It is commonly stated that certain stock market indices, such as the S&P 500 and MSCI world, have average annual growth rates of around 8% per annum. Given this information the average index fund investor could easily be forgiven for modelling their portfolio growth based on this rate. I even did a post on about how long the financial independence journey would take using an 8% growth rate.
As we know, market returns vary considerably year-to-year, which means that the start and finish time of the investment journey will affect the overall returns an investor will experience. In addition to this, the annualized return figures stated tend to look at how much the index has grown from start to finish as opposed to the rate of return of a progressively accumulated portfolio. For example, between 2016 and 2019 the S&P 500 annual growth rates are as follows:
| 2016 | 2017 | 2018 | 2019 |
| 9.54% | 19.42% | -6.24% | 28.88% |
This means that the annualized growth rate if all investments occurred at the start of 2016 would be:
If $4,000 was invested at the start of 2016, at the end of 2019, the investor would have:
However, if you applied a dollar cost averaging method and invested $1000 at the start of each of the years the journey would look like this:
| Date | Return | Portfolio Value |
| 1/1/2016 | $1,000.00 | |
| 31/12/2016 | 9.54% | $2,095.40 |
| 31/12/2017 | 19.42% | $3,502.33 |
| 31/12/2018 | -6.24% | $4,283.78 |
| 31/12/2019 | 28.88% | $5,520.94 |
So, by the end of 2019 you would have $5,520.94 (total of $4,000 invested) which gives an annualized growth rate of 13.32%.
At this stage, you’re probably thinking, so what if some nuances in mathematics create different returns? Well, during an investment journey which can easily last 15 or 20 years you will probably end up investing $500,000, $1m or more and unless you win lotto it’s unlikely to be invested in 1 lump sum right at the start. It is more likely to be invested periodically in a dollar-cost-averaged fashion. This means that the year-to-year variation in market returns will affect the overall rate of return that should be used to model investment returns. It also will potentially affect predicted retirements dates, required savings rates and asset allocations.
Modelling the variation in returns
To demonstrate the variations in returns for different periods I’ll be looking at dollar cost averaged portfolios with durations of 15 and 20 years for the MSCI World ex Australia; the All Ordinaries index and a 60/40 combination portfolio between 1980 and July 2020. The simulation conditions are as follows:
- $1000 will be invested on last day of each month for the required time period.
- For the 15 and 20-year portfolios a total of $180,000 and $240,000 will be invested
- Each simulated portfolio will start on the last day of each quarter – 31/12, 31/3, 30/6 and 30/9 each year
- The 60/40 combination portfolios will be 60% MSCI World ex Australia and 40% All Ordinaries which approximates our own portfolio construction minus the property fund.
This modelling does not take into account:
- Investment and transaction fees
- Taxes on distributions or capital gains
- Currency fluctuation or hedging
Results
Portfolio values graphs
In these graphs each column represents the finishing value of a simulated dollar cost averaged portfolio that commenced at a particular date. In each graph the median simulated portfolio value is shown by the dark blue line and the total invested is shown by the red line.
15-year portfolio values
For the 15-year portfolios, there are 103 simulations for each different asset allocation. The results are as follows:
20-year portfolio values
For the 20-year portfolios, there are 83 simulations for each different asset allocation. The results are as follows:
Returns graphs
Similar to the portfolio value graphs, each column represents the annualized return of a simulated dollar cost averaged portfolio that commenced at a particular date. The returns are calculated using the “internal rate of return (IRR)” formula in excel. The median simulated portfolio return is shown by the dark blue line.
15-year portfolio returns
For the 15-year portfolios, there are 103 simulations for each different asset allocation. The results are as follows:
20-year portfolio returns
For the 20-year portfolios there are 83 simulations for each different asset allocation. The results are as follows:
Summary data
Each of the simulated portfolios has the following summary data that provides information on the median as well as the spread of the results.
