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Purchasing a house right now? Makes lots of sense

Updated: Dec 2, 2022



 

Purchasing a house is often a lifetime decision whose timing is mainly dictated by the events in our lives rather than a clear evaluation of the investment. Some of us happen to be looking for houses at “calm” times while others face times of high prices, rising interest rates, and high inflation; in short, what we are experiencing right now. This article is meant to help those stuck in similar situations by providing a practical framework and answering the question: “How have houses historically performed against common alternative investments at times of rising rates and inflation?”. We can anticipate the answer: “exceptionally well”. Actually, while houses beating government bonds is probably something we would expect, they even threaten the supremacy of the mighty index funds. While a possible simplified analysis would multiply an initial investment times an annual appreciation of the underlying asset, the results would likely differ from the real cash an investor would get from a real investment. This article focuses on the actual amount of money we would collect in time in our bank account. The math must include additional contributions in time, different purchasing costs in time, changes in interest rates, dividends, bonds’ coupons changing with the underlying interest rates, etc. This article summarizes all of that in a few intuitive charts.


While history does not necessarily repeat itself, it is often a good starting point for decision-making. Therefore, here is the historical scenario referenced here:

  1. US assets and cash-flows in nominal terms, as they would show up in our bank account

  2. Being referencing US residential houses, alternatives must be assets we would invest in with similar confidence and for a similar length of time. The chosen ones are US government bonds with a 30-year maturity (as per the mortgage simulated on the house), and US equity index funds (based on the Dow Jones Industrial Average)

  3. As per our article “real estate investing against inflation” the comparison is placed back to the 70s, the most recent scenario of similar rates and inflation (figure 1)


Figure 1

A brief comment on the dynamics of an inflationary period


As per the 70s and figure 1, an inflationary period is likely to be characterized by 7-10 years of rising prices and interest rates (the latter enacted by central banks trying to limit the former). During that period, appreciation of assets is mainly a battle in nominal terms between inflation pushing them up and increasing rates bringing them down by discounting their cash-flows with increasing discounting rates. To properly navigate an inflationary period, being able to index cash-flows to inflation is critical for an asset, like a business able to increase prices as its expenses increase in nominal terms. Following that initial period, there is an inversion characterized by decreasing inflation and following decreasing rates. That trend determines the appreciation of assets in real terms by discounting in lower measure their future cash-flows. That is roughly what happened from the 80s through the 2020s, figure 1. In this period, inflation is still something mostly positive and contributing to some additional nominal appreciation.


Data used for the analysis


Here are three pictures summarizing the data used in the analysis; one for each product (sources will be provided at the end of the article):


Figure 2: historical price and rent of houses
Figure 3: historical bonds yield and mortgages rate
Figure 4: historical Dow Jones Industrial Average

Simulating the investments


Through the data above, an initial investment of $150k - an amount resonating in nominal terms with today’s values - is initiated in 1975 and simulated in time as per the followings:

  1. Investment in a US residential house selling for $300k, financed 50% with a 30-year mortgage (ending in 2005) and an upfront payment of $150k (mortgage fix-rate 9.09% in 1975, as per the grey colored line in figure 3). Subsequent mortgage payments made of principal and interests and increasing the equity in the house will be considered on an annual basis

  2. Investment in government bonds with a 30-year maturity (like the mortgage on the house) with an initial purchase of $150k (annual coupon 8.30% in 1975 as per the violet line in figure 3) and additional yearly purchases matching the yearly payments on the mortgage (principal + interests). Those additional purchases in time will have different coupons according to the spot value of newly issued bonds (figure 3). Those additional bonds will have maturity beyond 2005 since we will stick to contracts having a 30-yr life

  3. Investment in an index fund based on the Dow Jones Industrial Average with an initial purchase of $150k and additional yearly contribution matching the mortgage payments (principal + interests) as done for the bonds above. Those additional purchases will have different acquisition prices in time according to the spot price (figure 4)

Figure 5 below visually describes how cash-flows were calculated from the data shown before in the case of the real estate investment: from the initial $150k paid in cash and corresponding to the 50% initial equity in the house, it is calculated the appreciation of the house times the increasing-in-time equity in it, (+) plus the cumulative earnings (rent), (-) minus the cumulative mortgage contributions (principal + interests). More details and the other two discussions for the bonds and the index funds will be provided at the end of this post.


Figure 5: dynamics and math behind the cash-flows of the simulated real-estate investment

Result of the analysis


Figure 6 below starts from the initial $150k value of the investment - should any investment be immediately liquidated after the purchase, we would ideally receive the same $150k just invested – remember, we are dealing with nominal values, not adjusted for inflation and meant to match what we would see in our bank account. From that reference, it shows the “net worth” (i.e. the $ amount) that would show up in our bank account should we liquidate our investments at any point in time: the value of the asset at liquidation, increased by the cumulative earnings until that time, and decreased by the cumulative additional contributions and costs so far sustained. Of course, we are not considering maintenance and professional costs on the house, nor maintenance and brokerage fees on the financial products, nor we are dealing with taxes, etc. The same figure also shows the resulting compounding rate of each investment.


