27 May 2024

Knowing your Rate of Return (RoR) allows you to assess the effectiveness of your investments, compare the performance of different assets or strategies, and plan for your financial future. By accurately calculating your gains and losses, you can make informed decisions about optimizing your portfolio, set realistic goals for yourself, and achieve your desired financial outcomes.

This article will explore various methods to calculate portfolio performance. It will also discuss the different factors that can impact your bottom-line. It doesn’t matter if you plan to do the math yourself or use one of the dozen tools out there. You will understand what’s behind the numbers and when it’s best to use them.

It's pretty long and in-depth, so feel free to jump between sections in any order. There's no story here, just knowledge and formulas :)

For personal investments, you can use the following rate of return calculation methods:

**Single asset: ROI vs CAGR**

**More than one asset: Money Weighted vs Time Weighted Return**

👉 **Whenever you can, use Total MWR/IRR as it’s the best metric for individuals and works in most scenarios **👈

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It's important to note that many financial apps and brokerage platforms do not specify how they calculate the rates you see, which can lead to wildly different results across different systems. It's advisable to seek platforms that provide transparency in their calculations or consistently compare your results within the same system.

Simple Return on Investment (ROI) is the simplest way to see how much you've gained compared to what you've invested over time.

`Simple ROI = ((All Revenue + Current Value) / (All Expenses + Starting Value)) - 1`

Where:

`All Revenue`

is the total amount received from selling assets or receiving dividends.`Current Value`

is the current market value of your open positions.`All Expenses`

is the total amount spent on acquiring assets.`Starting Value`

is the value of your portfolio at the beginning of the evaluation period.

Simple ROI is best used when you evaluate a single position don't reinvest dividends or make changes over time.

For example, let's say you invested $10,000 in a stock at the beginning of the year, and by the end of the year, your investment is worth $12,000. Using the Simple ROI formula, your return would be:

`Simple ROI = (($0 + $12,000) / ($10,000 + $0)) - 1 = 0.20 or 20%`

However, Simple ROI has many limitations. It disregards the timing of your cash flows and will double-count the same amount of money if you sell an asset to buy a different one.

Consider the following scenario: You initially invest $10,000 in Stock A, which grows to $12,000. You then sell Stock A and use that $12,000 to buy Stock B. By the end of the year, Stock B is worth $14,000. The Simple ROI calculation would be:

`Simple ROI = (($12,000 + $14,000) / ($10,000 + $12,000 + $0)) - 1 = 0.1818... or 18%`

This result is misleading because it counts the $10,000 used to buy Stock A twice. The real gain should be based on the initial $10,000 investment growing to $14,000, which would be:

`Actual ROI = (($0 + $14,000) / ($10,000 + $0)) - 1 = 0.40 or 40%`

But to know that, you need to track where the money originated from. For example, by including only the money you've transferred in & out of the portfolio.

If you would not sell the Stock A, but only buy $10,000 more of it, then your gain from the initial buy would be slashed in half, as you have $22,000 of current value and $20,000 of inflows

🤔#### Where to use ROI?

As illustrated, simple ROI can give a misleading picture of your rate if you do certain types of trades, even occasionally. Yet, if you track only a single position, or track cash movements, ROI may be good and simple way to track your return.

Compound Annual Growth Rate (CAGR) shows the average yearly growth of an investment over a set period, assuming all gains are reinvested. Unlike Simple ROI, which looks at total return, CAGR considers the compounding effect over time, making it an annualized Return on Investment.

`CAGR = (Ending Value / Beginning Value)^(1 / n) - 1`

Where:

`Ending Value`

is the value of your investment at the end of the period.`Beginning Value`

is the value of your investment at the start of the period.`n`

is the number of years between the beginning and end of the period.

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Ending value will include cash flows that occurred within the time period. In other words, whenever you add or remove money, you impact the CAGR.

If you already have RoR calculated, you can annualize it with the following formula:

`CAGR = (RoR + 1)^(1 / Years) - 1`

When annualizing periods counted in days not years, you can use this instead:

`CAGR = (RoR + 1)^(365.25 / Days)`

🤔#### When to use CAGR?

