The terms risk and return are so common that you would think they are clearly understood. Not so. We tackle investment rates of return first.
Simple, annualized and compound returns.
The rate of return is one of many ways of measuring investment performance.
You start the year with $100 and end the year with $110, your rate of return is 10%. Easy. So easy that this is often referred to as the simple rate of return. The rate of return is a percentage not a dollar value. In the above example the return or investment gain is $10. To understand a rate of return you need to know the period over which the return is measured: typical reporting periods can be a year or less (e.g., one month, one quarter, the year to date (YTD)) or more than a year and decades.
Because the rate of return is a percentage, they are compounded rather than added. This can be illustrated by example. Suppose the rate of return for the first year is 10% and -10% for the second year. Adding the rate of returns would suggest that the return is zero over two years, which is incorrect. If you start with $100 and the rate of return is 10% you end the first year with $110. The rate of return during the second year is -10% so you end the second year with $99 (0.9*110). Over two years the rate of return is not zero but -1%. If this error is repeated over enough periods then over time the value of the investment would shrink to zero, so the difference between compounding and adding rates of return is important.
It is frequently convenient to compare returns over different periods. For example, consider investments A and B in the table below. There are 3 years of annual return data for A and 5 years for B. Computing the annualized return for each allows us to compare the performance of A and B. The annualized return for investment A is 5% which means that compounding a 5% return each year for 3 years is the cumulative rate of return over 3 years[1].
| Investment | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| A | 1.1% | 8.0% | 6.0% | | |
| B | 3.1% | 6.0% | 7.0% | 3.0% | 6.0% |
In other words, the annualized return gives an average annual return. The annualized return for Investment B is also 5% over the 5 years.
To see these ideas in action, consider the performance of the Vanguard exchange traded fund (ETF), VBAL.
| | Month End | Year to Date | 1 Year | 3 Year | 5 Year | Since Inception |
| VBAL | 1.52% | 4.92% | -2.30% | 8.07% | 4.87% | 4.39% |
The data period is given as ending 31 March 2023, so the Month End return is a simple rate of return for March 2023. The Year to Date rate of return is a compounded monthly rate of return for the first 3 months of 2023. The 1 Year return is the compounded monthly rate of return for the 12 months ending 31 March 2023. The 3 and 5 year returns are annualized returns. Finally, the Since Inception return is the annualized return starting on 25 Jan 2018 as noted in the footnote. The Since Inception return may cover different periods for different funds.
Another perspective is to report calendar year returns as shown below.
| | 2022 | 2021 | 2020 | 2019 | 2018 |
| VBAL | -11.37% | 10.27% | 10.24% | 14.91% | |
There is no annual return for 2018 since the fund started on 31 Jan 2018, so there is not a full calendar year of data. Calendar year returns tend to be more variable than the annualized returns. Even though VBAL is a balanced mix of stocks (60%) and bonds (40%) the annual returns show a high degree of variability from -11.37% (2022) to 14.91% (2019). Also note the difference between the 1 Year return of -2.30% and the 2022 return of -11.37%. Both are returns over 12 months, but the start of the 12-month period differs by 3 months. Investment returns change significantly from month to month; a slight change in the reporting period can have a big impact on performance.
Calendar year returns are useful for gaining a sense of how performance may vary from year to year but annualized returns (over 5 years or more) give a better sense of the long-term investment performance. In either case the return data is of past performance and not a predictor of future performance.
Total return and price return.
Investment returns are a combination of capital gains, dividends and interest. Stock market indices generally focus on price variations, excluding dividends. For example, the Canadian stock market (S&P/TSX) annualized price return, including capital gains but not dividends for the past 20 years ending March 2023, was 5.9% but the total return including dividends was 8.9%2.
Real rate of returns.
Most investors save today to consume in the future. We have learnt, especially recently, that prices go up, so $100 today is unlikely to have the same purchasing power in a few years. Price inflation erodes purchasing power. If prices are expected to increase by 4% annually then the minimum annual rate of return required to maintain purchasing power is 4%. So far, we have focused on the nominal rate of return which doesn’t account for the loss of purchasing power from inflation. The nominal rate of return minus the expected rate of inflation is the expected real rate of return3. Real rates of return can be particularly useful in retirement planning over several decades where even large increases in asset values can conceal a loss of purchasing power.
