How to Calculate the Rate of Return on a Portfolio

Your investment portfolio is designed to grow over time based on your portfolio objectives. Growth is measured by the rate of return on a portfolio. There are two ways to calculate the rate of return: dollar-weighted, also known as internal rate of return (IRR), and time-weighted. These two methods can produce surprisingly different returns. Both are valid — they just calculate numbers that have different meanings.

For Illustrative and Educational Purposes Only

To better understand the two methods, take the following two investors. Both deposit the same amount of money ($970,000) over the same two years but at different times. John lost money, and Mary came out ahead.

John deposited $100,000 in year 1, then added $870,000 in year 2. He ended up with only $900,000, losing $70,000. 

Mary deposited $870,000 in year 1, then added $100,000 in year 2.  She ended up with $1,107,900, gaining $137,900.

The dollar-weighted return is negative (6.6%) for John, while Mary has a positive return of 7.2%. This makes intuitive sense. The dollar-weighted return is the overall rate the funds have to earn during the time period to result in the ending value. This incorporates the effect of compounding over time. 

Now let’s look at their annualized rates of return under the time-weighted method:

The time-weighted return is positive 8.2% for both John and Mary. That doesn’t seem intuitive – how can that be? John lost $70,000, and yet he has a positive time-weighted return? It is, however, the correct time-weighted return. The return is calculated by measuring gains and losses for each period when cash flows are deposited or withdrawn. 

Here is how the time-weighted return is calculated:

For John

• Take the ending value for Year 1 of $130,000 and divide by the $100,000 deposited. The growth is 1.3 times or a 30% gain for Year 1, the first time period.
• Next, take the Year 2 ending value of $900,000 and divide by $1,000,000, the value at the beginning of Year 2. There is a decline of 0.9 times or a 10% loss.
• Now, average and annualize these two returns as follows: multiply the 1.3 times gain from the first time period by the 0.9 times decline for the second time period, and the result is a 1.17 times gain, or a 17% gain, for the two-year period.
• Lastly, divide this gain by two and round to 8.2% annualized. 

For Mary

• Take the ending value for Year 1 of $1,131,000 divided by $870,000 deposited. The growth is 1.3 times or a 30% gain for Year 1, the first time period. 
• Next, take the Year 2 ending value of $1,107,900 and divide by the $1,231,000, the value at the beginning of Year 2. There is a decline of 0.9 or a 10% loss. 
• Already you can see their calculated gains and losses are the same!
• To annualize, do the same math: multiply the 1.3 times in gain in Year 1 by the 0.9 times decline in Year 2 for a 1.17 times gain or a 17% gain for the two-year time period. Then, divide by two and round to 8.2%.

John made his big deposit after the investment earned 30%. So, he earned 30%, but only on a small deposit. The dollar-weighted return will be different than the return reported by the investment whenever the investor deposits or withdraws money during the year. Thus, this method of measuring returns is not a good one to use when comparing results to benchmarks or mutual fund investments. John’s poor dollar-weighted return had more to do with the timing of his deposits than the performance of the underlying investments themselves.

How then should an investor evaluate these two different rates of return? If an investor doesn’t add or withdraw money during the measurement period, the dollar-weighted return will be identical to the time-weighted return. Problem solved? Not really, since there will typically be inflows and outflows of cash in the real world.

The time-weighted return is the recommended and widely accepted method for reporting performance on professionally managed portfolios. And, it is the required method when performance is advertised. This method excludes the fortunate or unfortunate impact of investor cash flows from its measurement.

Resource Consulting Group (RCG) utilizes time-weighted rates for performance reports, as prescribed by our industry. We discuss this time-weighted approach in the disclosure at the end of your client quarterly reports. However, money management programs like Quicken calculate the dollar-weighted return on investments.

As always, your RCG advisor is here to guide you on your portfolio objectives and address your rate of return questions.

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