It's best suited to compare single positions with different holding periods, as it gives you the average annual return.

However, it's still not suitable for assessing performance of portfolios. The same as ROI, it completely discards the timing of transactions, assuming the growth-rate to be constant and always from day-one.

Time Weighted Return is a way to calculate investment performance that ignores the effects of cash inflows and outflows. It focuses only on how well the investments themselves are performing. This makes TWR useful for evaluating an investment strategy because it shows the returns from the assets alone, without considering when or how much money was added or removed.

**Divide the Period**: Split the total evaluation period into smaller sub-periods based on when cash inflows or outflows occurred.**Calculate Sub-period Returns**: For each sub-period, use the formula:`Rn = (Ending Value - (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)`

`R1, R2, ..., Rn`

: Return for each sub-period.`Ending Value`

: Portfolio value at the end of the sub-period.`Beginning Value`

: Portfolio value at the start of the sub-period.`Cash Flow`

: Net cash added or removed during the sub-period.

🦉#### Cashflows at the beginning or end of period

The above formula assumes that the cash flow happens at the beginning of the period, meaning you buy the asset and then observe its growth by the end of the period.

However, if the cash flow happens at the end of the period, the formula changes to:

`Rn = (Ending Value - Cash Flow - Beginning Value) / Beginning Value`

**Link Sub-period Returns**: Combine the result from each sub-period using this formula:`TWR = [(1 + R1) * (1 + R2) ... * (1 + Rn)] - 1`

🦉#### TWR < -100% when cash flow is bigger than value

Including fees in cash flows can make your Time-Weighted Return (TWR) negative. If your investment grows afterward, the TWR can drop even more due to the geometric link between periods.

To fix this, restart the TWR calculation whenever

`Rn`

goes below 0, treating it as a new initial investment. Present the resulting rates separately or add them together.

Dividends are a key part of the returns from an asset. By including them in cach flows, we remove their effect from TWR. To include them in returns, adjust the ending value by the amount of received dividends. The formula for a sub-period would be:

`Rn = (Ending Value + Dividends - (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)`

You can do the same for fees by subtracting them from the ending value.

Sometime you might buy or sell the asset at a discount or premium, for example when exercising stock options. This includes any fees you might pay as well. Using this value as Cash Flow will reflect them in the return. To completely remove this impact, you can use Market Price * Quantity for the cashflow - the market value that flows in or out instead. In other words:

`Sub-period Return = (Market Value Before Current Cash Flow / Market Value After Last Cash Flow) - 1`

🤔#### When to use TWR?

TWR is ideal for assessing the performance of your asset selection and allocation strategy. It's especially useful for comparing different portfolios or investment managers, as it removes the effects of cash flows that they can't control.

**Key points**

If you own a single asset, TWR will equal the asset's market price movement and won't include your timing or position size.

If there are more assets, TWR will reflect changes in the allocation balance between them.

Money Weighted Return is a performance metric that takes into account the timing and size of cash flows in and out of an investment portfolio. It gives you a rate that is easy to relate to, as it’s like the interest rate you’d earn on a deposit account with the same cash flow pattern.

Imagine you have a deposit account. You transfer the same amount of money in or out whenever you buy or sell an asset in your investment portfolio. MWR is the fixed interest rate this hypothetical account would need to match your actual investment performance.

🧐#### Is IRR the same as MWR?

Money Weighted Return (MWR) is sometimes referred to as Internal Rate of Return (IRR). IRR is a broader financial metric used to assess the profitability of investments or projects. Because IRR is a more well-known concept, many platforms will present your returns as IRR.

Most of the time, MWR/IRR is annualized, which means it represents the average annual return over the investment period. Annualized MWR is particularly useful for comparing investments over longer periods or with different holding periods.

😵💫#### Annualizing periods below one year

When annualizing returns over short time periods, such as a month, the resulting figure may be overly inflated. This is because it assumes that your monthly return (which can be quite high or low during times of market volatility) remains constant every month of the year and compounds over time.

