Don’t have a mathematical brain? The good news is, help is at hand. The level of numerical sophistication you require to handle your personal finances and investments is, in any case, more basic than you might think. There are really just five key concepts you need to grasp.
Do you suffer from arithmophobia? No, we aren’t talking about arachnophobia here, but the anxiety that many people feel when dealing with something we encounter far more frequently than spiders — numbers.
This condition can range from a general discomfort around numbers and avoidance of mathematical tasks to a severe phobia that significantly impacts on daily life, work and career opportunities.
Arithmophobia is also remarkably common, and there are several reasons why. Many people have negative experiences of maths in school. Some had parents who struggled with numbers. Many people, of course, find it genuinely difficult to process numerical information, but many others have wrongly assumed that they’re just “bad at maths”.
There are many things that arithmophobics can find challenging, and one of them is handling their personal finances. They avoid getting to grips with their bills, credit cards, taxes, budgeting or savings because they feel anxious about maths. They particularly struggle with long-term investing.
There’s no escaping the fact that, to understand investing properly, you do need a certain degree of numeracy. But the good news for those who feel daunted by mathematics is that the level required to be a successful investor is relatively basic.
Five things to focus on
Here, then, are five elementary mathematical concepts that every investor should understand.
Arithmetic
At a fundamental level, investing entails plenty of simple arithmetic. Calculating things like stock returns, profits and losses, dividend yields and the interest earned on fixed-income investments — these all involve elements of addition, subtraction, division and multiplication.
Strange as it may seem, even supposedly sophisticated investors ignore what the late index fund pioneer Jack Bogle called the relentless rules of humble arithmetic. For Bogle, the most important equation in investing is this: “Gross return in the financial markets minus the costs of financial intermediation equals the net return actually delivered to investors.” In other words, if you can reduce the cost of investment management you will almost certainly end up with higher returns, after fees and charges.
The simplest way to reduce your costs is to use low-cost passive funds. In a short paper called The Arithmetic of Active Management, the Nobel Prize-winning economist William Sharpe explained how, “properly measured, the average actively managed dollar must underperform the average passively managed dollar, net of costs.” Note, this isn’t an opinion — it’s just arithmetic.
Compounding
“Money makes money,” Benjamin Franklin once wrote. “And the money that money makes, makes more money.” What Franklin was describing is the power of compounding — the extraordinary way in which wisely invested capital grows over time.
It’s vital that investors understand the principle of compounding, and, in particular, the value of starting to invest as soon as you can and of putting as much money away early in your investing career as possible. That way, you really do reap the benefits by the time you come to retire. By way of illustration, more than 90% of Warren Buffett’s total net worth has been made since his 60th birthday.
Another reason why it’s important to grasp this concept is that compounding applies to costs as well. As Jack Bogle once put it, the danger is, “the magic of compounding returns (can be) overwhelmed by the tyranny of compounding costs.”
Averages
Also essential for investors is a basic grasp of averages. The average return of a market index, for example, serves as a benchmark against which investors can compare the performance of their investments.
Crucially, averages of historical performance data, such as the average annual returns of different types of asset over many decades, provide investors with valuable insights to help them make informed decisions and to construct portfolios that can maximize expected returns at given levels of risk.
Averages also provide a sense of perspective about market volatility. It’s easy to fall into the trap of focussing too heavily on recent numbers, or on numbers at the extremes. There are bound to be years of stellar performance, as well as years investors would rather forget, but it’s only long-term performance that really matters, and that’s what average return figures capture.
Percentages
Percentages are another key concept in investing. Properly understanding them helps investors to evaluate the returns of different investments and make accurate comparisons.
Fees and charges are typically presented as percentages of assets under management. Risk levels and portfolio diversification metrics are often quantified using percentages as well.
So investors need to understand percentages to calculate the cost of investing and its impact on returns, and to make sensible decisions about such things as risk management and asset allocation.
But investors often struggle with percentages. For instance, they fail to grasp that losses hurt more than gains; if, say, you lose 20% this year, you would need a 25% gain to get back to even. People also misunderstand what percentages represent once they reach three figures. If, for example, your money grows 100%, your wealth doubles, and a gain of 200% would triple your money.
Statistics
Last but not least, investors should have a basic knowledge of statistics. By knowing how to analyze historical data properly, investors can gauge the volatility of investment returns, assess the probability of adverse outcomes, and to choose an appropriate asset allocation.
Understanding statistics is essential for evaluating the performance of investments and comparing them against different benchmarks.
A statistical mindset also encourages critical thinking and scepticism, which are especially important in analyzing news and opinions in the financial media and when looking at adverts for investment products and services. It helps in questioning assumptions, interpreting data correctly, and avoiding common biases that can lead to mistakes.
That’s all the mathematical sophistication you need
Of course, we’ve only scratched the surface of financial mathematics here. You can, if you want, look into it in much more depth. A knowledge of differential calculus, for instance, can be helpful in understanding how things like interest rates change over time and how that affects your financial situation. Knowing the basics of linear algebra can also help when dealing with multiple variables.
But if you’re reasonably conversant with those five key things we’ve touched on — arithmetic, compounding, averages, percentages and basic statistics — you have all the mathematical knowledge you need as an investor.
What, then, can you do if you don’t feel equipped in these areas?
Here at rockwealth, we’re supporters of National Numeracy, an independent charity that helps to raise levels of numeracy among both adults and children and to promote the importance of everyday maths skills. Steven Williams, the founder of rockwealth Brighton, has recently become a Numeracy Champion.
National Numeracy has a wide range of resources for anyone wanting to improve their numeracy, including resources specifically designed to help them manage their finances. It also provides training courses and workshops for organisations, workplaces and schools.
So why not sign up for the National Numeracy Challenge? It’s s a free, online learning tool to help you improve your everyday maths skills in manageable steps whilst building your number confidence. While you’re at it, why not sign up for National Numeracy Day 2024 on Wednesday 22nd May?
Rest assured, if you do feel arithmophobic, you’re in good company. But there’s plenty of help and support at hand. So don’t let your fear of numbers hold you back any longer — at home, in the workplace or as an investor.
TEENAGE OR YOUNG ADULT CHILDREN?
A question we’re often asked at rockwealth is, Can you recommend a book for a teenager or young adult to help them understand money and investing? Our suggestion would be a book called Own It! by Iona Bain. Iona is herself a Numeracy Champion, who struggled herself with maths at school. She wrote Own It!, she says, “to demystify savings, pensions and investing for a new generation.”
CAN WE HELP?
If you’re looking for a financial planner, why not get in touch?
We’re based in Brighton and serve clients across the South-East of England.
If we can’t help you, or feel you would be better speaking to someone else, we will be happy to point you in the right direction.
© rockwealth MMXXIII