Mostly interest is compounded on a monthly, quarterly or semiannual basis. Hypothetically, with continuous compounding, interest is calculated and added to the account’s balance every infinitesimally small instant.

Hence this is an important concept in stock market though it is not possible in practice. Stock market returns are assumptive to continuously compounding.

Let’s say,

- i = Interest Rate
- n = Number of compounding periods
- t = Time
- P = Principal Invested
- T = Total Account Value
- T = P x (1 + (i/n)) ^ (n x t)

Now let’s assume a 10,000 INR investment earns 15% interest over the next year. Here are the possible scenarios possible based on when the interest is compounded.

- Annual Compounding = 10,000 x (1 + (15% / 1)) ^ (1 x 1) = 11,500
- Semi-Annual Compounding = 10,000 x (1 + (15% / 2)) ^ (2 x 1) = 11,556.25
- Quarterly Compounding = 10,000 x (1 + (15% / 4)) ^ (4 x 1) = 11,586.50
- Monthly Compounding = 10,000 x (1 + (15% / 12)) ^ (12 x 1) = 11,607.55
- Daily Compounding = 10,000 x (1 + (15% / 365)) ^ (365 x 1) = 11,617.98

But what is the compounding period in stock market?

Do you close a position annually, semi-annually, quarterly, monthly or daily?

No, it is absolute chaos. You invest some of it, You positional trade some of it, You day trade some of it. Also, money doesn’t grow all the time. It goes justdial too. (In our forum, we refer Justdial as a significant money loss trade)

So the concept of continuous compounding is there! So, in this case, our n, number of compounding periods tends to infinity.

Even if you change the initial investment amount to 1 cr, the total difference would only amount to 358.

Meanwhile, let’s take I which is called the logarithmic return or continuously compounded return or force of interest where

- P = Principal Invested
- T = Total Account Value

T_P means Total Account Value at time P; T_P means Total Account Value at time P+1. As we used P as a notation for the principal amount, you might be confused on this P, P+1 part. These annotations are different. T_P and T_P+1 just mean different times like let’s say the start of a year and end of a year.

Under an assumption of reinvestment, the relationship between a logarithmic return I and a logarithmic rate of return i over a period of time of length t is I = it

Wait, in case you are confused, You must read again. Logarithmic return is just returned over time t. If t =1, we call it the annualized logarithmic rate of return.

When we refer to stock market returns, it is always annualized logarithmic rate of return. Hence,

So, it matches our old definition in a reverse way.

Whereas i is our interest rate of continuously compounded return and hence also called logarithmic rate of return.

Under an assumption of reinvestment, the relationship between a logarithmic return I and a logarithmic rate of return i over a period of time of length t is I = it