The biggest financial goal of many people is to buy a house.
Purchasing a residential property is what they save for. It’s what they work for. It’s why they don’t go out on Friday night and why they make their lunches at home. It’s also why their friends call them boring/cheap. But they don’t care. Owning a property is the dream.
But should it be? Most begin this financial journey without actually contemplating if it’s a wise financial decision or not. Many don’t investigate. Many don’t check.
Even if you do attempt to check, there is no clear answer out there. Debate rages on. It does seem that owning has become the accepted optimal strategy in most financial circles but this conclusion is by no means definitive. What’s more, there seems to be no hard-and-fast rule to determine which is better.
Some have attempted to make the case for certain rules of thumb (such as the “5% rule” and “rent if rent is cheaper than your mortgage payments”) but these are, sadly, inadequate.
I will be examining this problem from a purely financial perspective. Of course, this is naive. Other factors like pride of ownership and the freedom associated with renting will play a huuuuuge part in what is ultimately your decision. However, getting to grips with the financial situation can very much aid your decision-making process.
It is this situation that we will look at in this article.
As a financial transaction, owning vs. renting is unique. For a start, it’s probably one of the biggest decisions you will ever make. The stakes are high. Secondly, it has the strange feature that you have to live in your investment. It affects your life in an incredibly meaningful way. Financials are often a secondary factor for this very reason.
Neither option presents a particularly appetising investment option. When you are renting you are paying a substantial portion of your monthly income for, from an investing perspective, nothing in return. That certainly doesn’t seem like a good idea. When you own you take on a back-breaking amount of debt, making your incredibly fragile as a financial entity. Hmmm, not much joy here either.
But everyone has to put a roof over their head. Renting and owning are the only options we have (for now).
The costs associated with renting are easy to compute. Simply look at your rent (including bills) for each month (1). This is how much it costs to house yourself in that grotty flat in your “up-and-coming” area that you live in or that 4-bed house in the countryside.
Other charges are too small to affect the analysis. In fact, the government is actually trying to ban these little extra costs.
Average UK rent: £700.
Most young people (aside from the lucky bastards who got rich) who want to buy a house are faced with the same seemingly-unsolvable problem: lack of capital. Luckily, in finance, there is a well-established, tried-and-tested, trump card in this situation: leverage (2).
A mortgage is a loan secured against the value of a house. Using a mortgage, wannabe-home-owners can make a deposit with a mortgage-issuing institution who will lend you the remaining capital required to purchase the house. Happy days.
Mortgage rates (the interest rate you will have to pay on your loan) come in three main varieties: fixed, variable and tracker (3). Fixed-rate mortgages offer you a, funnily enough, fixed rate of interest for the whole duration of the fixed length of the contract. Variable-rate mortgages have a rate which the issuing institution can change but usually coincide with the Bank of England Base Rate. Tracker rates track this BoE rate exactly (with a premium).
These rate structures can be combined into one mortgage agreement. The most common is to have a fixed rate for some set period which then becomes a variable rate. Therefore, this is the structure I will be modelling.
Deposit. Usually somewhere between 10-50% of the house value.
Stamp duty. Again, varies depending on house value. Currently suspended due to Covid but in normal times you can expect to pay anywhere between 0% and 15% of the house value.
Conveyancy. This is the legal process of purchasing a property. About £1,500.
Survey. This is to examine the state of the building and its construction (to make sure the foundations aren’t made of papier-mâché). Roughly £1,000.
Mortgage valuation fees. The mortgage provider also wants to know the property value and they charge you for the pleasure the cheeky fuckers. £250.
Mortgage arrangement fees. This is the “cost” of putting the mortgage arrangement together. It’s almost as if mortgage providers try and extract as much money out of you as possible. Slap £1,500 on the bill for this one.
Note: I am assuming that mortgage costs, mortgage broker costs and estate agent fees don’t exist. You don’t need to buy furniture right? Nah, I’m sure you’ve got your own. Therefore, the total of £4,250 (not including stamp costs and the deposit) is likely to be a slight underestimation. Stamp costs and deposits will obviously depend on the house value.
Average UK house value: £239,196.
Ongoing costs are sneaky. People often don’t take them into account when comparing owning to renting. Luckily for you but unluckily for me, I am not most like most people.
Ongoing costs include utilities (water, electricity and gas), ground rent (paying the person who owns the actual land), building service charge, parking, house maintenance, entertainment (TV, broadband and internet), council tax, insurance and others!
