什么是年回报率？

What is annual rate of return?

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Annual rate of return refers to the return on an investment over a certain period of time, usually expressed as a time-weighted annual percentage. Sources of returns can include dividends, capital returns and capital appreciation. The annual return is measured relative to the original amount invested and represents a geometric mean rather than a simple arithmetic mean.

Main points

• Annual return or annualized return is a measure of how much an investment increases on average each year over a specific period of time.
• Annualized returns are calculated using the geometric mean, showing the effect of compounding on annual returns.
• Annual returns are more useful than simple returns when one wishes to observe how an investment performs over time or to compare the performance of two investments.
• Annual returns can be applied to a variety of assets, including stocks, bonds, mutual funds, ETFs, commodities and certain derivatives.

Understand the annual rate of return

Annual returns apply to a variety of assets, including stocks, bonds, funds, commodities and certain types of derivatives. It is the de facto standard method for comparing the performance of liquid investments. This method is considered more accurate because it takes into account adjustments for compound interest. Different asset classes typically have different annual returns.

Annual return on stocks

Annual return, also known as annualized return, represents the increase in a stock's value over a specific period. The information required for the calculation includes the stock's current price and purchase price. If a stock split occurs, the purchase price will need to be adjusted accordingly. After determining the price, first calculate the simple return percentage and then annualize it.

Simple return is calculated as the current price minus the purchase price, divided by the purchase price.

Annual return calculation example

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Suppose an investor buys a stock on January 1, 2024 for $20 and sells it on January 1, 2029 for$35, making a profit of $15. The investor also received a total of$2 in dividends over the five-year holding period. The investor's total return over five years is $17, equivalent to 85% of the initial investment (17/20).

To achieve an 85% return over five years, the required annual rate of return can be calculated using the compound annual growth rate (CAGR) formula:

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Annualized returns, unlike typical averages, truly reflect an investment's gains or losses, while also showing the difficulty of making up for losses. If the initial investment loses 50%, a 100% gain will be needed in the next year to make up the difference. The annualized rate of return helps balance investment results for better comparisons, since possible gains and losses can vary widely.

Note: Annual return statistics are often quoted in promotional materials for mutual funds, ETFs, and other individual securities.

Annual rate of return for 401(k) account

The methods vary when calculating a 401(k) account's annual return in a given year. First you need to calculate the total return. The initial and final values ​​for the observation period need to be determined. Any account contributions during this period must be deducted from the final value for subsequent calculations.

After determining the adjusted final value, divide it by the initial balance. Then subtract 1 from the result and multiply that number by 100 to calculate the percentage of total return.

What is the modified Dietz formula?

The modified Dietz formula is a method of calculating annual returns that takes into account cash flow. It compounds returns during each period.

Are there any other ways to calculate annual returns?

You can calculate the return on a monthly basis and then multiply the result by 12 to get the annual return. There are many calculators online that can do these calculations for you.

How to calculate the overall return on investment?

Return on investment (ROI) is calculated by subtracting an investment's initial cost from its final value and dividing the result by the investment's total cost, including fees, commissions, and markups. Then multiply that result by 100 to get the percentage.

Conclusion

Calculating your annual rate of return reflects your profit or loss on a specific investment. For investors looking to capture growth in stocks, bonds or mutual funds, this metric is critical and can be used to compare the performance of liquid investments.

If you are not sure whether you have calculated your annual rate of return correctly, it is recommended to consult a professional so you can plan your next investment decision.

References

[1] TIAA.org. "All FAQs About Personal Rate of Return."

[2] CFI Education. "Annual Return."

[3] TIAA. "All FAQs About Personal Rate of Return."

[4] Investor.gov. "Annual Return."

About TheQuantHackers

TheQuantHackers is a cutting-edge community composed of a group of people from the world's top universities and quantitative finance practitioners, dedicated to exploring the infinite possibilities in the fields of artificial intelligence (AI) and quantification (Quant). Our team members come from world-renowned universities such as the University of Cambridge, Oxford University, Harvard University, ETH Zurich, Peking University, and the University of Science and Technology of China. Our external consultants come from first-class companies such as Microsoft, HSBC, Citadel, Man Group, Citi, Jump Trading, and top domestic private equity companies.$\begin{aligned} &\text{CAGR} = \left ( \left ( \frac{ \text{结束值} }{ \text{开始值} } \right ) ^ \frac 1 { \text{年数} } \right ) - 1 \\ &\textbf{其中:} \\ &\text{CAGR} = \text{复合年增长率} \\ &\text{年数} = \text{持有期（年）} \\ \end{aligned}$

假设某位投资者在2024年1月1日以20美元的价格购买了一只股票，并在2029年1月1日以35美元的价格出售，从中获得15美元的利润。在五年的持有期内，该投资者还获得了总计2美元的股息。该投资者在五年内的总回报为17美元，相当于初始投资的85%（17/20）。

为了在五年内实现85%的回报率，所需的年回报率可以通过复合年增长率（CAGR）公式计算：

$\begin{aligned} &\left ( \left ( \frac { 37 }{ 20 } \right ) ^ \frac 1 { 5 } \right ) - 1 = 13.1\% \text{ 年回报率} \\ \end{aligned}$ 年回报率是指投资在一定时间内所带来的回报，通常以时间加权的年百分比表示。回报的来源可以包括股息、资本回报和资本增值。年回报率是相对于投资的最初金额进行衡量，代表几何平均值，而非简单的算术平均值。

主要要点

• 年回报率或年化回报率是衡量投资在特定时期内平均每年增加多少的指标。
• 年化回报率是通过几何平均数计算得出的，显示年回报的复利效果。
• 当希望观察投资随时间表现或比较两个投资的表现时，年回报率比简单回报更为有用。
• 年回报率可以适用于多种资产，包括股票、债券、共同基金、ETF、商品及某些衍生品。

理解年回报率

年回报率适用于各种资产，包括股票、债券、基金、商品和某些类型的衍生品。它是比较流动性投资表现的事实标准方法。此方法被认为更准确，因为它考虑了复利的调整。不同的资产类别通常会有不同的年回报率。

股票的年回报率

年回报率也称为年化回报率，表示股票在特定期间内价值的增加。计算所需的信息包括股票的当前价格和购买价格。如果发生过拆股，购买价格需进行相应的调整。在确定价格后，首先计算简单回报百分比，然后再进行年化处理。

简单回报的计算公式为当前价格减去购买价格，再除以购买价格。

年回报率计算示例