What is a Compound Annual Return?

The annual compound rate of return is the rate of return for the annual compound interest calculation. The compound rate of return is generally calculated on a cycle basis, and the cycle of the annual compound rate of return is one year.

Compound annual rate of return

Compound rate of return is generally calculated on a cycle basis

Basic calculation formula

BS model for European subscription

Suppose you have 1W now and you have an investment project with a 15% annual return and compound interest calculation.

Then your income is 1W * (1 + 15%) ^ n

Equivalent to profit rolling.

The magical power of compound interest and the importance of compound interest have been clear to many people. Many people have declared that "don't become rich overnight, but lasting profits." In fact, many people still think of "profiteering", but it is no longer High yields in a single year, "earning 100 times", etc., but deformations such as "35% long-term compound yield" and "10,000 times not a dream".

Munger always said, "It is necessary to understand both the importance of compound interest and the difficulties of compound interest." In fact, many people despise the difficulties of compound interest, and some people easily assume that "I only need to make 35% profit in a year ..." This is obviously a lack of mathematical common sense, unrealistic illusions about long-term returns, and underestimates the difficulty of securities investment.

I think it's easy to have two illusions.

Illusion 1: As long as the "overall" yield is good for most of the years, the losses in individual years should not be a problem;

Illusion 2: If there is no major loss, a small loss or a small profit, the other years are moderately profitable, and the long-term yield should be good.

Here are two cases to verify these two illusions.

Let's start with the first case.

Scenario A: Continuous profit of 15% for 10 years;

Scenario B: Continuous profit of 25% for a total of 9 years, and a loss of 50% in the last year;

Scenario C: Continuous profit of 35% for a total of 8 years, and losses of 40% and 50% each in the last 2 years

We can see which situation will prevail in 10 years.

Case A Case B Case C

1 15 25 35

2 15 25 35

3 15 25 35

4 15 25 35

5 15 25 35

6 15 25 35

7 15 25 35

8 15 25 35

9 15 25 -40

10 15 -50 -50

Cumulative yield 3.046 2.725 2.310

Compound yield 15.0% 14.1% 12.7%

The results are very interesting. The most inconspicuous case A actually prevailed. Cases B and C with Huanghuang's "long-term profit history", because of a significant loss in a certain year, greatly reduced the long-term yield. The "negative compound interest" caused by major losses has caused great damage to long-term investments. This is also the cruelty of investment. It is absolutely necessary to avoid "failures" and "significant losses." Risk awareness must be given priority. "Do not lose money" as the first principle of investment is not covered.