The calculation of the annualized portfolio return will answer one question: what is the compound rate of return received from the portfolio over a certain investment period? Although a variety of complex formulas are used to calculate annualized returns, once you understand some of the important concepts, the calculations will be fairly easy to do.
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Part 1 of 2: Understanding the Basics of Calculation
Step 1. Know the key terms
When discussing annual portfolio returns, there are several key terms that come up over and over and should be understood, as follows:
- Annual Return: the total return received on an investment during a given period, including dividends, interest, and capital gains.
- Annualized Return: The annual rate of return that is inferred by extrapolating the returns measured over a period of less or more than one year.
- Average Return: The return received over a given period by taking the total return realized over the long period and spreading it evenly over the shorter period.
- Compounding Return (Compounding Return). Returns that include interest reinvestment returns, dividends and capital gains.
- Period (Period): A specific time span for measuring and calculating returns, for example in daily, monthly, or yearly terms.
- Periodic Return (Periodic Return). The total return on an investment measured over a specific time span.
Step 2. Learn how compounding works
The compounding of investment returns grows from the profits that have been obtained. The longer your money is compounded, the faster it will grow, and the bigger the annual return will be. Think of it like a snowball that expands as it rolls down an iceberg.
- Let's say you invest IDR 100,000 and get 100% return in the first year so that at the end of the first year, your investment balance is IDR 200,000. If you earn only 10% in the second year, that means you earn $20 at the end of the second year.
- However, if you earn 50% yield during the first year, your investment balance at the beginning of the second year is IDR 150,000. The 10% yield in the second year is $15,000 instead of $20,000. The results obtained are 33% less than the first example.
- Furthermore, let's say you lose 50% in the first year, and the investment balance in the first year remains Rp. 50,000. You need to make a 100% return in order to break even (100% of $50 = $50, and $50 + $50 = $100).
- The size and timing of profits play a very important role when considering compound returns and their impact on annualized returns. In other words, annualized returns are not a reliable yardstick to measure actual profit or loss. However, annualized returns are a great tool for comparing different investments against one another.
Step 3. Use time-weighted returns to calculate the compound rate of return
To find the average of things, such as daily rainfall or weight loss, you can use the simple average formula or the arithmetic mean. This technique may have been learned in school. However, the simple average formula does not take into account the impact of each periodic return on the others, or the timing of each return. To obtain an accurate average, the geometric time-weighted return formula is used. (Don't worry, we will guide you in using this formula.)
- The simple average formula cannot be used because all periodic returns are interdependent.
- For example, let's say you want to tabulate an average return on investment of $100 over two years. You earn 100% in the first year (meaning, the investment balance at the end of the first year is IDR 200,000). In the second year, you lose 50% (meaning the remaining investment balance is IDR 100,000 because IDR 200,000 – (IDR 200,000 * 50%) = IDR 100,000). This figure is the same as the initial balance of the first year's investment.
- The simple average formula (arithmetic mean) will simply add up the two returns and divide by the number of periods (in this example 2 years). This result would indicate an average return of 25% per year. However, when you connect the two, it is known that you are actually getting nothing.
Step 4. Calculate the total return amount
First of all, you have to calculate the total return over the calculated time span. For simplicity's sake, this example will ignore deposits and withdrawals made. To calculate the total return, two numbers are needed: the starting and ending values of the portfolio.
- Subtract Final Value from Initial Value.
- Share with your Initial Value. The result is your Return.
- In the case during the period the company loses due to coercion, subtract the ending balance from the beginning balance. Then, divide by the initial balance and assume the result is negative.
- Add addition before division. Thus, you get an overall percentage of the return.
Step 5. Memorize the Total Rate of Return formula in Excel
The formula is Total Return Rate = (Final portfolio value – initial portfolio value)/initial portfolio value. The formula for Compound Rate of Return = POWER(1+Total Rate of Return), (1/year))-1.
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For example, if the initial value of the portfolio was $1,000,000 and the final value seven years later was $2,500,000, the calculation would be as follows:
- Total Return Rate = (2,500,000-1,000,000)/1,000,000 = 1, 5.
- Compound Rate of Return= POWER((1 + 1.5), (1/7))-1 = 0.1398 = 13, 98%.
Part 2 of 2: Calculating Annualized Returns
Step 1. Calculate your annualized return
If the total rate of return has been calculated, plug the result into the following equation: Annualized Return=(1+ Return)1/N-1 The result of this equation corresponds to the annual return on investment over the measured time span.
- In the exponent (rank), the number “1” represents the unit being measured, which is 1 year. If you want to be more specific, you can use “365” to calculate daily returns.
- The letter “N” represents the number of periods being measured. Therefore, if you are calculating returns for 7 years, swap the letter "N" for the number 7.
- For example, let's say that over seven years your portfolio grew from $1,000,000 to $2,500.
- First, calculate the overall return: (Rp 2,500,000-1,000,000)/Rp 1,000,000 = 1.50 (rate of return 150%).
- Next, calculate the annualized return: (1 + 1.50)1/7-1 = 0, 1399=13, 99% annual return!
- Use the normal sequence of mathematical operations: solve the calculations in parentheses first, then raise, and do the subtraction.
Step 2. Calculate the semi-annual (semi-annual) return
Let's say you are looking for a semi-annual rate of return (returns are given twice a year, every six months) over a period of seven years. The formula used remains the same, you only need to adjust the number of periods being measured. The end result is your half yearly return.
- In this case, you have 14 semi-annual periods of seven years.
- First, calculate the overall return: (Rp 2,500,000-Rp 1,000,000)/Rp 1,000,000 = 1.50 (rate of return 150%).
- Next, calculate the annualized return: (1 + 1.50)1/14-1 = 6, 76%.
- You can convert this number to an annual return multiplying by two: 6.76% x 2 = 13.52%.
Step 3. Calculate the annualized equivalent
You can also calculate the annualized equivalent of shorter-period returns. For example, you only have a 6 month return and want to know the annual equivalent. Again, the formula used remains the same.
- Say over a period of 6 months, your portfolio increases from IDR 1,000,000 to IDR 1,050,000.
- Start by calculating your overall return: (Rp1,050,000-Rp1,000,000)/Rp1,000,000=0.05 (5% return over 6 months).
- Now, if you want to know the annualized equivalent figure (assuming this rate of return and compound return continues), the calculation is as follows: (1+0.05)1/0, 50-1=10, 25% annual return.
- Regardless of the time period, if you follow the formula above, your performance can always be converted into an annual return.
Tips
- You need to know and understand how to calculate annualized portfolio returns, because annual returns are numbers that are used to compare yourself with other investments, industry benchmarks and investment monitoring. Annual returns have the power to confirm your stock investment prowess and help uncover potential mistakes in your investment strategy.
- Do an exercise with sample numbers so that you are more familiar with calculating using this formula.
- The paradox mentioned at the beginning of this article is simply an acknowledgment of the fact that investment performance is usually judged against the performance of other investments. In other words, a small loss in a declining market can be considered better than a small gain in an increasing market. Everything is relative.
