Sunday, November 10, 2013

Flawed Logic Everyone Uses to Support Buying a Home

The Claim

Some people equate renting a home to "throwing away money each month" when compared to buying a home. That is, they think that if they buy a home, they "invest" the rent in the home in the form of a mortgage payment each month vs. "throwing it away" on rent paid to someone else if they don't own the home themselves. They make the claim: "buying a home is better than renting a home because renters throw away money each month whereas buyers invest the money in the home itself, and therefore don't lose anything other than the interest on their mortgage payments." This is horribly flawed logic.

It recently occurred to me that a lot of people might think this and so I wanted to quickly write a blurb about exactly why this logic doesn't make any sense. To be clear: the reason why the claim is wrong isn't subjective or qualitative; the claim is straight-up wrong because of basic, simple, although unintuitive, economic principles. It's wrong because of what you learn in econ 101, so if you every thought the choice between buying/renting was obvious, you should really read and understand what I've written below.

Opportunity Cost (Definition and Explanation)

In order to understand why the claim is wrong, we first need to understand the concept of opportunity cost. Explanations of opportunity cost are all over the internet but I'll explain what it is here for completeness.

Simply put, opportunity cost is the cost of not doing something. To understand how it works, we'll go through a short example.

Suppose I charge you $100 to leave work an hour early on Friday. Then, the cost of leaving work is obviously $100. That is, if you leave work early, you will lose a hundred dollars. What's tough for people to understand is that not taking money is the same as giving money away. To see that these two things really are the same, we can go back and modify our previous example slightly. Now, instead of charging you $100 straight-up to leave work early, I take $100 from you (before-hand, against your will so it's not a part of your decision) and offer to give it back to you if to stay that extra hour. These two situations are actually identical economically and the key question you have to ask to see this is "what's the cost of leaving work?" in each case. The cost of leaving work is the difference between how much money you have if you leave and how much money you have if you stay. In the first situation, you have -$100 if you leave work and $0 if you stay so the cost of leaving work is: -$100 ($ you have if you leave) - ($0) ($  you have if you stay) = -$100. But in the second situation, you again have -$100 if you leave (because I took it before-hand) and $0 if you stay. These payoffs are identical to the first situation and so the cost again is -$100 even though I'm taking based on your decision in the first case and offering based on your decision in the second case. We call the $100 charge a "cost" in the first case and an "opportunity cost" in the second case by definition because you "lose" $100 in the first case (cost) but you "choose not to take" (opportunity cost) the $100 offered to you in the second case.

Opportunity cost will be important for the rest of the explanation so be sure to check out Wikipedia if my example still doesn't really make sense.

Why the Claim is Wrong

Alright, so now that we understand opportunity cost, we can understand why renters aren't really "throwing away money" compared to buyers. In order to see this, we have to factor in not only the mortgage payments buyers make but the opportunity cost they incur by not renting out their home. The best way to do this is with an example.

Let's supposed you've saved up $1MM (lucky you!) and you're trying to figure out what you want to do about your living situation. You're going to choose between the following two decisions that almost every American faces and analyzes (usually incorrectly):
  1. Rent a home worth $1MM and save the money you're not spending on rent (or invest it, it doesn't really matter). Suppose this rent costs you $X a month.
  2. Buy a $1MM home and live in it.
What's the difference between these two situations? To see this we will need to leverage our understanding of opportunity cost. In particular, we'll compute your monthly costs when you rent and compare them to your monthly costs when you buy.

The Renting Case:
In the case where you rent, you have an up-front cost of $X per month (cost of the rent) and that's it (easy-peasy). This is money most would consider "thrown away." It's identical to situation (1) where the owner of the home is your boss and renting is "leaving the office." You get charged money to stay in your home (cost), just like you get charged money to leave the office.

The Buying Case:
Oh, in this case you don't have any costs per month because you're awesome and you own the house, right?
No money being thrown away, right? WRONG! Go back and read the opportunity cost section, bud! While it's true you have no "rent" cost, you're forgetting about the opportunity cost of living in the home! If you can rent your home out for $X a month, then you're technically giving up (throwing away) $X per month by living in the home as opposed to renting it out to someone else. And, because money given up is money lost (see the opportunity cost section), you're technically losing $X per month in situation (2) as well, making you no better off than in situation (1). This is hard to wrap your head around but the key is to understand that not taking a renter's money is the same as paying the rent yourself. And just like you throw away money by renting from another person, you also throw away money when you refuse to let other people pay you to live in the home you own. It's identical to situation (2) in the opportunity cost section: you get money taken away up-front (by the old owner/your boss in the example), then you get offered it back if you choose to leave the home (by renters/your boss in the example). Now you give up money to stay in your home (opportunity cost), just like you give up money to leave the office.