A retiree may want, for example, to withdraw $40,000 annually from an investment portfolio of $1 million. For simplicity we assume the rate of investment return is the same every year and expected inflation is 3%. If the investment rate of return is 4% then the investment gain matches the withdrawal, and the portfolio value stays at $1 million but the purchasing power of the $40,000 withdrawal is eroded to less than half within 24 years. Conversely, if the retiree chooses to maintain their purchasing power by increasing the withdrawal by the rate of inflation, then the purchasing power of the portfolio will dwindle to less than half within 16 years and run out of money in 28 years. When considering rates of return for planning over decades it is vital to understand the difference between nominal and real returns.
Investment return in the presence of withdrawals and deposits.
Inflows and outflows to investment accounts complicate the calculation of the investment rate of return. If you start the year with $100, contribute $10 on 1st January and end the year with $120 the rate of return is 9.1% ((120 – 110)/110). If the contribution is made on 31st December, and you also end the year with $120 the rate of return is 10% ((110 – 100)/100). If the goal is to assess the underlying performance of the investments, the timing of contributions should not impact the calculation of the investment return. In our client reporting the rate of return calculation excludes the impact of contributions and withdrawals. This is the Time Weighted Rate of Return (TWRR) and in our performance reports is stated net of fees. TWRR has the advantage of not being influenced by cashflows that are beyond the control of the portfolio manager and provides a level playing field for comparing the performance of different investments.
An alternative performance measure that includes the effect of cash flows is the Money-Weighted Rate of Return (MWRR), also called the Internal Rate of Return (IRR). Despite the description as a rate of return we recommend considering the TWRR as the primary measure of investment return and MWRR/IRR as one of many methods of measuring performance. IRR is subject to abuse. In some investment areas such as private equity and some real estate investments the investment manager does have control over the timing of cashflows from investors into the underlying investments, leading one researcher to state, “…IRR is uninformative and can be highly misleading; it typically exaggerates true performance.”4
Of course, investors can and do choose to time their investment decisions and comparing the TWRR with the MWRR highlights the difference between investment returns and investor returns.
Mind Games.
The difference between investment returns and investor returns can be explained by taxes, fees and most importantly, investors trying to anticipate market direction.
Morningstar5 annually reviews the difference between investment returns and investor returns and for the 10-year period ending Dec. 31, 2021, concluded that investor’s returns underperform their underlying investments by 1.7% annually, through a combination of poorly timed purchases and sales.
Peter Lynch was the fund manager of the Fidelity Magellan fund from 1977 to 1989. During his tenure Lynch achieved a 29 percent annualized return. But Lynch himself pointed out that the average investor in his fund made only around 7 percent during the same period.6
The difference was largely explained by investors leaving the fund when performance faltered and piling in when performance was good, having missed the recovery. Investors are also prone to believing that even short periods of outperformance are representative of skill rather than luck. In the Magellan example Lynch beat the S&P 500 Index in 11 of 13 years which seems unlikely by chance. However, if 500 coin flippers flip 13 coins each, the winner will on average flip 11.63 heads7. In this case we make a cognitive error by assuming that Lynch was representative of fund managers whereas he is noticed for being the most successful from a large pool. A conclusion that is only obvious with hindsight.
If investors calculate their rate of return and conclude their investments are trailing other similar investments is this sufficient evidence for changing their investment strategy? As the Peter Lynch example illustrates, over performance (and underperformance) is susceptible to confusing chance with skill.
Making bad decisions based on insufficient performance data is not confined to individual investors. A review of 3400 large pension managers concluded that if plan sponsors had stayed with fired investment managers their performance would be no different from those actually delivered by the newly hired managers!8
Conclusion.
Consistent and reliable measurement of the rate of investment return is a key performance measure and can provide a useful comparison with investment benchmarks and whether personal financial goals are achievable.
Some caution is required. The interpretation of rate of return numbers can be influenced by the choice of the return period, inflation, inclusion of dividends and interest, taxes, fees, contributions and withdrawals. Even then there may not be sufficient data to determine if the investment performance is significantly different from what would be expected by chance.