Calculating MWR is not easy and requires trial-and-error to do it accurately. It’s not something you would do by hand, but spreadsheet programs like Excel and Google Sheets have a function called `XIRR`

. To use it, you need:

table of your cash flows and their dates

include the value of your assets at the beginning of the period in the cash flows of the first day (as if you bought them that day at the date’s market price)

include the value of your assets at the end of the period in the cash flows of the last day (as if you sold them that day at market price).

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You can access the Google Spreadsheet with formulas here

MWR is the most recommended calculation method for private investments. It enables you to assess your performance as an investor, as it takes into account how your actions affected the returns, apart from the market.

By comparing MWR vs TWR you can see the impact of your timing, cash flows or fees. The bigger the difference between the rates - the bigger the impact. Just remember, that TWR is usually not annualized and MWR is!

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It's probably the best metric to measure performance of private investments, but it's also the most expensive to calculate. Therefore some tools may opt for simplified calculation methods, which can still be labeled as MWR, but may give you highly inaccurate results in suboptimal cases. This is where the most differences between the numbers come from.

When you have a complex, highly volatile portfolio, it can be very hard or impossible to find a valid number. In those cases, the tools you use might give you a wrong result or no number at all. (e.g., Excel will return an error).

In general, IRR is expensive to calculate and there are many different ways to do it. Each tool will use a different one, and some of them may give highly inaccurate results in suboptimal cases. When numbers from two different tools don't match, always check if the dollar amount is roughly the same.

IRR and ROI are different in one key way: IRR considers the time your money was invested, while ROI does not. This difference is not necessarily good or bad.

In some cases, you may want to know your total gains from all the money invested over a period. For example, if you did Dollar Cost Averaging, you can compare Simple ROI to TWR to know what your results would be if you invested everything on day one.

However, most of the time, you need a number that allows you to compare investments realistically. For this purpose, IRR (or TWR) is the better choice.

When evaluating your investment performance, consider more than just the raw returns. Other factors can impact your bottom line and should be considered when making investment decisions.

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Each Rate of Return calculation method mentioned above can be used to include these components.

Price Return represent the simple increase or decrease in the value of your investments based on it's price. They don't include any additional cashflows incurred or generated by the assets.

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The Management Fees for Funds and Toal Expense Ratio for ETFs are already included in the Price Rate.

Nominał Return includes the price movement and any regular income generated by the asset like dividends, interest or rent.

Total Return includes Price Return, dividends, interest, fees or any other expenses and revenues.

To calculate total return, include these additional cash flows on the dates they occurred.

☝️#### Comparing with benchmarks

It's worth noting that many benchmarks, such as the S&P 500 or the FTSE 100, are reported in price terms - without dividends. They also don't account for taxes, fees or inflation. When comparing your portfolio's performance to these benchmarks, it's essential to understand the limitations of the comparison.

Sometimes it's useful to see how much you're losing to fees and taxes, and thus be motivated to minimize them. Another time you may want to check how well your ETFs are tracking the underlying index. It's best if your tool give you a choice of different Rates of Return.

Taxes can have a substantial effect on your investment returns. You may be subject to various forms of taxation, depending on your jurisdiction and investment account type. They affect you at different stages:

Taxes already paid or withheld by the broker

Taxes on realized gains that you're due to pay in the future

Potential taxes you would owe on unrealized gains - as if you had to liquidate all your holdings at current market value

After-tax Return typically include the Tax Paid. If the tool can calculate your due taxes, it's best to include them as well, as they're your future liability.

Unrealized After-tax Return (or Potential After-tax Return) would include all three kinds of tax. It's good to know this number, because it keeps your returns close to reality. But as unrealized gains are only “on paper”, you should definitely track them separately.

To calculate After-tax Return:

Add the Tax Paid as a negative cashflow when it occurs.

Add the Tax Due and Unrealized Tax as negative cashflows at the end of the calculation period. Since they haven't been paid yet, they decrease your investment's current value.

