# How is Average Rate Of Return calculated?

## Introduction

Average rate of return (ARR) is an important metric used to measure the performance of a given investment. It is calculated by dividing the total expected return of an investment over a specified period of time by the amount invested. This metric provides investors with valuable insight into how their investments are performing and can be used to compare different investments. In this article, we will dive deeper into ARR, discussing how it’s calculated and its importance to investors. We will also provide an example of how ARR is used in practice so that you can better understand this concept. By the end, you should have a strong grasp on what ARR is and why it matters for your portfolio.

## The Meaning of Average Rate Of Return

The average rate of return (ARR) is a measure of the profitability of an investment over time. It is calculated by dividing the total return of the investment by the number of years it was held. The ARR is useful for comparing different investments and for assessing the riskiness of an investment.

The total return of an investment includes any income from the investment, such as interest or dividends, as well as any capital gains or losses from selling the investment. The total return may be positive or negative.

If an investment has a positive ARR, it means that it has generated more money than it would have if it had been invested in a savings account or other low-risk investment. A negative ARR indicates that the investment has lost money.

The ARR is not a perfect measure of profitability, as it does not take into account the timing of cash flows. For example, an investment that generates a 10% return in one year and then loses 10% in the next year would have an ARR of 0%. However, this does not necessarily mean that the investment is break-even; it may still have made or lost money depending on when the cash flows occurred.

Similarly, the ARR does not take into account the reinvestment of earnings, which can impact the overall profitability of an investment. For example, if an investor earns $100 from an initial investment of $1,000 and reinvests those earnings back into

## The Formula for Average Rate Of Return

The average rate of return is the mean of all the periodic returns achieved by an investment over a specified period of time. The formula for calculating the average rate of return is:

Average Rate of Return = (Periodic Return 1 + Periodic Return 2 + … + Periodic Return n) / n

where,

n = number of periods

For example, if an investor earns a 10% return in year 1, a 5% return in year 2, and a -2% return in year 3, then the average rate of return over those three years would be:

((10%+5%-2%)/3) = 4.33%

## How to interpret the Average Rate Of Return

The average rate of return is the mean of all the individual returns over a specified period of time. To calculate it, you first sum up all the individual returns and then divide by the number of periods.

For example, let’s say you have a portfolio with two assets: stock A and stock B. Stock A has a return of 10% in year 1, while stock B has a return of 5%. The average rate of return for your portfolio would be (10% + 5%) / 2, or 7.5%.

There are a few things to keep in mind when interpreting the average rate of return:

1. It’s important to remember that the average is just that – an average. It doesn’t tell you what will happen in any given year, only what has happened on average over time.

2. The longer the time period used to calculate the average, the more accurate it will be. A one-year return isn’t very informative, but a five-year or ten-year return gives you a much better idea of how your portfolio is likely to perform going forward.

3. The average rate of return doesn’t take into account risk. Two portfolios could have identical returns but different levels of risk, and this wouldn’t be reflected in the average. This is why risk should always be considered when making investment decisions.

## An example of how to use the Average Rate Of Return

If you’re wondering how to calculate average rate of return, here’s a quick example. Let’s say you have a portfolio of three stocks with the following annual returns:

Stock A: 10%

Stock B: -5%

Stock C: 20%

To calculate the average rate of return, simply add up the returns for each stock and divide by the number of stocks in the portfolio. In this case, the average rate of return would be (10 + (-5) + 20) / 3, or 8%.

Keep in mind that this is just a simple example – in reality, calculating average rate of return can be quite complex. But this should give you a general idea of how it works.

## Conclusion

In conclusion, the average rate of return is a key metric for assessing an investment’s returns over time. It provides investors with a reliable measure by which to compare different investments and assess their performance. Calculating the average rate of return can be complex, but it doesn’t have to be. By understanding the concepts behind it and learning some of the basic formulas associated with it, you’ll be able to calculate this important statistic more easily and make more informed decisions about your investments.