Figure 6

Let us conclude by discussing the critical takeaway


There is a possible critical takeaway from this entire post, and that is not exactly about the winning investment. The fact that houses and funds indeed seem to race toward the winning line should not be the main concern. The exact value could vary depending on how the reader would structure the details of the comparison. For example, it may be preferred to simulate everything on a monthly basis rather than on an annual one. Or, it could be preferred to simulate subsequent investments in bonds by purchasing shorter maturities rather than maintaining the same 30-yr one of the mortgage. Or, a different investment strategy on the index fund could be incorporated – here, maintaining fixed contributions at fixed intervals in time results in a “dollar-cost-averaging” purchasing. Finally, specific transactional and maintenance costs could be added. As long as the simulation reflects what the investor is thinking to implement, it would return an indication of the potential outcome and, more importantly, of the parameters to focus on to increase the chances of success.


The possible major takeaway is that saving solutions are seldom something that can be exactly identified to constitute good or bad opportunities in specific conditions. In general, it has always been that bonds are a quite safe but not too rewarding opportunity, index funds are something always performing at the top of the bunch, and houses are assets often returning a good value. It may be added that the underlying risk is what guarantees that constant gap in performance, but that would deserve a discussion of its own. The underlying assumption is of course to be evaluating a long-term investment, that is why we say “investment”; we would otherwise talk about "speculation" or "trading", which could indeed expose spot opportunities.


Say someone thought houses were a bad investment at this time because of the relatively high prices and cost of capital on mortgages. While that might be true compared to a few years ago, living in the present it could be argued that, while inflation is threatening money sitting at the bank, rising rates would affect many investment solutions in similar ways. As higher rates affect the cost of capital on mortgages because they are the reference they are built on, they would also negatively affect the valuation of the constituents of an index fund because they are the reference the rate discounting their cash-flows are built on. So, assuming a long-term view (the only one allowing a discussion about “saving” opportunities), the gap in performance across investments is likely not to have dramatic changes. Finally, it could be added that the argument just made is more likely to be limited to assets of the same nature, like houses and index funds which are equity investments. Investments in debt like bonds may have dynamics determining quite opposite results at specific times. However, again, in the long term, we would likely go back to usual gaps in performance – please note, because of their nature, calling bonds “assets” could be argued to be wrong depending on the discussion.


To conclude, the paradox of this article could be the vague result, almost qualitative, compared to the extremely quantitative approach used to build it - again, the details of the math behind the cash-flows are provided immediately below. However, that is the point: when complex situations are examined in their underneath dynamics, that complexity is likely to emerge. While top-down views are effective for purposes of reporting and presentation, an apparently less clear bottom-up analysis is likely to return a better understanding of the critical dynamics and parameters to be monitored during implementation.



This post does not constitute in any way investment recommendation


For questions, suggestions, or comments, please feel free to reach out riccardo@m-odi.com or connect through Riccardo's LinkedIn


 

Digression on the math of the three investments and their cash-flows:

  • The house will require monthly additional payments representing the principal and the interests of the mortgage - the analysis replicates the practice of maintaining payments constant therefore changing the mix of principal and interests in time. We will consider everything on a yearly basis rather than monthly. Those payments will allow additional equity in the house to be gained from the initial 50%. In time, the value of the investment is equal to (+) the selling price of the house (figure 2) times the equity we reached, (+) increased by the cumulative rent either gained until that time or saved (data in figure 2), (-) decreased by the cumulative principal and interest paid until that moment. Note, to determine the yearly payments on the mortgage we used the exact formula determining the constant monthly amount and we multiplied it by 12 months

  • Similarly, at any point in time, the value of the bond is equal to (+) the spot price (calculated through the math of bonds and using the spot rate of figure 3), (+) increased by the cumulative coupon received from 1975 till the year of liquidation or maturity (the coupon varies in time as we purchase bonds corresponding to different rates as per figure 3, violet colored line), (-) decreased by the additional purchase of bonds in time in amounts equal to the payments made in principal and interests on the house’s mortgage. Note, to determine the value of the bond at any point in time from the spot rate of figure 3 we used the exact formula of the bond (which is the discounting of an annuity)

  • Finally, for the index fund we have (+) the value of the index at any moment times our holdings in it, (+) increased by the cumulative dividends distributed so far by the constituents of the index, (-) decreased by the additional purchasing in time (increasing our holdings in the index). Note that the Adjusted Closure of the index already accounts for the dividends


Dynamics and math behind the cash-flows of the simulated real-estate investment
Dynamics and math behind the cash-flows of the simulated bond investment
Dynamics and math behind the cash-flows of the simulated index fund investment
 

Sources of the data:

  • US inflation: https://fred.stlouisfed.org/series/FPCPITOTLZGUSA

  • Average house price: https://fred.stlouisfed.org/series/ASPUS

  • 30-year mortgage rate: https://fred.stlouisfed.org/series/MORTGAGE30US

  • 30-year government bond yiels: https://fred.stlouisfed.org/series/DGS30

  • DJIA quotes: https://www.wsj.com/market-data/quotes/index/DJIA

  • Mortgage periodic payment and outstanding loan amount formula: https://www.wallstreetmojo.com/mortgage-formula/

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