LoadingLoading
Compound annual growth rate refers to the rate of return an investment needs to earn each year in order to grow from an initial balance to a final balance over a given interval of time.
Compound annual growth rate refers to the rate of return an investment needs to earn each year in order to grow from an initial balance to a final balance over a given interval of time. CAGR assumes that all profits are reinvested at the end of each period of the investment's life.
To calculate the CAGR of an investment:
The CAGR formula gives an annualized rate of return, which is useful for comparing the performance of different investments over time.
The compound annual growth rate is not a true rate of return, but a representative number. It essentially describes at what rate an investment will grow if it grows at the same rate each year, with profits reinvested at the end of each year. For stock market investors, this is especially useful for comparing the performance of different stocks. CAGR does not take into account the discount rate, which is critical when assessing the present value of future returns.
In reality, such sustained performance is unlikely. However, CAGR can be used to smooth returns, making them easier to understand and compare to other methods.
Let's say you invest in a portfolio
<!-- @@@ -->13,000 (30% increase in first year).
19,000 (35.71% increase from January 2020 to January 2021).
We can see that on an annual basis, the annual growth rates of the portfolios vary widely, as shown in parentheses.
CAGR, on the other hand, smooths out an investment's performance and ignores the huge differences between 2018 and 2020 and 2019. The CAGR during this period was 23.86% and can be calculated as follows:
<!-- @@@ -->10,000}\right )^{\frac{1}{3}}-1\times100=23.86% $$
The 23.86% CAGR over a three-year investment period can help investors compare different investment options or predict future value. For example, suppose an investor is comparing the performance of two unrelated investments.
In any year during that time, one investment may grow while another declines. This might happen when comparing high-yield bonds to stocks, or real estate investing to emerging markets. Using CAGR will smooth the annual returns over the entire period, making the two options easier to compare.
As another example, suppose an investor buys
<!-- @@@ -->64,900. Three years later, in December 2020, the stock price rose to
<!-- @@@ -->176,000. [1] What is the CAGR?
Using the CAGR formula, we know we need:
64,900
So to calculate the CAGR for this simple example, we enter the data into the formula as follows: [(
<!-- @@@ -->64,900) ^ (1/3)] - 1 = 39.5%.
CAGR can be used to calculate the average growth rate of an individual investment. As we saw in the example above, an investment's annual growth rate can appear erratic and uneven due to market fluctuations.
For example, an investment might grow by 8% one year, decline by -2% the next, and grow by another 5% the next. CAGR helps smooth returns when expected growth rates are volatile and inconsistent.
The geometric mean generated by CAGR can be used to compare different types of investments with each other. For example, suppose in 2015 an investor would
<!-- @@@ -->10,000 into a stock mutual fund. Equity fund returns will be uneven over the next few years, so comparing the two investments will be difficult.
Assume that at the end of five years, the balance in the savings account is
<!-- @@@ -->15,348.52. Using CAGR to compare these two investments can help investors understand the difference in returns:
<!-- @@@ -->10,000} \right )^{\frac{1}{5}}-1 \times 100= 1.00% $$
and:
<!-- @@@ -->10,000} \right )^{\frac{1}{5}}-1 \times 100= 8.95% $$
On the face of it, equity funds appear to be a better investment, with returns almost nine times greater than savings accounts. On the other hand, one drawback of CAGR is that by smoothing returns, CAGR cannot tell investors how volatile or risky a stock fund is. However, CAGR can be used in the MAR ratio to adjust for risk. Combining CAGR with metrics like net present value (NPV) can provide a more complete picture of an investment's potential.
CAGR can also be used to track the performance of one or more companies on various business metrics. For example, over a five-year period, a big box store's market share CAGR was 1.82%, but over the same period, its customer satisfaction CAGR was -0.58%. In this way, comparing the CAGR of various metrics within a company can reveal their respective strengths and weaknesses.
Comparing the CAGR of business activities of similar companies will help assess the relative merits of the competition. For example, Big Sales' customer satisfaction CAGR may be much better than Superfast Cable's -6.31% customer satisfaction CAGR over the same period.
Understanding the formula used to calculate CAGR is an introduction to the many other ways investors can evaluate past returns or estimate future profits. This formula can be worked out algebraically as a formula to calculate the present or future value of money, or to calculate a minimum hurdle rate for returns.
For example, say an investor knows they need
<!-- @@@ -->15,000 available for investment. So, what is the average rate of return they need to achieve this goal? The CAGR calculation can be used to find the answer to this question as follows:
<!-- @@@ -->15,000} \right )^{\frac{1}{18}}-1 \times 100= 6.90% $$
This version of the CAGR formula is just a rearranged present value and future value equation. For example, if an investor knows they need
<!-- @@@ -->10,000 and the CAGR of an investment sold on September 9, 2018 for $16,897.14.
