Sensitivity Analysis

Every model is built on assumptions, but it’s important to understand how significant these assumptions are.

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What’s the most important factor when buying a property to rent it out?
We ran Causal's sensitivity analysis on our Should you buy a property to rent it out?. The output variable, Net Gain
The difference in wealth, after 7 years, between buying a property + renting it out and investing into stocks instead
, depends on inputs Annual Appreciation
The annual percentage increase in the property's value
, Baseline Growth
The annual percentage growth of the stock market
, Monthly Rent
The income you receive from renting out the property
, Maintenance Cost
The annual cost of owning the property, as a percentage of its value
, and Downpayment
The amount paid up-front for the property
.
Click on a bar to see the
sensitivity chart for that variable.
VariableImportanceAnnualAppreciationBaselineGrowthMonthlyRentMaintenanceCostDownPayment45 %41 %7 %6 %1 %
-$200k-$100k$0$100kNet Gain2%3.5%5%6.5%8%Annual Appreciation
This chart shows the relative importance of each input variable with respect to the output variable.
This chart shows the effect of varying one input variable while keeping the rest fixed.

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Discussion

Overview

This sensitivity analysis was run on our Should you buy a property to rent it out? model. The model compares two scenarios:

  • Buying a property with a mortgage and renting it out (Scenario A)
  • Investing that same money in the stock market (Scenario B)

It's crucial to understand the dynamics at play when making a significant financial decision, and building a model is often the best way to accomplish this. In any model, it's important to understand which input variables (model assumptions) have the largest effect on the outcome.

If a variable is significant in a model, more time should be spent estimating the range of possible values it can take on, to properly understand the range of possible outcomes in your model.

This analysis considers the net gain in wealth from Scenario A compared to Scenario B (the baseline) after 7 years.

We look specifically at 5 input variables in our model, varied over the range given in square brackets:

  • Annual Appreciation [2% – 8%] — the (percentage) annual increase in the property's value
  • Baseline Growth [-2% – 10%] — the (percentage) annual growth of the stock market
  • Down-payment [$50k – $200k] — the amount paid up-front when purchasing the property
  • Monthly Rent [$800 – $2k] — the monthly income received from renting the property
  • Maintenance Cost [1% – 3%] — the annual cost involved in owning a property, as a percentage of the property value

The bar chart shows the relative importance of each variable with respect to the output (see the Technical Details section for a precise explanation).

The line chart shows the effect on the output of varying one input variable, while keeping the rest fixed at the middle of the specified range. This ignores interaction effects, so it should be used as a way of understanding the high-level relationship between each input variable and the output.

We can see that Annual Appreciation and Baseline Growth are the most significant factors in deciding the outcome. Intuitively, this makes sense because these variables result in compounding effects each year.

Surprisingly, the down payment doesn't matter much at all, despite the large range of values we considered ($50k to $200k).

Technical Details

This analysis uses a variance-based approach. The method decomposes the variance of the output and attributes it to the corresponding inputs. Note that the sensitivity results are dependent on the input ranges. The input ranges specify the variance of the inputs.

The line charts show how the output variable varies if we vary the selected input variable – all other inputs are kept at their mean (the middle point of the range). The bar chart shows the total-effect indices of the inputs. Beware: the line chart might hide certain interactions between variables. In many models, interaction effects can be important:

Imagine a toy company that is constraint by their logistics network. Increasing their production speed will not increase their revenue since their logistics network can't deliver the additionally produced goods. Also, buying more delivery trucks doesn't increase revenue on its own. The toy company needs to increase both the production speed and their logistics network. Neither production speed nor the throughput of their logistics network will show any changes in the line charts. However, the total-effect index shown in the bar chart can capture those higher-order dependencies.

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