Investment returns vary from year to year, and although the return does have a long-term average, account balances rise and fall as the market changes from year to year. MaxiFi’s Living Standard Monte Carlo risk analysis will help you understand how this annual variation impacts your annual living standard and discretionary spending. The Living Standard Monte Carlo helps you to see if you are taking too much risk, more risk than you need to, or perhaps too little risk with your investments as you explore different investment strategies and spending behavior settings. For a discussion of sequence of returns risk, see this case study.

The explanation below focuses on how to get started using MaxiFi's Monte Carlo analysis. For more detail about the Monte Carlo concepts in MaxiFI, see Understanding MaxiFi's Monte Carlo Risk Analysis.

You can read this page to learn more about deterministic and stochastic planning approaches and how they work in MaxiFi Planner.

## How to Get Started

To begin, after opening the application and entering your data, navigate to Dashboard and Reports and choose to run the Risk Analysis report. The easiest way to begin is to just select preset investment strategies for your Base Strategy (MaxiFi automatically sets up two default approaches—"Safe" and "Risky"—to compare with your Base). Using this quick start approach, you choose from among our group of common investment strategies—for example, "Always Conservative" or "Always Moderate"—and use the drop down selectors to assign an investment strategy for each of three pools of money:

- Regular Assets
- Retirement Assets (spouse/partner)
- Retirement Assets (spouse/partner).

This approach is a quick way to get started, and once you see a report you can come back and fine tune things later. Once you have selected your investment strategies, you are ready to proceed to the next screen and set spending behavior.

### Creating Custom Assets and Investment Strategies

If you want to build custom assets and investment strategies, use the "manage assets" and "manage investment strategies" links on the Risk Analysis setup screen. An **asset** is anything with a return history such as a mutual fund or stock or bond position. An **investment strategy** is an asset or group of assets assigned to one of the three groups of assets listed above. An investment strategy can be built to remain constant or change over time.

The easiest way to create a custom investment strategy is to start by customizing an existing strategy and adjust percentages, ages, and assets in the strategy rather than starting from scratch. To create a custom asset, you will need at least 10 years of return history on your asset. Help instructions in this area will guide you in creating your custom assets and strategies.

### Setting up Spending Behavior

This next screen asks you to set up your spending behavior. This setting is important because how you spend each year relative to the actual returns you get in the market (for better or for worse) can have an important impact on your planning model. Cautious spending (spending in a way that assumes your rate of return is less than expected) can provide a hedge against the risk of an aggressive asset allocation. Appropriate spending behavior (for example, spending as if your rate of return is lower than the historical average) is just as important as appropriate asset allocation, a principle that conventional Monte Carlo ignores.

*spend as if*you are only earning an average a 3.5% return. This spending approach would be an example of building a model that approaches each year "cautiously" relative to your anticipated return. You could also do the opposite and model aggressive "as if" spending. Your assumptions about safe rate of return do not need to be the same as your investment strategy. Indeed, it has been said: "if you invest aggressively, you should spend cautiously; if you invest cautiously, you can spend aggressively." Trying different combinations of investment strategies and spending behaviors is a way to learn about their importance to your particular planning model. It is reasonable to assume the same spending behavior for each of the three investment strategies as a place to begin and establish a benchmark for comparison.

The two distribution charts seen here illustrate the same investment strategy but with different assumptions about spending behavior. The one that tips upward reflects a conservative spending behavior and the one that tips downward reflects an aggressive spending behavior.

## Understanding Monte Carlo Reports

A thorough risk analysis is not just about statistics of risk and reward but also about the subjective sense of whether the reward is worth the risk, and every person has his or her own sense of that trade off. The *Index of Expected Lifetime Utility* includes this subjective and personal sense of whether a risk is worth it in this risk analysis. The following video will provide a general overview Monte Carlo and in particular of the expected utility function beginning at 9:10 minute into the video.