Before performing a CAGR calculation, investors need to know the fractional remainder of the holding period. They held the position for 213 days in 2013, one year each in 2014, 2015, 2016 and 2017, and then 251 days in 2018. The investment is held for a total of 5.271 years, calculated as follows:
The investment was held for a total of 1,924 days. To calculate the number of years, divide the total number of days by 365 (1,924/365), giving you 5.271 years.
The total number of years the investment has been held can be put into the index denominator of the CAGR formula as follows:
<!-- @@@ -->10,000} \right )^{\frac{1}{5.271}}-1 \times 100= 10.46% $$
The most important limitation of CAGR is that because it calculates a smoothed growth rate over a period, it ignores volatility and implies that growth over that period is stable. Returns on investments are uneven over time, unless they are held to maturity in bonds, deposits, or similar investments.
Additionally, CAGR does not take into account when investors add funds to or withdraw funds from the portfolio during the measurement period.
For example, if an investor holds a portfolio for five years and injects money into the portfolio during that time, the CAGR will inflate. CAGR would calculate the rate of return based on the starting and ending balances over five years and would essentially treat the money deposited as part of the annual growth rate, which would be inaccurate.
In addition to the limitations of smooth growth rates, CAGR has other limitations. When evaluating investments, a second limitation is that no matter how stable a company or investment's growth has been in the past, investors cannot assume that growth rates will remain the same in the future. The shorter the time frame used for analysis, the less likely it is that the CAGR achieved by historical results will match the expected CAGR.
The third limitation concerns representational limitations. Assume that an investment fund in 2016 was worth
<!-- @@@ -->71,000 in 2018
<!-- @@@ -->81,000, and $126,000 in 2020. If a fund manager were to claim in 2021 that their CAGR over the past three years was an astonishing 42.01%, that might technically be correct. However, they'll be missing some important information, like the fact that the fund's CAGR over the past five years was just 4.73%.
CAGR measures the return on an investment over a certain period of time. Internal rate of return (IRR) also measures an investment's performance but is more flexible than CAGR.
The most important difference is that CAGR is relatively simple and can be calculated manually. In contrast, more complex investments and projects, or investments with very large cash flows in and out, are best evaluated using IRR. The best tools for using IRR include financial calculators, Excel, or a portfolio accounting system.
Those interested in a deeper understanding of CAGR and other financial topics may consider taking one of the best investing courses currently available.
CAGR is a measurement tool used by investors to calculate the rate at which a quantity grows over time. The word "compound" indicates that CAGR takes into account the effect of compounding or reinvestment over time. For example, let's say you have a company that grows from 30 million in revenue over the course of 10 years. In this case, the CAGR is approximately 25.89%.
The key difference between CAGR and growth rate is that CAGR assumes that growth rates "repeate" or "compound" every year, while traditional growth rates do not. Many investors prefer to use CAGR because it smooths out the volatility of the annual growth rate. For example, even a successful company that performs extremely well may still experience a few underperforming years over the course of its growth. These bad years can have a significant impact on the individual year's growth rate, but have a relatively small impact on the company's CAGR.
Can. A negative CAGR would represent losses over time, not gains.
To compare the performance and risk characteristics between various investment options, investors can use risk-adjusted CAGR. A simple way to calculate risk-adjusted CAGR is to multiply the CAGR by (1-) the investment's standard deviation. If the standard deviation (i.e., risk) is zero, the risk-adjusted CAGR is unaffected. The larger the standard deviation, the lower the risk-adjusted CAGR.
CAGR is a valuable metric for investors to evaluate the performance of their investments over time. By smoothing annual returns, it provides a clearer view of an investment's growth trajectory. However, while CAGR can help compare different investments and predict future value, it does not account for volatility or risk. Investors should use CAGR in conjunction with other metrics to make informed decisions while understanding its limitations in providing a complete picture of an investment's performance.
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.
[1] Yahoo Finance. “Amazon.com, Inc. (AMZN) Historical Data.”
