In this article, Madalet Sessions demonstrates the value of considering risk, in addition to return, when investing. To illustrate, she simulates a range of potential outcomes using historical data, to assess the impact of both risk and return on achieving long-term investment objectives. If the past is anything to go by, the results suggest that risk management enhances the prospects for better relative returns over time.
This article first appeared in Glacier’s Funds on Friday.
Let’s look at the steps that were taken to perform the simulation.
Step 1: We constructed three illustrative strategies.
Using historical return data from the ASISA SA – Multi-Asset – High Equity category between 1 May 2017 and 30 April 2024, we constructed the following strategies from the funds that had full track records over the period:
- The High-Risk strategy, which applies the range of monthly returns generated by the three single manager funds with the highest standard deviations in the category.
- The Low-Risk strategy, which applies the range of monthly returns generated by the three single manager funds with the lowest standard deviations in the category.
- The Average Return strategy, which applies the range of monthly returns generated by the three funds that delivered returns closest to the category average.
Figure 1 below shows the risk (standard deviation) vs. return scatter of the funds in the category and the funds we used to construct these investment strategies.
Figure 1: Risk/return scatter for the ASISA SA – Multi-Asset – High Equity category between 1 May 2017 and 30 April 2024, with the nine funds highlighted
Source: Morningstar data and Denker Capital calculations
Step 2: We used historical returns to generate a range of potential outcomes for each strategy.
Figure 2 shows the range of outcomes delivered by the nine funds over the seven years. For example, looking at the three High-Risk funds, figure 2 shows that those funds generated monthly returns below -4.9% 18 times (out of 252 monthly observations). The Average Return funds delivered monthly returns in excess of 7.4% five times.
Figure 2: Historical range of monthly returns from the nine different funds in the three strategies
Source: Morningstar data and Denker Capital calculations
For all three strategies, the annualised returns over the period equalled the category average annualised return of 7.2%[1] (not to be confused with the monthly returns in excess of 7.4% in the chart above). Although past performance is not a guide to future performance, purely for the purposes of the simulation, we assumed that investors can expect the same range of monthly returns over the next 20 years.
Step 3: We simulated investment outcomes for the different risk profiles to create potential 20-year investment experiences.
We did this using Monte Carlo simulations, which entailed running a number of ‘what if’ scenarios (in this case we used 500) to show the range of possible outcomes.
We used a uniform distribution to randomly select monthly returns from the past seven years from each of the distributions to build up a potential 20-year experience. We repeated this exercise 500 times for each of the different strategies to produce 1,500 potential outcomes. For interest, figure 3 shows the 1,500 outcomes as a risk-return scatter.
Figure 3: Risk/return scatter of the 500 simulations over 20 years
Source: Denker Capital calculations
Having done the work… did we learn anything useful?
The Low-Risk strategy had the highest likelihood of achieving the annualised return outcome.
- About half of the 500 Low-Risk strategy’s simulated 20-year investment experience resulted in an annualised return of between 6.6 % and 8.8% per annum.
- The High-Risk strategy achieved this outcome less than half as often.
- The Average Return strategy achieved this outcome 37% of the time.
If investment success is measured by the likelihood of achieving an expected return (in this case, the average of 7.2%), then the Low-Risk strategy is clearly superior.
Figure 4: Simulated range of annualised returns from the three different strategies over a 20-year investment horizon
Source: Denker Capital calculations
The High-Risk strategy offered the most potential for outsized returns.
- The chart above also illustrates why risk taking is so attractive to some. The High-Risk strategy generated a return over 20 years of more than 13.1% per annum in some instances, even though the expected return is closer to half that.
- The Low-Risk strategy and the Average Return strategy hardly ever succeeded at this in these simulations.
Unfortunately, taking risk also has a downside.
In our simulated outcomes, the High-Risk strategy consistently included an outcome in which annualised returns were below 0% over the 20-year horizon. The probabilities are small, but even with an average return of 7.2%, investors were exposed to the possibility of having less than what they had started with after 20 years.
Let’s look at another set of data summarising our findings.
By construction, we ensured that the process applied the same month’s return for all three risk strategies. This was to create the same relational effects between the different risk strategies as has existed over the last several years. This allowed us to consider relative performance across the strategies.
The table below shows the probability of a strategy generating the best, worst and middle-of-the-road outcomes (with the highest probabilities in bold). Note that if risk management added no value, then the probabilities would be equal at 33.3%.
Table 1: The probabilities of the strategies generating certain outcomes
Source: Denker Capital calculations
Our simulation has left us with three conclusions.
- Risk management improves the odds of better relative returns for investors.
- The Low-Risk strategy had better odds, than luck alone would suggest, for delivering the best (top third) performance.
- The Average Return strategy had the least chance of delivering the best relative performance of the three strategies.
- The High-Risk strategy had roughly the same chance of delivering the best performance as luck would suggest (33.3%).
- Risk taking is not always rewarded.
- The High-Risk strategy generally generated the lowest returns.
- The odds of the Low-Risk strategy underperforming were roughly equal to what chance would dictate (33%).
- The Average Return strategy offered relatively low odds of being the worst outcome.
- All investment strategies have associated trade-offs.
- The Low-Risk strategy had the greatest likelihood of delivering attractive relative returns in the long run. However, these gains came at the expense of being middle of the road. The strategy did not reduce the risk of worst-case outcomes for investors (this would be the result of a ’lucky streak’ for the riskier strategies).
- The Average Return strategy was most likely not the worst return strategy.
- The only strategy that offers potential for much better than the expected return is the High-Risk strategy.
Our simulation suggests that relative return prospects can be enhanced by considering risk.
While we used the ASISA SA – Multi-Asset – High Equity for the purposes of this simulation, we expect to see the same results across a number of the categories (such as equity and flexible funds). Although past performance is not a guide for future returns, our simulation shows that there is value in understanding the risk management processes of portfolio managers.
Howard Marks said, ‘Investors should favour strategies and managers that emphasise limiting losses in declines above ensuring full participation in gains.’
We hope that in this article we’ve illustrated the merit behind Marks’ thoughts.
[1] The High-Risk strategy had an annualised standard deviation of 15.9%, the Low-Risk strategy 6.8% and the Average Return strategy 9.7%.