In conclusion: when you rent you pay $X a month up-front and when you buy, you still pay $X a month in opportunity cost if you live in your home. Thus, renters and owners throw away equivalent amounts of money and there is no obvious advantage to buying a home vs. renting forever.

A Home is Just an Investment in Real-Estate

So what do you gain by buying a home versus renting forever? The only thing you get is an investment in the real-estate market and nothing more. If you think real-estate is going to boom, buy a house, otherwise, invest in something else and rent. To see why this is the case, we again use an example.

Let's suppose, again, that you've saved up $1MM  and you're ready to decide between two different options:
  1. Use all the money to buy a house and rent it out to someone for $X a month.
  2. Put all the money in the stock market.
In both of these situations suppose you're renting (living in) a different $1MM house and you're paying $X a month. This makes living costs the same in both cases so we don't have to worry about them. So what's the difference between the first and second option? Well, in the first case you're investing in the real-estate market and in the second you're investing in the stock market, but that's about it. In the first case, you'll get rent payments ($X a month, maybe you use them to pay for your rent at the other house), in the second case you'll get dividend payments. In the first case you'll sell your house if you feel like it and in the second you'll sell all your stocks. If the real-estate market looks like a better investment to you than the stock market you'll take option (1), otherwise you'll take option (2) but other than that, one isn't much different than the other. A home is an investment vehicle just like a share of stock when you rent it out.

So what does this have to do with anything? Well, suppose you want to stop paying your $X/month rent and instead take option (1) and live in the house you invest in. Nothing changes. You're still investing in the real-estate market like before only instead of getting $X/month from renting out the home you bought (and paying $X/month for your other place), you give up $X/month in rent for the home you bought (and stop paying $X/month in rent at the other place). Net, you're in exactly the same position you were in as a home renter as you were in as a home owner.

Some Actual Reasons to Buy a Home

So by now you should be convinced that home renters don't throw away more money than home owners and, additionally, that all owning a home affords you (over someone who rents exclusively) is an investment in the real-state market. But, all that said, there are still some very interesting reasons why buying a home could be better than renting one and I'm going to go over them here.

A Mortgage Gives You "Leverage"
Suppose you have $1MM. If you want to invest in the stock market, typically all you can do is use that $1MM to buy a bunch of shares of stock. If the shares go up by 1%, you make a 1% return on your $1MM and that's it. However, when you buy a home, you can typically buy one that's worth much more than the amount of capital you happen to have on-hand. Going with this example, you can use your $1MM to get a $2MM mortgage and buy a $2MM home. Banks like giving loans on homes but they're generally not receptive to people who come in asking for money so they can "invest in the stock market." As such, you can use bank loans to your advantage when investing in real-estate in a way you can't when investing in normal stocks. Why is this good? Because now, if the value of your home goes up 1%, you've actually made a 2% return on your $1MM investment. That is, you're using "leverage" to amplify your returns. Of course, this is true for the downside, too, but if you're damn sure the real-estate market is going to boom, getting a little leverage and buying a home can get you rich pretty quick.

You Can Deduct Interest Payments from Your Taxes
This is one of the biggest advantages to taking on a mortgage in my opinion, mainly because it makes your effective interest rate lower. To understand how it works, let's look at an example.

Suppose you pay $12,000 in interest payments one year. If you make $100,000 that year in taxable income, then you can deduct the $12,000 from your taxable income, which means you'll only pay taxes on the remaining $88,000 of income you earned. If your tax rate is 25%, then without the deduction you pay $100,000 * .25 = $25,000 in taxes. With the deduction, you only pay ($100,000 - $12,000) * .25 = $22,000. A savings of $3,000. In general, the amount you save is (amount you pay in  interest) * (marginal tax rate),

Overall, this has the effect of *effectively* decreasing your interest rate. If you pay R% as your interest rate, and if your marginal tax rate is T%, then your "effective" interest rate because of the deduction is actually R% * (1 - T%), which is lower than R% alone. Pretty nice.