| Median | Mean | Std dev | Highest | Lowest | |
| MSCI World ex Australia 15-year | $318,261 | $367,758 | $160,076 | $682,793 | $150,408 |
| All Ords 15-year | $385,255 | $406,421 | $85,939 | $601,701 | $254,210 |
| MSCI World ex Australia 20-year | $493,663 | $590,324 | $392,433 | $1,882,279 | $259,576 |
| All Ords 20-year | $671,226 | $729,867 | $176,007 | $1,110,864 | $450,285 |
| 60/40 split 15-year | $345,232 | $385,636 | $133,159 | $633,276 | $196,480 |
| 60/40 split 20-year | $538,593 | $644,602 | $308,924 | $1,643,358 | $355,888 |
| Median | Mean | Std dev | Highest | Lowest | |
| MSCI World ex Australia 15-year | 7.21% | 7.66% | 5.39% | 16.18% | -2.43% |
| All Ords 15-year | 9.51% | 9.86% | 2.47% | 14.72% | 4.44% |
| MSCI World ex Australia 20-year | 6.71% | 6.90% | 4.21% | 17.81% | 0.77% |
| All Ords 20-year | 9.36% | 9.82% | 1.94% | 13.55% | 5.89% |
| 60/40 split 15-year | 8.19% | 8.76% | 4.08% | 15.31% | 1.15% |
| 60/40 split 20-year | 7.47% | 8.25% | 3.21% | 16.72% | 3.77% |
What the results show
As you can see from the graphs and table presented above there is significant variability of the returns produced across the different time periods. Over the hundreds of simulations, some broad trends start to emerge:
- The vast majority of portfolios had a positive return – only the poorest performing portfolios for the MSCI World ex Australia index over the 15-year periods produced negatives returns. All of these portfolios finished their journey between 2009 and 2012.
- In all cases the standard deviation of returns is lower for the 20-year durations than the 15-year durations
- The All Ordinaries produced higher median returns than their equivalent MSCI World Ex Australia portfolios
- Median returns varied between 6.71% and 9.51%
- Combining the portfolios produced summary values that are between each of the portfolios
- When running the simulation over a 20-year period there was less chance of negative returns for the MSCI World ex Australia index when compared with a 15-year period
- In all cases, simulated portfolios that have duration of 20-years produced lower standard deviations than simulated portfolios with a 15-year duration
Concluding thoughts
This simulation shows that there are large variations in portfolio returns which heavily depend on the start and finish dates of an investment journey. This makes financial modelling tricky and means that it is impossible to say with a high degree of certainty how long it will take to reach financial independence. While this modelling has revealed some very positive outcomes, such as starting investing in the early 1980s, it also demonstrates that there is a significant chance of poor investment outcomes. My guess is that this depends heavily on the returns achieved when the bulk of investments were made; so, if returns were stronger during the early part of an investment journey this would result in a high weighted cost of capital which creates a drag on returns.
For the combined portfolios the median annualized growth rates were 7.47% and 8.19%. To me, this implies that using a 7% portfolio return for modelling our own portfolio growth is reasonable. A sobering thought, however, is that median means that there is a 50% chance that returns will be lower than this value.
As investors there is a desire to increase the probability of favourable returns and reduce the probability of unfavourable returns. In the field of personal finance, however, this is only true to the extent of us achieving our goals. In either case, the big question remains, if certain returns are unsatisfactory, what tools do we have to reduce the probability of them eventuating during our own personal finance journeys?
It is clear that this topic requires further investigation, however my initial thoughts are as follows:
- Because the portfolios simulated over 20-year periods showed lower variability of returns than their 15-year counterparts; lengthening an accumulation period would seem to reduce risk.
- Investing exclusively in Australia (All Ords) produced higher returns with less variability than the rest of world, however there is no certainty that this trend will continue into the future. It would be wise to reduce the risk of excessive home-country bias
- In the event of unsatisfactory returns a household’s savings rate becomes a very important factor in being able to retire. This is also true for being flexible about earning an income after becoming financially independent or retiring.
I hope that this post has been as thought provoking for you reading it has been for me writing it. If anything, these simulations highlight the fact investing periodically can have results that vary significantly based on the start and finish dates of an investment journey.
Engineer your freedom
References
Macrotrends, 2020, S&P 500 Historical Annual Returns, Macrotrends, viewed 6/9/2020, <https://www.macrotrends.net/2526/sp-500-historical-annual-returns>
Dimensional, 2020, MSCI World ex Australia Index (net div. AUD), Dataset viewed 3/9/2020 <https://returnsweb.dimensional.com/>
Dimensional, 2020, S&P/ASX All Ordinaries (Total Return), Dataset viewed 2/9/2020 <https://returnsweb.dimensional.com/>