要计算一项投资的 CAGR：
CAGR 公式给出了一个年化的回报率，这对于比较不同投资随时间的表现非常有用。
复合年增长率并不是一个真实的回报率，而是一个代表性的数字。它本质上描述了如果投资每年以相同的速度增长，并且在每年末将获利再投资，则投资将以何种速度增长。对于股市投资者来说，这对于比较不同股票的表现尤其有用。CAGR 并不考虑折现率，而折现率在评估未来回报的现值时至关重要。
实际上，这种持续的表现是不太可能出现的。然而，CAGR 可以用来平滑回报，使其更易于理解并与其他方法进行比较。
假设你在一个投资组合中投资了 $10,000，回报情况如下：
$14,000（从2019年1月到2020年1月增长7.69%）。
我们可以看到，按年计算，投资组合的年增长率差别很大，如括号中所示。
另一方面，复合年增长率平滑了投资的表现，忽略了2018年和2020年与2019年之间的巨大差异。在此期间的 CAGR 为 23.86%，可以按如下公式计算：
$$ CAGR=\left(\frac{$19,000}{$10,000}\right )^{\frac{1}{3}}-1\times100=23.86% $$$19,000}{$
要计算一项投资的 CAGR：
CAGR 公式给出了一个年化的回报率，这对于比较不同投资随时间的表现非常有用。
复合年增长率并不是一个真实的回报率，而是一个代表性的数字。它本质上描述了如果投资每年以相同的速度增长，并且在每年末将获利再投资，则投资将以何种速度增长。对于股市投资者来说，这对于比较不同股票的表现尤其有用。CAGR 并不考虑折现率，而折现率在评估未来回报的现值时至关重要。
实际上，这种持续的表现是不太可能出现的。然而，CAGR 可以用来平滑回报，使其更易于理解并与其他方法进行比较。
假设你在一个投资组合中投资了 64,900。三年后，到2020年12月，股价上涨至每股 13,000（第一年增长30%）。
因此要计算这个简单示例的 CAGR，我们将数据输入公式如下：[(19,000（从2020年1月到2021年1月增长35.71%）。
我们可以看到，按年计算，投资组合的年增长率差别很大，如括号中所示。
另一方面，复合年增长率平滑了投资的表现，忽略了2018年和2020年与2019年之间的巨大差异。在此期间的 CAGR 为 23.86%，可以按如下公式计算：
10,000 投入一个股票共同基金。股票基金在接下来的几年回报将是不均匀的，因此比较这两项投资将会很困难。
假设在五年末，储蓄账户的余额为 15,348.52。使用 CAGR 比较这两项投资可以帮助投资者了解回报之间的差异：
\text{储蓄账户 CAGR} =\, \left ( \frac{\$ 10,510.10}{\$ 10,000} \right )^{\frac{1}{5}}-1 \times 100= 1.00\% $$$ 10,510.10}{\$10,000}\right )^{\frac{1}{3}}-1\times100=23.86\%
在三年投资期间的23.86% CAGR 可以帮助投资者比较不同的投资选择或预测未来的价值。例如，假设一位投资者正在比较两项无关投资的表现。
在这段时间的任何一年，一项投资可能增长，而另一项投资则可能下跌。这可能发生在比较高收益债券与股票时，或者房地产投资与新兴市场时。使用 CAGR 将平滑整个时期的年回报，使这两种选择更易于比较。
作为另一个例子，假设一位投资者在2017年12月以每股 \text{股票基金 CAGR} =\, \left ( \frac{\$ 15,348.52}{\$ 10,000} \right )^{\frac{1}{5}}-1 \times 100= 8.95\% $$$ 15,348.52}{\$ 10,000} \right )^{\frac{1}{5}}-1 \times 100= 8.95\%
从表面上看，股票基金似乎是更好的投资，其回报几乎是储蓄账户的九倍。另一方面，CAGR 的一个缺点是，通过平滑回报，CAGR 无法告诉投资者股票基金的波动性或风险有多大。然而，CAGR 可以在MAR比率中使用，以调整风险。将 CAGR 与净现值（NPV）等指标结合使用，可以更全面地了解投资的潜力。
CAGR 还可用于跟踪一个或多个公司各种业务指标的表现。例如，在五年期间，大销售商店的市场份额 CAGR 为 1.82%，但在同一期间，其客户满意度 CAGR 为 -0.58%。通过这种方式，比较公司内部各项指标的 CAGR 可以揭示各自的优势和劣势。
比较类似公司的商业活动的 CAGR 将有助于评估竞争的优劣。例如，大销售的客户满意度 CAGR 可能与超级快线电缆在同一时期的 -6.31% 客户满意度 CAGR 相比，好得多。
理解用于计算 CAGR 的公式是投资者评估过去回报或估算未来利润的许多其他方法的入门。该公式可以代数运算为计算货币现值或未来值的公式，或计算回报的最低障碍率。
例如，假设一位投资者知道他们需要 64,900。三年后，到2020年12月，股价上涨至每股 \text{所需回报} =\, \left ( \frac{\$ 50,000}{\$ 15,000} \right )^{\frac{1}{18}}-1 \times 100= 6.90\% $$$ 50,000}{\$ 15,000} \right )^{\frac{1}{18}}-1 \times 100= 6.90\%