Your Downside Ain't Bad
Suppose you put your $1MM in the stocks and they all went to $0. Now you have $0-- that sucks! But now suppose, instead, you took out a huge mortgage and bought an $8MM home instead. If things work out well, your up-side is magnified 8x, way better than investing in stocks. But what happens if things go bad? Well, if the real-estate market tanks, you can just stop paying your mortgage and let the bank foreclose on your home, putting you at $0 just like you would have been had you invested in stocks (lots of people did this when the housing bubble burst in '08). So, let's compare the two examples again. With stocks, you make a 1% return on investment for every 1% the stocks go up and -1% for every 1% the stocks go down. With a home, however, you make 8% for every 1% the real-estate market goes up, and, if the real-estate market tanks, you make -1% for every 1% the real-estate market goes down when you default on your loan. Overall, this asymmetric payoff can make buying a home look pretty attractive, not that I'm encouraging anyone to default on their loans, which a very serious thing...

Real-Estate Could be a Good Investment
I won't go into this, but if you think real-estate is a better investment than anything else, buying a home is a great way to invest.

One Last Kindof Weird Thing

One side-effect of living your life by the principle of opportunity cost (the correct way to live your life, by the way), is that if you own a home and its value sky-rockets, you should move out. Why? Because your "rent" (the opportunity cost of living in your home) just went up in a sense. Every month you live in your home you're forfeiting ridiculous amounts of lost rent from people who would be willing to pay much more to live in the place than you would. As such, you need to always be asking yourself "what would my rent be if I didn't own this place" and be willing to move to a cheaper area if that number is too high, or risk paying a very high opportunity cost.

11 comments:

  1. There's one thing you miss, I think. By living in real estate I own, I choose "opportunity cost" which doesn't come out of my pocket, rather than "cost," which does. Economically, the two are the same, but in practice, they are not. My fixed mortgage rate is locked in -- my monthly cost is not dependent on the whims of the market, whereas rent can change drastically year to year (and it's probably not going down). I don't have to shop for a new place or move my stuff unless I want to move, whereas places I rent could ask me to move out on pretty short notice. That security and predictability and time saved is definitely something of nontrivial value.

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  2. Hm...............

    My understanding is that one of the main benefits of buying a house is that you can create wealth by making improvements to it? That is, if you buy a small, dinky little house with crummy landscaping, leaky windows + no air conditioning for $100k, you can invest $20k on some flowers, solar-efficient windows and AC, throw a big open house and sell it for something like $140k. So like since renters can't legally rent out their rental, there's also an opportunity cost with renting a house in that renters can't profit off making improvements to it...

    (Granted I doubt most Americans truly create that much wealth by customizing their houses/my mom thought 'grey' would make a lovely color for the living room before it was repainted..../but a lot of people like the pursuit of home "improvement" and Home Depot)

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  3. You're looking at it from the point of view that you have $1 million in cash to "invest". I think the primary benefit of paying off a mortgage instead of paying rent is that, with a mortgage, a percentage of what you're paying every month is in essence saved. So after paying your mortgage for 30 years, you're left with at least a $1 million dollar house assuming the house hasn't depreciated in value, as opposed to $0 in the case where you're paying rent. Obviously once your mortgage is paid off, you're totally right. Maybe this is obvious, but it feels left out of post. Thoughts?

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  4. Siggi, unfortunately that argument's flawed for the same reason the original argument was. The reason why is that I think you're forgetting that the rent and the mortgage are computed differently and the way in which the renting rate is computed "prices in" the benefit you lose had you actually become the owner of the house after X years. Here's an example:

    Home costs $1MM and the annual interest rate is 3%, making the monthly interest rate 3/12 = .25% (suppose). Then, the "proper" rent you should pay on a house (all else equal) is the discounted cash flow to infinity. That is, the rent per month, r, should be such that:
    r + r * (1/1.0025) + r * (1/1.0025)^2 ... = 1MM
    r sum_{i=0}^{\infty} (1/1.0025)^i = 1MM
    r 1/(1-1/1.0025) = 1MM (geometric series formula)
    r = 1000000 * (1-1/1.0025)
    r = $2493/mo

    SO: if you're renting a $1MM home, you'll pay ~2493 per month.