That’s a substantial bill.
Unfortunately, as much as I searched the internet by reaching the 17th page of my google search inquiry, scurrying down multiple Wikipedia rabbit-holes and loading 9 different youtube tabs simultaneously, I was not able to find a definitive value for ongoing costs. As much as it pains me, we must estimate. Based on several recommendations, I have assumed that annual ongoing costs are equal to 1% of the property value.
Building a Model
Before building a model we need some input parameters.
I chose two properties in the town in which I live, Guildford. these properties were as similar as possible. Both were located close to the station (the commute is unbearable otherwise), had 3 bedrooms, 1 bathroom and two “reception rooms” whatever those are. Both were detached with a nice little garden. Perfect destinations for a young couple looking to move outside of London to settle down. Rent (including bills) was £1,885 per month and the property was listed at £635,000. As you can see, Guildford is fucking expensive.
By perusing mortgage-comparison sites I was able to find a fixed/variable mortgage of £476,250 (0.75 LTV). This 20-year mortgage had a 10-year fixed-rate period. The fixed rate was 2.69% and the variable rate was 3.59% (4). The fixed mortgage payments were given as £2,567.98 per month.
These are all easy to calculate: they are either fixed or proportionate to property value, which is known.
All of the figures for calculating the amount paid in the fixed period are given or easy to calculate. Remember, we assume that annual ongoing costs are equal to 1% of property value.
Before looking at the variable period we must first asses our remaining loan value at the end of the fixed period. To do that, we need to understand some basic mortgage mathematics.
Using our figures we determine the loan value at the end of the fixed period to be £269,925.
To calculate the total paid during the variable period we need to know the monthly payments are going to be in this period. These are not given by the mortgage comparison websites and need to be calculated.
To compute these payments we need both the total loan outstanding at the start of the variable period, helpfully calculated above, as well as some more of that good-old trusty mathematics.
The total costs owning are £941,577 and the total costs for renting are £452,400.
Maybe this whole property-owning malarkey is overrated?
What’s the better deal?
Not so fast!
Although you are likely to spend less money renting, this isn’t our primary concern. What we are really interested in is what is the better deal? In a strictly financial sense, of course.
To determine this we need to develop a model with a bit more sophistication.
By adding assumptions about some economic variables and computing other more granular variables we arrive at a set of numbers from which we can determine rent, mortgage payments, loan value, etc. for each month of our mortgage.
I assumed that the renter saves some proportion of his excess (monthly owning costs – rent) and invests it into his investment account. It was also assumed that their rent was increased with inflation at the end of each year.
The figures in the red boxes are editable. These determine the figures outside of the red boxes which then help to determine the outputs for each month.
These monthly outputs are then assessed at the end of the mortgage term, generating the outputs on the variables sheets.
The key figures to focus on here are the figures in the green boxes. This compares the net worth of the renter vs. the owner (both are debt free at the end of the mortgage).
As you can see, although the renter spent less during the period and invested more, the owner has the advantage of owning the property at the end of the mortgage period, which is actually worth more than the renter’s invested savings (even assuming a generous 6% rate of return).
You can find the model here. Enter your own values and see what’s the better deal!
Clearly, the outputs of this model are highly sensitive to the input variables. It is not possible to derive a general conclusion purely by considering these specific circumstances alone.
However, by changing the input variables and observing the impact on net worth we can examine the sensitivity of net worth to these changes.
Specifically, let us consider the relationship between % owner excess (the proportional owner net worth excess) and the input variables. So a value of 1 (100%) for % owner excess would correspond to the net worth of the owner being double that of the renter. The following charts were generated in R by considering such a relationship: they each show changes of only the input variable on the x-axis vs. the resulting changes in % owner excess on the y-axis. The inputs were varied between what I would consider to be most-likely ranges (be careful: as we are comparing outputs this assumption is fine in this context but very dangerous in others).
As you can see, portfolio return and interest rate negatively affect the % owner excess (POE) and house price growth positively impacts POE, as expected. The effect of inflation was previously unclear. It can often have substantial consequences for investors and, as we can see, that is the case here: it has dramatic consequences for the POE.
I then altered to inflation and interest rate assumptions to generate what some might consider to be a more realistic scenario:
In the inflation scenario, I let portfolio return, the interest rate and house price growth all be functions of inflation (spreads). Interestingly, the direction of the effect of inflation remains the same but its severity decreases and it is now concave, rather than convex, to inflation.
