Calculating the annualized return on your investment portfolio answers a question: what is the compound interest rate I earned on my portfolio for the investment period? While the formulas for calculating it may seem complicated, it is actually quite easy to use them once you understand a few basic concepts.
Steps
Part 1 of 2: Starting with the Basics
Step 1. Learn the most important terms
When it comes to annualized returns on your portfolio, there are some terms that will pop up repeatedly and it is important that you know them. Are the following:
- Annual Return: Total return earned on an investment over a calendar year, including dividends, interest and capital gains.
- Annualized return: annual interest rate obtained by extrapolating the returns measured over periods shorter or longer than a calendar year.
- Average Return: Return typically earned over a period, calculated by dividing the total return achieved by shorter intervals.
- Compound Return: The return that includes the results of the reinvestment of interest, dividends and capital gains.
- Period: A specific time frame chosen to measure and calculate returns, for example a day, a month, a quarter or a year.
- Periodic Return: The total return on an investment measured over a specific time interval.
Step 2. Learn how compound returns work
They represent the total growth of the investment, considering the returns already earned. The longer the money grows, the faster it will and the higher your annualized returns (think of a rolling snowball, the bigger it gets the faster it moves).
- Imagine investing € 100 and earning 100% in the first year, ending it with € 200. If you only earn 10% in the second year, you will have earned € 20 on your € 200 at the end of the second year.
- However, if you assume that you only earned 50% in the first year, you will have € 150 at the beginning of the second year. The same 10% gain in the second year would only lead to $ 15 instead of $ 20. There is a 33% less difference than the yield of the first example.
- To better illustrate the concept, imagine losing 50% in the first year, leaving you with $ 50. At that point you will have to earn 100% just to break even (100% of 50 € = 50 € and 50 € + 50 € = 100 €).
- The size and time horizon of earnings play an important role in the calculation of compound returns and their effect on annualized returns. In other words, annualized returns are not a reliable measure of actual gains or losses. However, they are a good tool for comparing different investments with each other.
Step 3. Use the weighted yield to calculate the compound interest rate
To find out the average of many things, such as daily rainfall or weight loss over the course of several months, you can often use simple arithmetic mean. This is probably a concept you learned in school, however simple averaging does not consider the effect that periodic returns have on future ones. To take this factor into account you can use a weighted geometric mean (don't worry, we'll walk you through the formula step by step!).
- It is not possible to use the simple average because all periodic returns are dependent on each other.
- For example, imagine that you want to calculate the average return of $ 100 over the course of two years. You earned 100% the first year, so you had $ 200 at the end of year 1 (100% of 100 = 100). In the second year you have lost 50%, so you are back to the starting point (100 €) at the end of year 2 (50% of 200 = 100).
- The simple (or arithmetic) average would add the two returns and divide them by the number of periods, in the example two years. The result would suggest that your investment had an average return of 25% per year. However, if you compare the two returns you will find that you have not gained anything. The years cancel each other out.
Step 4. Calculate the total return
To get started you need to calculate the total return over the desired period. For clarity we will use an example where no deposits or withdrawals were made. To calculate the total return you need two numbers: the initial value of the portfolio and the final one.
- Subtract the starting value from the ending value.
- Divide the number by the starting value. The result is the total return.
- In case of losses in the considered period, subtract the final value from the initial one, then divide by the initial value and consider the result as a negative number. This operation allows you not to have to add a negative number algebraically.
- Subtract before dividing. This way you will get the total return percentage.
Step 5. Learn the Excel formulas for these calculations
Total Interest Rate = (Final Portfolio Value - Initial Portfolio Value) / Initial Portfolio Value. Compound Interest Rate = POWER ((1 + Total Interest Rate), (1 / year)) - 1.
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For example, if the initial value of the portfolio is € 1000 and the final value is € 2500 seven years later, the calculation would be:
- Total interest rate = (2500 - 1000) / 1000 = 1.5.
- Compound interest rate = POWER ((1 + 1.5), (1/7)) - 1 = 0.1398 = 13.98%.
Part 2 of 2: Calculating the Annualized Return
Calculate Annualized Portfolio Return Step 6 Step 1. Calculate the annualized return
Once you have the total return (as described above), enter the value in this equation: Annualized Return = (1 + Return)1 / N-1. The result of this equation is a number that corresponds to the annual return over the life of the investment.
- To the exponent (the small number outside the brackets), the 1 represents the unit we are measuring, which is a year. If you want to be more specific you can use "365" to get the daily return.
- The "N" represents the number of periods we measure. So, if you want to calculate the return over seven years, substitute 7 for "N".
- For example, imagine that over a seven-year period your portfolio has increased from € 1,000 to € 2,500.
- To begin with, calculate the total return: (2,500 - 1,000) /1,000 = 1.5 (a return of 150%).
- Then, calculate the annualized return: (1 + 1, 5)1/7-1 = 0, 1399 = 13, 99% annual return. Done!
- Use the normal mathematical order of operations: first do the ones in parentheses, then apply the exponent, finally subtract.
Calculate Annualized Portfolio Return Step 7 Step 2. Calculate half-yearly returns
Now imagine you want to calculate semiannual returns (those obtained twice a year) over the same seven-year period. The formula remains the same; you just need to change the number of measurement periods. The final result will be a half-yearly return.
- In this case there are 14 semesters, two for each of the seven years.
- First calculate the total return: (2,500 - 1,000) / 1000 = 1,5 (150% return).
- Then, calculate the half-yearly return: (1 + 1, 50)1/14-1 = 6, 76%.
- You can convert this value to the annual return by multiplying by 2: 6.66% x 2 = 13.52%.
Calculate Annualized Portfolio Return Step 8 Step 3. Calculate the annualized equivalent
You can calculate the annualized equivalent interest of shorter returns. For example, imagine you had a six-month return and want to know the annualized equivalent. Again, the formula remains the same.
- Imagine that in six months your portfolio has grown from € 1,000 to € 1,050.
- Start by calculating the total return: (1,050 - 1,000) /1,000 = 0.05 (a return of 5% in six months).
- If you are interested in knowing what the annualized equivalent interest is (assuming the rate remains the same and considering compound returns), the calculation would be as follows: (1 + 0.05)1/0, 5 - 1 = 10, 25% yield.
- Regardless of the time frame, if you follow the formula above, you will always be able to convert the performance of your investment into annualized returns.
Advice
- Learning to calculate and understand the annualized returns of your portfolio is important, because the annual return is the number used to compare your choices to other investments, as an absolute reference and with your peers. It is very useful for confirming your skill on the stock market and, above all, for identifying any shortcomings in your investment strategy.
- Try the calculations with some example numbers, so you know these equations. With practice, operations will become natural and easy.
- The paradox mentioned at the beginning of the article is purely a reference to the fact that the performance of an investment is usually compared to that of other investments. In other words, a small loss in a shrinking market can be considered a better investment than a small gain in an expanding market. It's all relative.
