A Quant’s Approach to Buying vs Renting

Tab 1…., Tab 2…., Tab 1.., Tab 2. I was anxiously clicking back and forth between two tabs on Zillow.com for the DC area. One shows the “For Sale” homes in a popular young professional neighborhood, and the other “For Rent” in the same area. Two nearly identical townhouse apartments were on the market, one for a selling price of $375K and the other listed for rent at $1,995 per month. When Googled “Is it better to buy or rent” the results give everyone’s opinion from self-proclaimed financial gurus prophesizing the common adage “Renting is for Suckers” to van living pseudo-philosophers who subscribe to the belief that “You don’t want to be tied down to one place man.” Even Chat-GPT gives me a very ambivalent answer stating, “The decision between buying and renting is complex and depends on many uncertain factors”.     Fortunately, the company I work for Hubbard Decision Research (HDR), specializes in making decisions given many uncertain factors. Applied Information Economics (AIE), developed by HDR’s founder Douglas Hubbard, provides a practical statistical framework for making this decision or others with high degrees of uncertainty. It employs methods proven by a large body of peer-reviewed academic research and empirical evidence on improving human expert judgments. As a management consulting firm, we are routinely hired by some of the world’s largest companies and government organizations to apply this framework to large difficult decisions. The same framework can be applied to personal financial decisions in a 4-step process.   Step 1: Define the Decision Should I buy or rent an apartment? Given that I don’t have any personal preference for homeownership itself, which decision is more likely to lead to a better financial outcome?   Step 2: Model What We Know Now To model this decision, a Monte Carlo simulation was used to generate 1,000 different possible scenarios based on defined probability distributions for the variables that influence the decision. This may sound complicated at first glance. References to simulations bring up mental images of the Matrix or Dr. Strange using the Time Stone to see 14 million different simulations and only one way to defeat Thanos. But when explained, it’s quite straightforward. Rather than using a fixed value for a variable I’m unsure about such as “Time until reselling of home”, I use a range with a confidence interval. I’m not sure how long I would potentially live in the apartment, but I’m 90% sure it would be between 3-15 years. While I may not possess an infinity stone to see all these simulations, I do possess a tool equally as powerful for practical decision-making: Excel. In Excel, standard cashflow models were built to show how my financial inflows and outflows would compare if I rented or bought one of the apartments, and the net present value (NPV) of the difference was calculated.     These cashflows were calculated based on 17 different variables that have an impact on the decision. For variables, I am uncertain about, the model randomly samples from a confidence interval provided. The Model repeats this 1000 times and records the Simulated Value, and Cashflows for each simulation.     Based on the recorded simulated values and cashflows, the model generates a probability distribution for possible NPVs, which will suggest an informed decision. If the expected NPV (average NPV across all situations) is positive, the decision should be to buy; if it is negative, the decision should be to rent.     The big caveat is this is based on a probability-weighted outcome, and there is a chance the model suggests the wrong decision. However, there are ways to reduce this probability by conducting additional measurements. Step 3: Measure What Matters: One of the benefits of using Monte Carlo simulations versus deterministic models with fixed values is that we can calculate the expected value of perfect information (EVPI). It is how much a person should be willing to pay to eliminate their uncertainty about a variable. The calculation is essentially the probability of being wrong multiplied by the cost of being wrong. By measuring and ranking EVPIs, we obtain a practical list of the most important uncertain variables to spend time measuring or conducting additional analysis on. If initially, I’m unsure what my mortgage rate would be and give a 90% confidence range of between 4-9%, the maximum I would be willing to pay a bank to give me a precise mortgage quote guarantee would be the EVPI. In this case $1,407.     The cost for me of spending 15 minutes to get an online mortgage quote is well below this EVPI value. After doing so, I received a quote of 6.7%. Replacing this range with the fixed value and rerunning the model results in a narrower distribution of NPVs as seen below and thus reducing my uncertainty about the decision.   Changing the mortgage rate from a range to a constant also changes the EVPIs of other variables. While in the original model, I had 4 variables with EVPI values, the updated model shows the only variable worth conducting additional measurement on is the estimated annual increases in home prices over the period of ownership. Unfortunately for me, I do not have a magic crystal ball, nor an oracle I can con pay to tell me precisely what home prices will do in the future. I could spend hours researching the market mechanisms of home price increases to come up with narrower range estimates for the lower and upper bounds. However, based on the EVPI, I do not think the slight reduction in uncertainty is worth it. I can confidently move on to making my decision.     Step 4: Make Better Decisions: The final model results show the expected value of buying versus renting the apartment is $-79,072. In 93.8% of the simulations, I would be better off renting the apartment vs buying the apartment. This conclusion could change as new information becomes available and if mortgage rates start to decrease, but for now I can very confidently make the decision that I’m financially better off renting than buying.   Other Applications of AIE: This was a simple example of how Applied Information Economics can improve personal financial decisions. The same steps can be applied to practical large-scale business investments. At Hubbard Decision Research, we routinely apply the same step-by-step process to multi-million or even multi-billion-dollar decisions. We also provide training to improve our client’s ability to quantify anything, build probabilistic models, and not only make better decisions but make better decision-makers. For more information, explore the rest of the website or contact us at info@hubbardresearch.com.