Similarly, in the interest rate scenario, I let portfolio return and house price growth be functions of the interest rate (again, as spreads). Now the role of interest rates has completely changed. Above some low level, they seem to increase the POE, rather than decrease it as previously. It seems that at higher levels the effects on house price growth out-weigh the increases in variable interest payments and portfolio returns.
There isn’t much to explain here, even I was able to understand this easily. A rent increases, owning becomes a more favourable option. As the renter saves more, renting becomes a more favourable option. The sky is blue, grass is green, and water is wet.
If you’re owning, keep costs low. Especially ongoing costs.
Notice the importance of house value in the severity of the relationship above. With a cheaper house, the mortgage becomes much more affordable and the interest payments less severe. The relationship is extremely concave.
This is slightly unfair as rent is remaining constant throughout this time. If we set rent as a function of house value (by using a constant proportion that we observed in the original analysis) we can see the effect of house value changes more clearly.
Now the relationship has flipped on its head.
Low house prices imply low rents, which means the renter can save more and invest it, leading to a lower POE.
Increasing LTV seems to benefit the owner in a linear fashion. This is probably because the smaller upfront cost means that the renter’s investment account does not grow as large.
POE is concave to the term length (I assumed here that the fixed component was always half of the total). There seems to be some optimal term around the 20-year mark.
Unsurprisingly, increasing interest payments rapidly turns the POE negative. It also seems that it’s better for the owner (comparatively) to pay less earlier on. By paying less they reduce the renter excess and the amount they are willing to save and invest. This may not be a good strategy for the owner but, relative to the renter, it seems that it is.
Bringing it all together
The results of the sensitivity analysis for our specific example can be summarised by the following table:
I may have lied to you earlier.
Sensitivity is not, in actuality, that easy.
You see, although this table is interesting and could be potentially informative we must ensure that we remember several things that weaken any conclusions that you could make based on the information contained within it.
These relationships are specific to this particular example. Changing the input variables may affect not just the strength of the relationships but also the directions. The effect of changing these variables is very much dependant on the other values of the other input variables. Even in the case of changing known input variables, the observed relationship that input has with POE is heavily influenced by unknown input variables.
In addition to this, the majority of this sensitivity analysis assumes that the input variables are independent when, in reality, they are not. As we saw with the examination of the sensitivity to economic variables, removing our independence assumption can reverse the established conclusions. This idea is expanded upon later.
The unknown size of and interdependence between these unknown input variables severely limits the utility of this type of sensitivity analysis.
The Great Unknown
What are these “unknown input variables” and what are they likely to be in reality?
Well, assuming you know everything possible about the house, your mortgage, how much you’re planning to save if you rent, etc., the unknown variables are the economic ones: inflation; portfolio returns; the interest rate; and house price growth.
Looking at the chart of annual RPI (5) change, we get a sense of the potential for inflation. It has fluctuated mostly between +20% and -20% with what seems to be a structural change around 1900.
The stock market does not always go up. In fact, we see that it typically returned somewhere in the region of +20% to -20% annually (6), with some notable exceptions. It is important to note that this is only stock market returns. In reality, you can compose a portfolio of all kinds of different assets.
The BoE base rate seems to have three phases of behaviour. First, it was constant. Then, in the early 1800s it started to fluctuate between roughly 2.5% and 7.5%. At around 1950 it seems it really started to be utilised as a tool for economic manipulation, resulting in incredibly high rates (to combat inflation) and incredibly low rates (to combat economic contraction).
House Price Growth
Unfortunately, I was not able to find any long-term data for house prices in the UK (even though this report from Schroders suggests it exists somewhere…). House price growth seems to be fairly erratic in recent history, with more growth than shrinking. Importantly, this is growth in the average UK house price. House price growth seems to be fairly localised, resulting in markedly different prices in different areas. It may also be the case that there are substantial differences within an area depending on micro-locations. A property close to the station might vary differently than one further-out with a nice garden due to working habits and the consequent need for good transportation link to London, for example.
Historicism has been historically ineffective
As always, we must be very careful when considering historical data. Although I feel like I’m beating not just a dead horse but a horse’s skeleton at this point, I feel a moral obligation to at least mention this important caveat. I should really write a separate article about this soon…
What is becoming somewhat of a catchphrase for me: history shows us what can happen, not what will happen, not necessarily what is likely to happen. Consider historical data with this in mind.