Where one investment strategy has a probability of more reward than another, we might ask: is the risk worth the expected gain? The expected utility function allows us to not merely look at the raw risk and reward statistics but to also include your personal risk preference in the calculations about the decision. With the expected utility function, we look not just at which choices have the higher probability of higher reward, but we can also take account of how you feel about the outcomes. A lot of upside probability may not be worth the risk of even a slight downside probability to you (but it may be worth it to another person with a different level of risk aversion). Once you identify your personal risk aversion level in the grid (how do you feel about the risk of having a lower standard of living?) we can then use the expected utility function formula to show you which strategy you will feel best about given your level of risk aversion. It won't just be the strategy with the highest possible reward, it will be the strategy with the highest possible reward but adjusted to account for your feelings about whether the reward is worth it or not. The grid identifies these trade offs based on your personal view of risk showing you whether an investment strategy is worth it (some number greater than 100) or not worth it (some number less than 100).^{1}

The second screen after the slideshow introduction—the Per-Adult Living Standard Comparison—shows an overview of each of the three investment strategies. These horizontal bars represent all the living standards produced and display them relative to their distribution around the middle or median per-adult living standard. The middle 50%, for example, are represented as the dark blue band. You can think of these bars as showing you how tightly clustered or dispersed your living standard will be, taking the hundreds of scenarios as a whole, around the middle (the orange line). The extremes of the far left and the far right represent outside statistical possibilities given your spending behavior and asset allocation.

Risk has several dimensions as we see in these charts shown. One kind of risk is having a lower average living standard through life. Another kind of risk involves having that living standard distributed widely either side of the middle. By offsetting one kind of risk you often invite another. In these charts, the lower median living standard enjoys a more tightly clustered set of possible living standards either side of the middle. In other words, the disadvantage of a lower average living standard is offset by having most of the possible living standards clustered closely around that middle which suggests a more predictable living standard (less variation) from year to year.

### The Range and Standard Deviation

Each report provides up to three alternate sets of charts that provide some perspective on the risk entailed in the investment strategy and spending behavior. The first, as discussed above, shows the plans not across time but rather "all at once," allowing you to see at a glance the middle and the deviation from the middle in the models as a whole.

### Living Standard Distribution

The next chart presents all of the living standards produced in the simulation across time allowing you to view the range or distribution of possibilities in any single year. In other words, any single year across the chart can be viewed as a vertical slice of the distribution of possible living standards in that year. As time progresses moving left to right on the chart, the range of possible living standards in any given year tends to get wider as the distribution of possibilities from low to high fans out. The shaded regions show how tightly clustered the possible living standards are around the median. Those within 50% and 80% of the median are the ones you are most likely to experience and thus should be most concerned about. Those on the outside edge of the cone (the outside 5%) represent statistically lower possibilities. This chart tips upward on the right because the spending behavior (see above) is conservative. The model underspends each year pushing unspent wealth each year into the future causing the chart to tip upward to the right.

### Living Standard Trajectories

The third chart shows five of the hundreds of living standard trajectories from very low to very high. While most trajectories will locate around the middle (see the chart above), ending up on a higher or lower trajectory with lots of ups and downs over the years is a possibility you should not ignore. Each line represents a possible annual living standard path for one of hundreds of lives lived. Each trajectory represents a higher or lower average spending than another trajectory. Each trajectory has a lifetime average and the chart displays five of these trajectories according to their relative lifetime average in the group (5th percentile means that among the hundreds of trajectories, 95% did better). The trajectories may in some years dip below the levels in the range report above it. In other words, where the range report might show in the year 2030 a range from say 75,000 up to 150,000 from the 5th percentile to the 95th, the trajectory report might show the the living standard at say 65,000 in the year 2030. In this case, the 65,000 that year is in the 4th or 3rd or some other lower percentile and is not contradicting the range report. The 5th percentile trajectory is the 5th percentile because over the life of the trajectory it ranks 25th among all 500 trajectories. But there can be years where it, or even the 25th percentile, can touch on amounts outside the range of 5th to 95th in the range cone chart above it. See also How Trajectories are Created

## Next Steps

Assessing the risk in your financial model is a matter of balancing risk and reward. One thing you learn from this unique analysis is that your asset allocation (the ratio of stocks to bonds for example) is important but not the end of the story. There's no reason to assume that you will blindly spend the same amount year after year regardless of how well or poorly your investments preform. You can adjust your safe spending levels to reflect the reality that you can underspend expectations based on historical averages and tilt your living standard upward through time. You can also model aggressive spending and observe the living standard downside of rigidly spending (or even overspending) your long-term historical average even when your investments are performing poorly. And finally, for those who are concerned about sequence of return risk learning how MaxiFi's risk analysis models can help understand how a sequence of poor returns in the first decade of withdraws can impact a model, this case study addresses that issue.

