What Is Finance?
Last spring, I was trying to figure out what to do with my life. For many years, I had been operating on autopilot: I was going to finish my PhD and spend the rest of my days in the secluded comfort of the ivory tower, researching and teaching mathematics, the subject that had been coursing through my veins from infancy. I was slow to catch on to the reality that I was not enjoying my research, not enjoying my teaching, and increasingly unable to see a future where I would be enjoying those things. I won’t torture you with the hows and whys, but I had reached a dead end.
It seems almost trite that I decided to pursue finance. After all, finance is the perfect industry for somebody with high-powered academic credentials and not a single clue. At least, it was before 2008. These days, fallen academics are increasingly rushing to the tech world as financial firms are operating with less abandon than one might be led to believe. As a result, I probably come off as even more clueless than I actually am: if I want to be a quant, I should probably hop in a time machine.
But for some reason, finance beckoned to me in a way tech never did. I was becoming increasingly aware of the ways in which the good and the bad in the world could be explained by economic considerations. From the state of our built environment, which I had become very passionate about, to global warming, economics was, to paraphrase Homer Simpson, the cause of, and solution to, all of life’s problems.
Finance, as I understood the term, had something to do with economics, so naturally I was curious. But there was one simple question that I found surprisingly difficult to answer: What is finance?
My first inkling of what finance is came from arguing with people about the cult of homeownership following the collapse of the housing bubble. We tend to massively subsidize owning a home, both on the national level through the mortgage interest tax deduction, and on the local level through tax codes and various regulations. Here’s a little libertarian koan for you: if homeownership is so important, why does the government have to subsidize it?
People tend to cite two factors in favor of homeownership. First, they say, buying a home is an investment. Your mortgage payments go to owning something, whereas you’ll never see your rental payments again. We subsidize homeownership in order to encourage good investment. Second, homeowners will care more about their community because they have more invested in it. If your community improves, the value of your house will go up, which is good for you. On the other hand, renters might oppose improvements for fear that their rent will go up. So homeownership is worth subsidizing because it creates positive externalities for the community.
Let’s deconstruct these arguments one at a time. The first can be pretty easily dispatched with. A home is a terrible investment for most people. Let’s first note that it’s a highly leveraged one unless you choose to buy outright. Traditionally, people put 20% down, which means leveraging 4-to-1. During in the housing bubble, it became fashionable to put less, or even none down. But even the baseline 4-to-1 is still quite leveraged: a 10% drop in your home’s value will halve your equity, and a 20% drop will annihilate it. Unless you truly believe the now-disproven notion that home prices will keep rising forever, a 20%-down mortgage is a massively risky investment.
Even ignoring the extra risk involved in leveraging, the returns look somewhat suspect as well. There are two parts to your investment: the land your home sits on, and the building itself. (We’ll ignore the puzzle of condos, where you in principle own a share of the land, but in practice have no way to cash in on it.) Land is certainly something that can appreciate greatly in value if you live in a desirable location: supply in your area is fixed, and demand will keep rising as long as your location stays desirable. Unfortunately, the desirability of your location is very likely positively correlated to your income. If you’re living in an industry hotbed, your job is very likely secure, so you don’t need your investment to rise as much. But if things take a turn for the worse, you might lose your job, only to discover that your house isn’t worth the paper your mortgage is printed on. In short, unless your occupation happens to be terribly countercyclical, the land where you live is exactly the kind of investment you don’t want to be highly leveraged in.
The other portion of your investment is the building itself. This isn’t so much an investment as a liability. Buildings, particularly ones that are lived in, need to be maintained, insured, and kept up to code. Put that on top of the land, which as we saw was already a dubious investment, and you just have something awful.
But what about renting? Isn’t it still true that when you buy a home, you should at least see some of that money back, whereas rental money is gone forever? To answer that, we have to understand exactly what your rental money is paying for. Your landlord owns the land your building is on. Land, as we said, can potentially be a good investment. So why bother maintaining a building at all? To amortize construction costs and pay for maintenance, insurance, taxes, and utilities, your landlord needs something in return. Those costs are precisely the costs you pay for when you own your home, but a landlord can likely manage them much more efficiently than you can! In sparsely populated areas, the overhead can be too great, which explains why you mostly see rentals in urban areas. But really, the only reason that we should see rental costs above what you might expect to pay owning a home (modulo perhaps the amount of DIY labor you wish to put in) is because we do so heavily subsidize owning over renting!
Now that we’ve broken down the investment myth using a bit of financial thinking, let’s move to the community myth. This one is a bit trickier because there seems to be a kernel of truth to it. Renters certainly don’t want their rents to go up. While in principle, a homeowner should want the value of their house to go up, this also means that their property taxes go up. Since most people tend to think very short-term about their finances (even though the homeowner mindset is supposed to be a hedge against this), aversion to higher taxes probably tends to lump homeowners in the same camp as renters.
This is not good! People should be able to benefit from improvements to their community. They should want progress, development, and wealth. But both this thought exercise and real-world experience tells us that renters and owners alike tend to oppose such niceties. But at least we’ve debunked the community myth: renters and owners alike do not want to improve their communities.
So far, we’ve used finance to make observations about how the world works, and what we’ve observed should disturb us deeply. We’ve seen that homeowners are making terrible, risky investments, and our communities are languishing because allowing communities to flourish is not in residents’ self-interest. But finance is more than just an observational tool: it is a creative framework. We can use financial reasoning not only to identify problems but to correct them.
A very basic example of a financial solution is homeowner’s insurance. Without it, owning a home would be an even risker proposition than I’ve outlined above. People understand why they need insurance: if their home burned down without it, they’d be destitute.