For example, imagine yourself in 1850 England. After sending your 11-year-old son chimney-sweeping for the day, you grab your top hat and cane and set off to work, avoiding pick-pockets down the narrow streets of London on your way to the Bank of England.
For the past 50 years, the pattern of inflation has been clear. Very clear. Predictable, in fact. Inflation oscillates between about -10% and +10%. You plan accordingly, factoring this into your macroeconomic models of the empire and scratching your forecasts for key economic variables on parchment with your favourite quil. Looking at the chart of UK inflation, however, we see that the fluctuations in inflation seemed to substantially settle over the next 50 years. Oh heavens.
The same can be said of someone forecasting mild fluctuations in 1900.
Or fast forward 100 years. Your great-grandson is, like you, working for the Bank of England. He is forecasting the Base Rate over the next 10-20 years (“forward guidance”). This seems simple: looking at the rate over the last 250 years we see that it has been fairly stable, fluctuating between about 2.5% and 7.5%. You assume this will continue. A maximum of 10% for the future rate seems sensible, if not a little over-cautious. Over 15% is impossible.
Within 25 years the base rate had reached 15%.
So how can we use this historical data, if it can be so misleading?
Firstly, historical data illustrates the pitfalls of using historical data. It also does give some kind of indication of what these variables are probably more likely to be (I don’t think I could fit more uncertainty into that sentence if I tried). When combined with deductive reasoning, it can give clues as to more-likely scenarios. Are interest rates more likely to be 2% over the next 20 years or 200%? Probably 2%. Are house prices more likely to grow by 10% each year over the next 10 years or fall 90% each year over the next 10 years? Probably grow by 10% (7). Unfortunately, due to the intrinsic complexity of these variables, these are really the only types of questions we can answer.
Having said this, I do feel comfortable allocating likely ranges to these variables and I think the resulting observations can be analytically useful. Using the ranges for the sensitivity analysis we can vary several variables at the same time randomly within these ranges and observe the effect on POE over several trials.
Let’s start by letting all variables vary randomly, using the ranges outlined above. So, observations of each variable of each trial will be selected from a uniform distribution with upper and lower bounds specified by these ranges.
As we can see, under this regime the POE varies wildly. This is actually not very informative, there is too much stochasticity and we can’t really draw any conclusions from this initial experiment.
I an attempt to rectify this we can introduce some realism into the model. We do this by adjusting certain variables.
Firstly, we set return and house price growth as spreads over inflation (both inflation + 0.025).
Both these variables are probably linked to inflation: as price levels rise, people can afford to spend more, in absolute terms, on houses and products. We set the interest rate as being equal to inflation, as this is the BoE’s primary tool for controlling inflation.
We also set rent as a function of the property value and we lower the SVR premium maximum to 10%, which is probably more realistic.
Alas, these adjustments do not seem to have made much difference. It is still unclear what the POE is likely to be for some unknown situation. What’s more, it seems that POE is fairly fat-tailed; in some instances owning will be a relatively very good decision and in others a relatively very bad decision.
Luckily, in reality, we know some input variables before deciding whether to rent or to own.
Now we let only the unknown variables (the economic factors, ongoing costs, SVR premium and renter savings rate) vary stochastically. All other variables we obtain from our lovely Guildford example above.
This probably the most important chart in this whole article. As you can see, when the known inputs are fixed, a much clearer picture of POE emerges. It seems that, in this instance, owning is the better option.
Let’s now assume that all non-economic variables are known: you are confident that your ongoing costs will be 1%, you have a mate at Barclays who can give you a “guaranteed” SVR premium and you know that if you rented you would save about 80% of the renter excess.
Again, we can’t draw many conclusions from this analysis (other than the fact that owning can go badly wrong!).
We need to introduce the notion of spreads. In the first chart below, we let the interest rate, portfolio return and house price growth be functions of inflation, as before.
The second chart illustrates a large return spread over house price growth. Owning is clearly favourable in the former scenario but more doubtful in the second.
Finally, we consider some extreme scenarios in which the inflation rate and the interest rate are disconnected from the other economic variables, which are allowed to vary stochastically.
Note that these are only some examples of the different scenarios you can test. Adding others will give you a more complete picture of the consequences of the decision that you face.
Although we lose significant detail by doing so, these results can be summarised by the following table:
By stress-testing the POE under various different analyses, you’re able to get a sense of what might be the best decision financially.
But you can never be certain.