When you get a feel for the way these variables work, you can use what you learn about investment strategies and spending behavior to set a safe rate of return in MaxiFI's for each of the three pools of money we described above and create a long-term planning model that reflects your tolerance for risk to your annual living standard. And of course you also want to visit your brokerage account or investment advisor and rebalance your regular and retirement assets to align with the conservative or aggressive investment strategies that make the most sense in your MaxiFi planning model.

1. Our Lifetime Expected Utility index is simply another educational tool in your decision about how to invest and spend your money through time. It is always a good idea to consult with your professional financial advisor. Economic Security Planning, Inc. does not provide personal financial advice of any kind, including investment advice. There are at least four major reasons the Lifetime Expected Utility Index may not capture your situation. First, the utility you derive in a given year from that year’s living standard may differ from that standard assumption that we and other economists make. Second, the joint distributions of returns we assume you’ll face based on the assets included in your investment strategies may differ from those we estimate from historical return data. Third, you may face risks not included in our analysis that may alter the lifetime expected utility of one strategy relative to another. Fourth, Monte Carlo results reflect draws of random paths of rates of return. Hence, each time you run our Risk Analysis Report you'll see at least somewhat different, but possibly very different, results.

The method behind picking the random returns for any given year involves a kind of predictive analysis that data analysts call regression analysis. This involves taking each asset in a portfolio and creating a regression model against an internal set of predictor assets, asset groups with well known correlations. Then for a given year, it draws a set of correlated random returns for the predictor assets and plugs those into the model giving the return for the portfolio asset. For any additional portfolio assets we use the same return values for the predictor assets in each asset's respective regression model to get their return for that year. The same return is used for an asset in a given year even if it is used in multiple portfolios. We then calculate a weighted portfolio average for each year using the relative shares of each asset. So there is a relationship between assets in each year in that they share same predictor returns used to derive the asset return.

**MaxiFi’s Monte Carlo: How the trajectories are created**

Once you’ve specified your investment strategy and safe rate of return, MaxiFi produces hundreds of possible living standard trajectories to show you the range of living standard trajectories you may experience.

MaxiFi repeats the following steps to generate the hundreds of living standard trajectories. In this description, we’ll assume you are 50 years old to make things concrete. But the same process is followed regardless of your current age. We’ll also assume you specified a 3.5 percent safe rate of return together with a 2.5 percent inflation rate. This implies a roughly 1 percent safe annual real return.

- MaxiFi draws, at random, a real return trajectory – a trajectory of annual real returns for your regular assets, your retirement account assets, and your spouse/partners’ retirement account assets (if applicable). These draws are based on your specified investment strategy, which can entail holding different portfolios (combinations) of assets over time.
- MaxiFi calculates what you should spend this year (at age 50) if you knew for sure you were going to earn, in each future year, the safe real return you specified. MaxiFi records your household’s living standard at age 50. Note that if you set a lower safe real rate of return, MaxiFi will calculate a smaller spending amount. Hence, your choice of the safe real rate of return controls your spending behavior. The lower the safe rate you set, the less you will spend in the present and, therefore, the lower the chances of having very low spending in the future.
- MaxiFi advances you by one year to age 51, but in calculating what assets you’ll have at age 51, it uses the actual real returns that it drew for you for age 50 in Step 1.
- MaxiFi calculates what you should spend this year (at age 51) if you knew for sure you were going to earn, in each future year, the safe real return you specified. MaxiFi records your household’s living standard at age 51.
- MaxiFi advances you by one year to age 52 and so on. In other words, it runs your household forward in this manner, calculating a living standard for your household for each year through your household’s last possible year of life.
- MaxiFi collects all your annual living standards and stores them as the first of your living standard trajectories.
- MaxiFi draws a new return trajectory and repeats steps 1 through 6.
After generating 500 living standard trajectories, MaxiFi ranks them based on their average annual living standard. It then displays five living standard trajectories (as well as their associated discretionary spending levels) – the trajectory with the 95th highest average annual living standard, the trajectory with the 75th highest average annual living standard, the median trajectory with the 50th highest average annual living standard, the trajectory with the 25th highest average annual living standard, and the trajectory with the 5th highest average annual living standard.