# Mathematical concepts useful for investors - Fractions and ratios, CAGR, Rule of 72, Probability

Investors can hone their abilities by mastering these four mathematical concepts. For those wondering how to manage money in the stock markets, investing in equities requires a combination of traits. One needs to be adept at research and analysis, have an understanding of behavioural finance, patience, adaptability, a robust temperament, and perpetual curiosity.

Mathematics is a small part of investing. If investing were really about mathematics, all the learned economists and mathematicians from famous B-schools would have been billionaires by now. Still, grasping a few mathematical concepts can be useful in your journey as an investor. Here are some of them:

1. Fractions and ratios

Financial statements showcasing the performance of a company are available to everyone. However, the differentiator would be a person who can ‘read between the numbers’. After all, these numbers on financial statements are absolute and hold no real value when read in isolation.

This is where the concept of ratios and fractions come into the picture. Ratios are a quantitative relationship between two numbers read in conjunction with one another.

For example, a Net Profit Ratio of 10% tells us that the company has earned INR 10 crore of profit on a revenue base of INR 100 crore. The absolute values hold no real value but the 10% profit margin is comparable across different financial years as well as across different companies in the same sector.

Ratio analysis can become a useful starting point of fundamental analysis of any financial statement. It gives the reader a healthy overview of the company’s performance in comparison to its peers or across time periods.

Once you understand the mathematics behind these fractions, it is very useful while calculating important fundamental ratios of the company such as debt to equity, return on capital employed, price to earnings etc.

Let’s look at price to earnings (P/E) ratio in greater detail. This is one of the most commonly used ratios comparing the earnings of a company with its market price. In other words, it reflects the valuation of a particular company.

For example, if the P/E is 10 times, it means the investor is willing to pay INR 10 (market price) to earn INR 1 (EPS). This also forecasts the growth expectations of the investor.

Related: Turnover ratios and their importance while making investment decisions

2. Percentages

Using percentages, investors can quickly calculate vital investment metrics such as net profit margin, interest payouts, and future growth. Percentages are quite useful to understand the power of compounding investment.

For example:

 Amount invested in equities CAGR Tenure/Time period Value of corpus Rs 10,000 10% 10 years Rs 25,937 Rs 10,000 15% 10 years Rs 31,058 Rs 10,000 20% 10 years Rs 40,455

If you invest Rs 10,000 in equities and earn a CAGR of 10%, at the end of 10 years your corpus would be worth Rs 25,937.

If you invest Rs 10,000 in equities and earn a CAGR of 12%, at the end of 10 years your corpus would be worth Rs 31,058.

If you invest Rs 10,000 in equities and earn a CAGR of 15%, at the end of 10 years your corpus would be worth Rs 40,455.

You can use an investment calculator to calculate the results.

Percentages are also handy to understand the impact of losses and gains. By way of example, imagine that the share price of a stock is Rs 400. If it falls by 20%, the price becomes Rs 320. However, the stock will need to gain by 25% to go back to Rs 400 from Rs 320. This highlights the importance of maintaining stop loss.

Therefore, an investor should be able to use percentages efficiently while taking investing or trading decisions.

3. Rule of 72

Rule of 72 is a handy formula that can be used to quickly calculate the number of years it would take for an amount to double if the interest rate is known. For instance, consider an amount of Rs 10,000. If the rate of interest on it is 9%, you have to divide 72 by 9. The answer in this case is 8. That is, it would take 8 years for Rs 10,000 to double.

This rule can also be used to estimate the value of inflation. For instance, assume that your expenses on groceries are Rs 3000 every month. If the average annual inflation rate remains 8% over the next decade, your expenses on groceries would be Rs 6000 a month after 9 years.

4. Probability

Investing in the stock market need not always pay off. No one can be completely right. However, your analysis should allow you to give more odds in your favour than against you.

An investment in a stock is primarily an investment in the future outlook of the company and the growth prospects of the business. As nobody can truly predict the future, one should try to improve the odds by analysing multiple parameters.

Some factors are valuation of the stock, profitability of the company, future growth prospects, quality of the management, growth sustainability etc. After analysing multiple indicators and parameters, you might decide that the company has a 90% chance of growing in the future.

The next step would be to understand whether you would be willing to invest in a company with a 90% chance of being right. This way, you can evaluate various investment opportunities.

So the probability of the odds being more in favour of you than against you will allow you to readily bet on the stock. In other words, there is no black-and-white approach to investing in the stock market, only your reasoned judgment can make you a sustainable and profitable investor.

Related: 6 Practical strategies to help reduce investment risk

Last words

The stock market need not be as complicated as it sounds. You merely need to dredge up some simple mathematical concepts that you learnt in school, and apply them in suitable situations in order to crack the success code for investing. Type of risks you should be aware of when investing.