Real Return take inflation into account and show you the actual purchasing power of your investment gains. To calculate it, you divide your return rate (nominal, total or after-tax) by the inflation rate, like this:

`Real RoR = (1 + RoR) / (1 + Inflation Rate) - 1`

For example, if your portfolio has a Total Return of 8% and the inflation rate is 2%, your real return would be approximately 5.88% (1.08 / 1.02 - 1). This means that while your investments grew by 8%, your purchasing power only increased by 5.9% after accounting for inflation.

If your portfolio has different currencies, it's good to see how currency exposure impacts your return.

**Capital Return**is the profit made from the assets in their original currencies. It excludes any effects from currency exchange rate changes.**Currency Return**is the profit or loss made solely from the changes in currency exchange rates. It excludes capital return.

To calculate both returns, follow these steps:

Choose a single Base Currency.

**Calculate Total Return in the Base Currency.**Convert all cash flows into the base currency using the FX rates from the dates the cash flows occurred. Then, calculate the total return as usual.**Calculate Capital Return.**It's the same as Total Return, but you use the FX rate from a single day - ideally when each position was opened or the first day of the calculation period. Calculate the return based on these converted values.**Calculate Currency Return**by subtracting the Capital Returns from the Total Returns. This will isolate the Currency Returns in the base currency.

This method works for both the Return amount ($) and the Rate of Return (%).

Let's illustrate the differences between different methods of calculating investment returns. We have an example portfolio with the following transactions:

**January 2020**: Purchased Asset for $10,000.**January 2021**: Our Asset is now worth $14,000. We sell 50% of it for $7,000 and keep the rest.**January 2022**: Our Asset is now worth $10,000 (up from $7k). We buy $5,000 worth of the asset at a 20% discount, so we spend just $4,000 on it. We now have $15,000 worth of the Asset.**January 2023**: Our Asset is now valued at just $10,000 (down from $15k) and we keep the position open.

Let's see what are the different rate of returns and how they’re calculated:

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You can access the Google Spreadsheet with formulas here

They’re pretty wildly different, right? Please note, that we start and end with $10,000, but we still have $3,000 in our pocket from the sale in 2021. This means, we have a 30% total return from our initial investment, ~9% annual, but none of the methods gave us that number!

When calculating investment returns, there's no one-size-fits-all method. Each calculation has its strengths and is suitable for different scenarios.

As a rule of thumb:

Money Weighted Return (MWR) / Internal Rate of Return (IRR) is often the best choice to measure individual portfolio performance

Time Weighted Return (TWR) is a great choice to compare investment strategies and different asset allocations

Simple Return or CAGR are suitable for single positions or buy & hold portfolios with limited activity

Include fees, taxes, and inflation to assess returns from your perspective, but do not use them when comparing with benchmarks. Unless you need to (de)motivate yourself ;)

Whenever possible, choose a tool that allows you to check more than one kind of Rate of Return.

Many tools and investors commonly use inaccurate names for the figures they present, because terms like "CAGR" or "IRR" are shorter than "Annualized Total Money Weighted Return". Generally, you can assume the following:

"Returns" usually refer to a simple Total ROI or CAGR, but can be anything really.

"IRR" often means a variant of Total MWR, typically annualized, unless there is "IRR p.a." or "Annualized IRR" somewhere as well.

Post-tax or Real returns are more complex and rarely seen, thus they are often described precisely. Otherwise, don't assume the return you see is adjusted for tax or inflation.

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Remember that many factors influence returns. Expect performance metrics reported by various tools to be different. And always verify what they actually include.

You can calculate your returns yourself using spreadsheets. But remember, that accurate calculation of RoR requires record-keeping of all cash flows. This is manageable with a few transactions but becomes complex and error-prone with higher trading activity.

ROI and CAGR are fool-proof, but can be used reliably only in handful of scenarios and limited time frames.

🧠#### Recommended tool

If you want an easy-to-use solution, try **Capitally**. It supports all the calculation methods mentioned in this article. It also lets you choose what to include in your returns, like fees or taxes (paid, due and potential). In the future, it will include real returns as well.

I hope this article helps explain how to calculate investment performance. If you have any questions or comments, feel free to ask on our community forum.

Rafał Lindemann

Capitally Founder