The reason insurance works is that people are willing to give up a small amount of money to avoid a big, if unlikely, risk. But in order for this deal to be profitable for the insurer, the small amount of money has to be greater than the insurer’s expected payout. Both sides are happy because you are more sensitive to the risk than the insurer, who can afford to pay to rebuild your house after a fire because they’ve been receiving premiums from lots of other people who don’t need to rebuild. Things like flood insurance are much more tricky, because floods tend to affect a lot of houses at once, so insuring a bunch of houses in the same area would expose an insurer to massive risk.
If homeowners buy insurance to protect against losing their house in a fire, then why shouldn’t they also buy insurance to protect against the value of their house going down due to decreased demand? Indeed, a number of such schemes appeared in the wake of the housing crisis, but consumers didn’t bite and pundits remain skeptical. One reason to be very skeptical of such a product is that it suffers from the same problem as flood insurance, but worse: in 2008 we saw housing prices plummet across most of the US.
Nevertheless, finance may still be able to provide a solution. Rather than purchasing insurance, a savvy homeowner could in principle participate in a Case-Shiller Home Price Index futures market. While financial derivative markets are typically only available to institutional investors, there’s no reason in principle that the power of such markets could not be brought to homeowners. Buying put options for the Case-Shiller Home Price Index is nearly equivalent to buying home value insurance, but potentially with less overhead and systemic risk.
In the interest of keeping the length of this introductory post (relatively) short, I’ll put off a discussion of how finance can solve the more thorny community problem to a future post. But I hope that I’ve laid out the basic idea: financial instruments like insurance and futures contracts exist to hedge risks. If an investment seems too good to be true, like houses did during the bubble, it’s probably because you haven’t considered the cost of hedging all the risk. Gambling can be fun, but when it comes to how we should run our lives, it seems prudent to not allow ourselves more risk than we’re willing to bear.
Everything I’ve said so far is what I thought finance should be. In reality, it’s largely a gambler’s world. Still, it seems, there’s value in learning to navigate this world. I heard through the Twitter grapevine that John Cochrane was going to be teaching an asset pricing course on Coursera, so I dove in. Thanks to John’s wonderfully lucid course, I’ve learned a little bit about what finance is. There are many beautiful stories written in the language of asset pricing, so I want to start by reviewing some of the vocabulary and then move on to some simple tales.
An asset, I believe, is something we buy that has no intrinsic value to us; all that matters is how much money it will return to us in the future. Already, this is a problematic definition, particularly when we apply it to something like a house, but even when we apply it to things like gold and Bitcoin and other investments that people tend to have more than a strict emotional detachment to. But I digress.
The central question of asset pricing is, unsurprisingly, what is the price of an asset? The answer takes a very nice form: \[p_t = E_t(m_{t + 1}x_{t + 1}).\] What this equation says is that the price \(p_t\) of an asset at time \(t\) is equal to the expected value (using only the information we have at time \(t\)) of the discounted payoff at the future time \(t + 1\). The payoff \(x_{t + 1}\) is the value of whatever our asset has turned into. If we’re pricing a stock, for instance, we could write \[x_{t + 1} = d_{t + 1} + p_{t + 1},\] where \(d_{t + 1}\) is a dividend that’s paid directly to us, and \(p_{t + 1}\) is how much our stock is now worth. The discount factor \(m_{t + 1}\) is more mysterious. It expresses the fact that an amount of money at time \(t + 1\) might be worth less or more to us than that same amount of money at time \(t\).
A fundamental model for the discount factor \(m_{t + 1}\) is the consumption-based model. In this model, \(m_{t + 1}\) splits up into the product of two factors: a future discounting constant \(\beta\), which describes how much we prefer money now to money later, and a coefficient of relative risk aversion \[\dfrac{u'(c_{t + 1})}{u'(c_t)},\] which describes how risk averse we at time \(t + 1\) relative to time \(t\). Observe that \[m_{t + 1} = \beta \dfrac{u'(c_{t + 1})}{u'(c_t)}\] is a stochastic discount factor: it depends on a variable, consumption at time \(t + 1\), that we don’t know at time \(t\), so its exact value is not known to us.
A basic fact we can observe from this formula is that we will prefer (i.e., be willing to pay more for) assets that pay out in bad times to assets that pay out in good times. This lets us restate our explanation of why insurance works: we are willing to accept a negative expected payoff for insurance because it pays us precisely when we need it most. The insurance company, which is more or less indifferent to the state of your house, only cares that it’s getting a positive expected payoff from selling you that insurance. The market works not because the market participants have different information, but because they have differing risk aversions.
This is the brand of finance I envisioned above: you can hedge risks by trading with somebody who is not exposed to them. Indeed, this is what I naïvely imagined a “hedge fund” to be! Instead, the “hedge” in “hedge fund” apparently refers purely to hedging drops in the market, and in practice, it’s meaningless. In practice, hedge funds aren’t trying to exploit differences between their discount factors and the composite “market” discount factor; rather, they are trying to find situations in which the basic pricing equation, \(p = E(mx)\), is wrong, assets that have for whatever reason been systemically mispriced. This explanation may yet be too kind: in the absence of mispricing, you can always gamble and try to cleverly hide the risks for as long as possible. Exploiting mispricings corrects them, and thus it serves an important function. Gambling does not. Determining who’s doing what is not, looking from the outside, an easy task.
At heart, I’m an idealist. That’s why I’ve spent most of this post giving my aspirational view of what finance is, or rather, what I want finance to be. But I’m willing to get down and dirty with the gamblers not just to pay the bills, but more importantly to see how the financial system really works. I’ll probably spend quite a few more blog posts riffing on the “what is finance” theme, since if I haven’t made it clear over the past 2,600 words, I’m still pretty hazy on the concept. I hope you’ll stick with me to see if I ever figure it out!