coupons per annum. Companies can change dividends but there is usually a dividend policy which would provide an indication of what to expect.
  2. Compare the amount to the stock or bond price, i.e. express it as a percentage and voila, you have your dividend yield. Say you have a stock trading at £10 per share and the company has announced that it would pay £0.50 dividend per share. That’s a dividend yield of 0.5 / 10 = 5%.
  3. All else equal, you want the investment with the highest yield.

But beware, high yields often mean that there is a risk premium for something – maybe the business sector is risky, or the company is in distress, or it has too much debt. As a rule of thumb dividend yields above 5% and bond yields above 6-7% suggest risk. Think about it this way: if the central bank’s interest rate is 0.5% and most companies are offering 3-5%, why would someone be prepared to pay say 9% to get access to your capital?

Also, don’t be lazy and just look at the yield number companies quote. You need to compare the returns to what it actually cost you to invest in the stock or bond. It’s your return, so personalise it!

The power of compounding

The best thing is, you can invest the dividends and improve your returns by taking advantage of compounding. What that means is that every time you earn a dividend or coupon and reinvest it, it becomes capital so the amount you are earning an yield on keeps increasing. The longer the time horizon and the higher the yield, the more you gain.

Here’s why:

  1. Say you’ve got your £1000 investment.
    • Over the first year the share price grows by 5%. So at the end of the year it’s worth £1,050
    • In addition, the company pays you 5% dividend. That’s another £50 = 5% x £1,000
    • Your total return is £100 = £50 capital gain + £50 dividend, or 10%
  2. You reinvest your dividend, so now your capital is £1100
    • Over the second year the share price goes up by 10%. You gain £110 = 10% x £1,100
    • Again, you get a 5% dividend. But this time that’s £55 = 5% x £1,100 because you reinvested the first year’s dividend. Your yield to cost is 5.5% = £55 dividend / £1,000 original investment
    • Your return for the year is £165 = £110 capital gain + £55 dividend
  3. Let’s recap. Over two years, you have gained £265 = (£50+£110 capital gain) + (£50+£55 dividends)
    • That’s 26.5% on your £1,000 investment
    • 16% is related to capital gains but part of that (0.5%) is the gain on the reinvested first year dividend
    • 10.5% is from dividends with another 0.5% in capital gains from the reinvested first year dividend

If you didn’t have the dividends then your investment would have made you less money:

  1. Year 1: 5% x £1,000 = £50 gain, taking you to £1,050 capital value
  2. Year 2: 10% x £1,050 = £105 gain, increasing the capital value to £1,155
  3. Total return: £155 gain / £1,000 investment = 15.5%

Understanding where you’re making your money is just as important as making money and ongoing returns from dividends and bond coupons are not to be sniffed at!

Absolute growth

Many funds compare their performance to a benchmark. Benchmarks are usually indices. For example, you might want to compare Shell to the FTSE 100 because it is a FTSE 100 company or just to other oil or natural resources majors in the FTSE 100. If you did the former, then you are comparing to the large-cap market. If you do the latter you are comparing to similar companies, competitors. Both can be valid approaches.

But beware, benchmarks are selected. In any event, do you want to make as much as the benchmark or increase your wealth? The best way to judge performance is to compare the absolute growth of investments and select the one that is doing best … or perhaps the second best, as they have an incentive to become top dog!


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