This analysis isn’t perfect. One major area of contention is the distribution of the unknown variables. I have used the uniform distribution because I don’t think it’s clear what values within the ranges are more likely in the future. This might not be the case. By estimating the distribution of the variables it’s possible that more realistic conclusions could be drawn. For example, is it more likely that the average interest rate for the period will be 3% or 20%? Possibly 3%, but here they are equally as likely. This could lead to a systematic upward bias in the economic variables. What’s more, realised values may actually lie outside of the ranges specified. Negative interest rates, say, are not possible in this world.
As stated previously, another problem is that these input variables fail to accommodate for inter-dependence between themselves. This can dramatically affect the outputs. Simply, there is no truly good method of accounting for these inter-dependencies as they are too complex. Traditionally, some have used correlations but this is not appropriate in this context (this is like trying to pick a lock with a rock). Changes in these variables don’t occur in isolation and acting as if they do, or proceeding as if the links are clear and simple, is a little naive at best.
As with everything considered over a long time frame in a complex environment, it’s difficult, if not impossible, to know what’s going to happen and what’s the right decision. Simplifying the problem and considering both the sensitivity of the output to changes in input variables and the reaction of the output to different hypothetical scenarios can help. But, at the end of the day, we are still faced with significant uncertainty.
Owning vs. renting as a financial proposition is coated in this uncertainty. Fortunately, or unfortunately, there are other factors that go into making the decision. Qualitative factors are incredibly important. Do you want to live in the same location for 10+ years? What are your attitudes towards debt (I am want to keep a safe distance from it)? Do you have the discipline to save the renter excess?
The analysis also neglects several other quantitative factors. The costs of investing are not considered. Government schemes are not taken into account. Buy-to-let, second-home purchases and other things are casually disregarded.
However, I stand by what I see as the main conclusion that we can draw from this exercise: there is no single definitive answer to renting vs. owning. And the problem is actually much greater than this. Although I am generally an endorser of heuristics, there isn’t even a rule of thumb that I could see as being particularly effective. Anyone preaching the use of a rule without a careful analysis of the specific situation is, therefore, wrong. Even when considering specific scenarios it is unclear to what extent “running the numbers” is useful. We can see what can happen under certain scenarios but the probability of each scenario is highly uncertain.
And this is what we really care about. When I get on a plane I know that the plane can crash but I don’t care because the probability is very low. Stochastic analysis is useful is making us aware of what can happen but less useful in terms of illuminating what is likely to happen.
Having said this, my intuition tells me that some kind of quantitative analysis outlined above is better than nothing, providing it is taken with a whole spoonful of salt.
After gathering all your input variables, I would recommend the following:
- Observe the investment account total vs. house price value at the end of the term period using the spreadsheet model.
- Check the sensitivity of the POE to changes in the unknown input variables, ensuring you vary the dependencies between unknown variables.
- Look at the possible outcomes when the unknown variables are allowed to vary stochastically.
- Look at the possible outcomes under different scenarios in which the unknown variables change in different ways.
Although it is impossible to arrive at an answer as to which is the better option, performing these tasks can help give you an indication. Combine this indication with qualitative considerations to arrive at your decision.
Given the uncertainty surrounding the quantitative side of the equation, I am starting the belive that your preferences should actually take prescedent in your decision-making proccess. Check the numbers, sure, but ask yourself “what is my gut telling me?”.
Much of what we know we can’t express in words and doesn’t seem logical on a surface level. There are flaws in our thinking, sure, but these are over-blown. Listen to what your gut is telling you. It’s often right. It’s not perfect and you’re going to have to live with the fact that you might make the “wrong” decision, but that’s life.
(1) I am including council tax in bills.
(2) I am not considering cash purchases. You are so rich at that point that you don’t need to think a lot about financial decisions, you just buy everything.
(3) I am not considering those weird contraptions called interest-only mortgages that leave you with all of the original debt that you went into the deal with. Ghastly things.
(4) The rates listed by mortgage issuers are annual but uncompounded. So, to get the monthly interest charged simply divide the rate by 12.
(5) We are using RPI instead of CPI because the dataset goes waaaay further back in time and, unlike CPI, it includes homeownership costs.
(6) This is only the price return, not total return. The total return is harder to determine historically and, as a result of this, the dataset is much smaller. You can see the total return of the FTSE 100 here.
(7) Because many of these variables are absolute, rather than real, much of their future trajectory depends on inflation. If we were to observe high inflation or hyperinflation then all bets are off really.