17 June 2020

6 minutes

While you need not be a math whiz to start investing in stock markets, knowing a few concepts around stock market mathematics can certainly go a long way in helping you analyse your investments better. So let’s brush up the basics today. Read on!

These stock market math formulas are relatively easy to understand and will help you choose the right stocks and funds. And most importantly, it will keep your expectations real.

Here are five fundamental algebraic and arithmetic equations that investors must know.

**Equation 1**

**Return on Equity (ROE) = (Net income / shareholder equity)**

You can use the company’s balance sheet and profit and loss statement to get this information and calculate this as a percentage value.

ROE is a classic measure of a company’s ability to put shareholders’ money to good use. It can tell you how effectively a company can turn equity investments into profits. Higher ROE is usually associated with a higher probability of returns.

However, it is important to remember that you cannot consider ROE as a standalone factor while selecting stocks. You need to compare it with the industry average too.

For example, the industry average ROE is different in the banking and financial services sector as compared to the pharmaceuticals sector. Also, ROE can be high if the company takes a lot of debt and its equity investment is low. Hence, look at all the factors before investing.

**Equation 2**

**F = P * (1 + R)****t**

where,

- F = Future value of the investment
- P = Present value of the investment
- t = The number of compounding periods and
- R = The periodic interest rate or the rate of return

The concept is called **“future value**” and is used by investors to get an estimate about the future value of their investments. So, you can assess how much you need to invest each year to reach your financial goals.

**Equation 3**

**Total Return = {( Value of investment at the end of the year – Value of investment at beginning of the year ) + Dividends} / Value of investment at the beginning of the year**

While Future Value is about predicting estimated returns on your investment, Total Return is about calculating the actual returns on your investments today. It is a simple calculation that includes dividend income too.

For example, if you bought a stock for ₹7,500 and it is now worth ₹8,800, you have an unrealized gain of ₹1,300. You also received dividends during this time of ₹350.

Total Return = {(₹8,800 – ₹7,500) + ₹350} / ₹7,500 = 0.22 or 22%.

You can use this calculation for any period. However, you must remember that this calculation does not factor inflation and offers you a simple mathematical return percentage.

**Equation 4**

**Stock price = V + B * M**

Where,

- V = Stock’s variance
- B = How the stock fluctuates with respect to the market
- M = Market level

The above formula is the Capital Asset Pricing Model (CAPM) and is used to assess the price of a stock in relation to general movements in the stock market.

**Equation 5**

**Price/Earnings Ratio (P/E) = Market price of Stock/Earnings per share**

This ratio helps you understand if the stock price of a particular company is overvalued or undervalued in the market. It is a simple calculation that tells you how much is the price of a share compared to its earnings per share.

The P/E Ratio is used to compare the price of a stock to other stocks in the same industry.

The market price of a stock is the cost of buying 1 share on the stock market and earnings per share is the annual per-share earnings reported in the company’s financial reports.

If the P/E for the company is lower than that for the industry, an investor should investigate further to discover the reasons for its low price. Depending on those reasons, an investor might buy or sell it.

Apart from the math behind stock market investments, you also need to understand an important mathematics calculation – Compounding.

Most of us are aware of the concept of compound interest. Just in case you have been away from mathematics for long, here is what it means:

In compound interest, you don’t receive any interest on your investments. Instead, the interest amount is reinvested and becomes a part of the investment capital.

**Example,**

Let’s say that you make a one-time investment of Rs.10,000 in a term deposit at the rate of interest of 10% per annum. You have the option of receiving interest every three months or reinvesting it. For the sake of this example, let’s assume both scenarios and see the difference.

**Scenario #1**

You choose to receive interest every quarter. Hence, your returns over 5 years will be as follows:-

Principal amount |
Rate of interest |
Period (months) |
Returns |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

10000 | 10 | 3 | 250 |

Total interest received |
5000 |

**Scenario #2**

You choose to reinvest the interest every quarter. Hence, your returns over 5 years will be as follows:-

Principal amount |
Rate of interest |
Period (months) |
Returns |

10000.00 | 10.00 | 3.00 | 250.00 |

10250.00 | 10.00 | 3.00 | 256.25 |

10506.25 | 10.00 | 3.00 | 262.66 |

10768.91 | 10.00 | 3.00 | 269.22 |

11038.13 | 10.00 | 3.00 | 275.95 |

11314.08 | 10.00 | 3.00 | 282.85 |

11596.93 | 10.00 | 3.00 | 289.92 |

11886.86 | 10.00 | 3.00 | 297.17 |

12184.03 | 10.00 | 3.00 | 304.60 |

12488.63 | 10.00 | 3.00 | 312.22 |

12800.85 | 10.00 | 3.00 | 320.02 |

13120.87 | 10.00 | 3.00 | 328.02 |

13448.89 | 10.00 | 3.00 | 336.22 |

13785.11 | 10.00 | 3.00 | 344.63 |

14129.74 | 10.00 | 3.00 | 353.24 |

14482.98 | 10.00 | 3.00 | 362.07 |

14845.06 | 10.00 | 3.00 | 371.13 |

15216.18 | 10.00 | 3.00 | 380.40 |

15596.59 | 10.00 | 3.00 | 389.91 |

15986.50 | 10.00 | 3.00 | 399.66 |

Total interest received |
6386.16 |

As you can see, by simply not receiving the interest every quarter, you stand to gain Rs.1386.16 on an investment of Rs.10,000 in 5 years.The beauty of compounding is that as the tenure increases, the gains start multiplying faster. To give you an idea, here is a calculation of the same investment for extended periods.

Investment of Rs.10000 @ 10% p.a. | ||||

5 years | 10 years | 15 years | 20 years | |

Receive interest | 5000 | 10000 | 15000 | 20000 |

Reinvest (compound) interest | 6386.16 | 16850.64 | 33997.9 | 62095.68 |

Difference | 1386.16 | 6850.64 | 18997.9 | 42095.68 |

As you can see, at the end of 20 years, compound interest can offer much higher returns. To take advantage of the power of compounding, it is wise to start saving and investing as early as possible.

As humans, when we don’t find certainty, we start looking at probabilities. What are the odds of something happening? The lower the odds, the higher the risk. The same applies to investments too.

For instance, when you are investing in a particular stock, there is no certainty around its performance in the future. Hence, you look at various aspects pertaining to the stock and look at the risk and reward. So, if the stock price is Rs.100 per share, then you will look at :

- Whether it is undervalued/overvalued?
- Is the company financially sound?
- Any certain events like elections or expected policy changes that can impact the price

Based on all this information, you will try to gauge if the said investment is a good idea. Let’s say that the company’s financials are around 70% sound (there are some minor issues but you give the company a 70% chance of making it through the economic downturns).

Should you invest Rs.10000 in the said stock now for a 70% chance of earning Rs.20000 at a future date?

The answer to this question determines the kind of investor you are. It highlights your investor profile, risk tolerance, and helps you make an informed guess. Yes, no mathematical formula can accurately predict the future price of a stock. Probability theory can only help you gauge the risk and reward of an investment based on facts.

I hope that this article helped you gain a better understanding of math in stock exchange investments. Remember, don’t try to predict the market and research the stock well before investing.

Happy Investing!

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