这一版本的 CAGR 公式只是一个重新排列的现值和未来值方程。例如，如果一位投资者知道他们需要 $50,000，并且他们认为预计年回报率为 8% 是合理的，他们可以用这个公式找出他们需要投资多少资金以达到其目标。
什么算作好的 CAGR 将取决于具体情况。但一般来说，投资者会通过考虑机会成本和投资风险来评估这一点。例如，如果一家公司在平均 CAGR 接近 30% 的行业中增长了 25%，那么相比之下，其业绩可能显得平平无奇。但是，如果整个行业的增长率较低，如 10% 或 15%，那么该公司的 CAGR 可能非常令人印象深刻。
一般来说，CAGR 越高越好。
投资通常不会在每年的第一天进行，并在最后一天出售。假设有一位投资者希望评估一项在2013年6月1日投资 $176,000。[1] CAGR是多少？
使用CAGR公式，我们知道我们需要：
CAGR 最重要的局限性在于，由于它计算的是一个时期内的平滑增长率，因此忽略了波动性并暗示该时期内的增长是稳定的。投资的回报随着时间的推移而不均匀，除非是持到期的债券、存款等类似投资。
此外，CAGR 也不考虑投资者在测量期间向投资组合追加资金或从中撤回资金的时间。
例如，如果一位投资者在五年内持有一个投资组合，并在此期间向投资组合注入资金，那么 CAGR 就会膨胀。CAGR 会根据五年内的初始余额和结束余额计算回报率，并且基本上会将所存入的资金视为annual growth rate的一部分，这将是不准确的。
除了平滑增长率的局限性外，CAGR 还有其他限制。当评估投资时，第二个限制是，无论一家公司或投资过去的增长有多稳定，投资者不能假设未来的增长率会保持不变。用于分析的时间框架越短，历史结果所实现的 CAGR 越不可能符合预期的 CAGR。
第三个限制是关于代表性的限制。假设一项投资基金在2016年时价值 64,900
因此要计算这个简单示例的 CAGR，我们将数据输入公式如下：[(81,000，以及在2020年时 $126,000。如果基金经理在2021年声称他们的 CAGR 在过去三年达到惊人的 42.01%，从技术上讲这可能是正确的。然而，他们将会遗漏一些重要的信息，比如该基金在过去五年的 CAGR 仅为 4.73%。
CAGR 衡量某项投资在一定时间内的回报。内部回报率（IRR）也衡量投资的表现，但比 CAGR 更灵活。
最重要的区别在于 CAGR 相对简单，可以手动计算。相比之下，更复杂的投资和项目，或者现金流进出非常多的投资，最好使用 IRR 进行评估。使用 IRR 的最佳工具包括财务计算器、Excel 或投资组合会计系统。
对更深入了解 CAGR 和其他财务主题感兴趣的人，可以考虑参加当前可用的最佳投资课程之一。
CAGR 是投资者用来计算某一数量随时间增长速率的测量工具。“复合”一词表明CAGR 考虑了随时间推移的复利或再投资效应。例如，假设你有一家公司，收入从300万美元增长到3000万美元，时间跨度为10年。在这种情况下，CAGR 约为 25.89%。
CAGR 与增长率之间的主要区别在于，CAGR 假设增长率每年“重复”或“复合”，而传统的增长率则没有。许多投资者更倾向于使用 CAGR，因为它平滑了每年增长率的波动性。例如，即使是表现极佳的成功公司，在其发展过程中可能仍然会经历几个表现不佳的年份。这些糟糕年份可能会对个别年度的增长率产生重大影响，但对公司的 CAGR 影响相对较小。
可以。负的 CAGR 将表示随时间的损失，而非收益。
为了比较各种投资选择之间的表现和风险特性，投资者可以使用风险调整后的 CAGR。计算风险调整后 CAGR 的简单方法是将 CAGR 乘以投资标准差的（1-）。如果标准差（即风险）为零，则风险调整后的 CAGR 不受影响。标准差越大，风险调整后的 CAGR 越低。
CAGR 是投资者评估其投资随时间表现的一个有价值的指标。通过平滑年度回报，它提供了投资增长轨迹的更清晰视图。然而，虽然 CAGR 可以帮助比较不同投资和预测未来价值，但它并不考虑波动性或风险。投资者应将 CAGR 与其他指标结合使用，以便做出明智的决策，同时理解其在反映投资表现全貌时的局限性。
TheQuantHackers是由一群来自世界顶尖高校和量化金融从业人员组成的前沿社区，致力于探索人工智能（AI）与量化（Quant）领域的无限可能。我们的团队成员来自剑桥大学、牛津大学、哈佛大学、苏黎世联邦理工学院、北京大学、中科大等世界知名高校，外部顾问来自Microsoft、HSBC、Citadel、Man Group、Citi、Jump Trading、国内顶尖私募等一流企业。
[1] Yahoo Finance. “Amazon.com, Inc. (AMZN) Historical Data.”
Upgrade to unlock all institutional-grade algorithms, derivative pricing engines, factor backtesting frameworks, and live QuantLab execution.
Explore Membership Access
Pre-order · £490Quantitative analytics platform
Waitlist closed — signal locked. Pre-order TQH TERMINAL now at £490 with launch-day delivery.