    Now suppose that instead of renting, you're going to take out a 10-year mortgage for $1MM. If the bank's nice, they'll charge you an interest rate of 3% and a monthly rate of .25%. So what are your monthly payments going to be under this scheme? Let's compute it (same analysis as above but for 10 years = 120 months instead of infinity):
    r + r (1/1.0025) + ... + r (1/1.0025)^119 = 1MM
    r sum_{i=0}^{119} (1/1.0025)^i = 1MM
    r (1 - (1/1.0025)^119) / (1 - 1.0025) = 1MM
    r = 1000000 * (1-1.0025) / (1-(1/1.0025)^119)
    r = $9701 / mo

    Whoa! So borrowing money to buy the house and paying it back over a 10 year period makes your monthly payments way higher than if you were just renting a place. That's called the "liquidity premium" (the premium you pay to get 1MM right now (liquidity) as opposed to 1MM payed over infinite time) and it fucks you up the ass. Indeed, if buying a house and paying the mortgage down over 10 years cost the same per month as renting it for that amount of time you'd have a pretty sweet arbitrage opportunity.

    The way to look at this that really drives the point home is to imagine the situation where you DONT live in the house. In the situation where you're a renter, you pay the landlord 2493 and the subletter pays YOU the same amount putting your net monthly value at 0. In the case where you buy, you pay the bank 9701/mo and get 2493 from the subletter, making your monthly payment -7208/mo for 10 years. After the 10 years, you get 2493/mo in profit. Hmm so let's see..
    -7207 + -7207*(1/1.0025) + ... + -7207 (1/1.0025)^119 + 2493 (1/1.0025)^120 + ... = 0 (!!!)
    So, as it turns out, the "present value" of the cash flows you get from buying a house and renting it out is exactly 0, same as the present value of renting it. So, at the end of the day, the liquidity premium you pay from borrowing 1MM is in fact so high that it actually exactly offsets the benefit of having the house forever as an owner.

    tldr: the catch is that your monthly payments are way higher with a mortgage to the point where they actually offset the benefit you get from having it forever.

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  5. You don't need the real estate market to "boom" in order to make money off of a real estate investment. Even if the real price of the house stays flat, then 5x leverage (as is standard) will earn you good returns on 2-3% inflation. You just need to avoid a severe real estate market crash and/or deflation.

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  7. This interactive chart sums it up.

    http://www.nytimes.com/interactive/business/buy-rent-calculator.html?_r=0

    Whether it makes sense to rent or buy boils down to the following:

    Carrying costs of ownership (mortgage interest, taxes, maintenance)
    Tax savings from interest payment
    Rent increases (inflation)
    Property value appreciation
    Opportunity cost - return on investment with the money that would have been used for the downpayment and closing cost had you bought the home instead



    As a renter for the past 10 years, one of the reasons why I have delayed ownership is because for the longest time the math never made sense.

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  8. Your comment about the downside risk of a leveraged investment versus an investment in the stock market is mathematically incorrect.

    If you have $200K to invest in either a $1M home (20% down payment) or $200K in the stock market and both assets decline by 10%. In the stock market scenario, you lose $20K ($200K * .9). In the house example, if a $1M house goes down by 10% you lose $100K ($1M * .9) on your initial $200K investment. The absolute value of the asset you buy is higher and thus the downside risk is also significantly amplified with leverage (5 times higher in this case). You are; however, correct in saying it is asymmetric because your upside is still significantly higher using a leveraged investment whereas your downside in both cases is still solely your initial investment. The same idea of leverage can be applied in the stock market through a margin account; however, due to the extremely high levels of government support for the housing market, in most cases your allowable leverage through a mortgage is much higher than that of a margin account to invest in the stock market.

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    Replies
    1. Well...it's incorrect for 99% of the population who use leverage to buy a house and not for investments in the stock market. Overall a thought provoking piece and I agree...the opportunity cost is the framework that should be used to look at these things. Not to mention, you get more flexibility as a renter at a young age when it's more likely to move around for things like jobs.

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  9. http://www.businessinsider.com/if-you-live-in-new-york-and-you-rent-youre-paying-a-huge-tax-you-dont-even-know-about-2013-6

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  10. Sal Khan actually just posted a really awesome video that goes into this whole thing in detail using a thorough example:

    https://www.khanacademy.org/economics-finance-domain/core-finance/housing/renting-v-buying/v/renting-versus-buying-a-home

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