Using Monte Carlo to Model Real Estate Portfolios

The Real Estate Financial Planner™ software allows you to model how a portfolio of Accounts and Properties perform over time.

If you’re modeling your portfolio using static values for variables, you might not see any variation in the results if you rerun a Scenario. But static values over long periods of time for things like the following is not a good model of reality:

  • Appreciation rates on property values and rents
  • Interest rates as you buy Properties over time
  • Rates of return on your stocks, bonds or other investments
  • Maintenance and capital expenses costs
  • Vacancy rates

We’re likely to see variation in how quickly or slowly a Property goes up or down in value.

In other words, if we plot the appreciation rate of a Property we own in our portfolio over time, it is not likely to look like this:

Static Appreciation Rate
Static Appreciation Rate

It is just not likely that a Property will go up in value each month at a rate of 3% per year.

With the Real Estate Financial Planner™ software we can use Rules to set the Appreciation Rate of the Property to be, on average, 3% per year. If we measure the increase for a particular month it might range from +13% to -10%… or really whatever we set the Rule to be. For this example, I used the following settings for the Rule to vary the Appreciation Rate.

Setting Variable Appreciation Rate on Property Rule
Setting Variable Appreciation Rate on Property Rule

That Rule means that the average Appreciation Rate will be about the same 3%. It should average out to be the same, but there are months when the property value can go down. There are also months the property value can go up faster than 3%.

The following chart shows the range of values we could have for the Appreciation Rate using this new Rule.

Frequency of Distribution of Appreciation Rate
Frequency of Distribution of Appreciation Rate

When we look at the Chart of Appreciation Rate again, this is what it looks like this time:

Variable Appreciation Rate
Variable Appreciation Rate

Does this really even matter? Maybe, maybe not.

Let’s compare the Net Worth of someone who buys just one Property. In one Scenario, they have a fixed Appreciation Rate of 3% and in the other Scenario, they have a variable Appreciation Rate that averages 3%. Here’s a Chart of Net Worth.

Net Worth - 2 Scenarios
Net Worth – 2 Scenarios

The difference on a single property over 40 years is about $10,000. It could just as easily have been the other way around, but in this comparison, the variable Appreciation Rate did $10,000 better than the static Appreciation Rate. If we ran the variable one again, we’re very likely to get slightly different results. Let’s do that.

Running it again, the Net Worth of the variable one was about $14,000 lower this time. Here’s the Chart.

Net Worth - 2 Scenarios - Second Run
Net Worth – 2 Scenarios – Second Run

What if we make a copy of the Scenario with the variable Appreciation Rate as a third run to the Chart? Here’s a chart comparing the 3.

Net Worth - 3 Scenarios
Net Worth – 3 Scenarios

As you run each one, there is some variation in how much the Property is worth and therefore what the ultimate Net Worth will be just buying the 1 Property.

I won’t do it here, but you can imagine what would happen if we vary more things like rent appreciation, taxes, insurance, maintenance, capital expenses, vacancy, stock market rates of return and more… all in the same Scenario. It is likely that the range of Net Worth would be wider.

I’m going to skip ahead and show you what running 10 variable Scenarios looks like with just varying the Appreciation Rate on a single Property.

Net Worth - 11 Scenarios - No Legend
Net Worth – 11 Scenarios – No Legend

And here is what it looks like in month 480 so you can more easily see the difference between the 11 different Scenarios (10 variable and 1 fixed). The 3% fixed Appreciation Rate happens to be the yellow one, the 3rd from the right.

Net Worth - 11 Scenarios - Month 480
Net Worth – 11 Scenarios – Month 480

If we were to summarize these into ranges of values, we might get a Chart like the one below. It shows Net Worth for 10 Monte Carlo runs summarized.

Net Worth - 10 Runs Summarized
Net Worth – 10 Runs Summarized

It is hard to see what is going on in the Chart above zoomed out, so here is the same Chart but only showing the last 30 months (months 450 through 480).

Net Worth - 10 Runs Summarized 450-480
Net Worth – 10 Runs Summarized 450-480

Each different shade represents percentile ranks. Shown in the image above are the 1-99% percentile, 5-95%, 10-90%, 25-75%, 40-60% and the 50th percentile (median) as a line.

We can also choose to look at the Appreciation Rate for Monte Carlo Scenarios to see the range of values that we have for Appreciation Rate. Here is a Chart showing the same 10 Monte Carlo runs that we were showing you above. I have shown you the full 480 months.

Appreciation Rate - 10 Runs Summarized
Appreciation Rate – 10 Runs Summarized

If we want to look at the actual dollars in Appreciation that we’re seeing for each month summarized for the 10 Monte Carlo runs, we can also look at the Appreciation Chart.

Appreciation - 10 Runs Summarized
Appreciation – 10 Runs Summarized

What if we bump up the number of Monte Carlo runs that we do. For example, let’s say we do 25 total runs instead of just 10? Here’s a Chart showing Net Worth for 25 Monte Carlo runs.

Net Worth - 25 Runs Summarized
Net Worth – 25 Runs Summarized

If we zoom into this one as well to see only months 450-480 like we did above, the Chart looks like the following.

Net Worth - 25 Runs Summarized 450-480
Net Worth – 25 Runs Summarized 450-480

For the 10 Monte Carlo runs, the values for the 1-99% ranged from $762,569.75 to $805,441.24. For 25 runs, the same 1-99% range varied between $757,458.15 and $803,737.34.

What if we look at the Appreciation Rate for 25 Monte Carlo runs? It looks like the following Chart.

Appreciation Rate - 25 Runs Summarized
Appreciation Rate – 25 Runs Summarized

If we look at the amount, in dollars, that we see in Appreciation per month for the 25 Monte Carlo runs, the Chart looks like the following.

Appreciation - 25 Runs Summarized
Appreciation – 25 Runs Summarized

If we were going to do a full on Monte Carlo model of a Property, I would recommend that we create separate Rules to vary the following variables that are related to Properties:

  • Appreciation Rate
  • CapEx Appreciation Rate
  • HOA Appreciation Rate
  • Maintenance Rate
  • Rent Appreciation Rate
  • Utilities Appreciation Rate
  • Vacancy Rate
  • Other Income Appreciation Rate if there are any
  • And, Other Expenses Appreciation Rates if there are any

I’ve gone ahead and created Rules to modify these variables. The following screenshot shows the Rules that we set up to model this.

Rules with Variables for Everything
Rules with Variables for Everything

Here are the results for Net Worth on 25 Monte Carlo runs.

Net Worth - 25 Runs Everything Variable
Net Worth – 25 Runs Everything Variable

If we compare that to the 25 Monte Carlo runs for just varying the Appreciation Rate you can see there is a lot more variation in Net Worth when we vary more of the options. In fact, the entire band is inside the band for the Scenarios with more variation.

Net Worth - 25 Runs Compared
Net Worth – 25 Runs Compared

We can see this a little more clearly if we zoom in to look at just months 450 to 480.

Net Worth - 25 Runs Compared 450-480
Net Worth – 25 Runs Compared 450-480

Also, you can see I included a line showing the difference between the averages of the two Monte Carlo Scenarios. That’s the dashed line and the labels for the values of the difference are shown on the right hand side of the Chart. The dotted “average” line in the middle of each band is the Expected Value from all the Monte Carlo runs. I will talk more about what that is and how to use it to make numbers-backed investing decisions in a future blog post.

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