Sunday, November 20, 2011

Characteristics of a Price Bubble

After the tech bubble and real estate bubble each burst, there is much discussion as to the next bubble. From what I can tell, there are two popular candidates: education, i.e. tuition, and health care, i.e. insurance premiums. In this post, I’ll discuss the two first bubble candidate. I want to first discuss in general terms what constitutes a bubble.
Define the capitalized value of an asset as the present value of its future expected net cash flows (revenues less expenses). A general formula looks like this:

P0 = CF/(r-g)

where P0 is the price of the asset (capitalized value today), CF is the net cash flow per period, r is the discount rate, and g is the expected growth rate in the cash flow. The discount rate should reflect the time value of money and all the risks faced by the asset holder due to the asset ownership.

For stocks, CF is the free cash flow available to equity holders (FCFE). Free cash flow is available for reinvestment in the firm or to be paid out to equity holders as dividends or stock buybacks. Negative free cash flow means the firm needs financing from outside, whereas positive free cash flow means the firm is generating more internal cash flow than needed to maintain its business.

The capitalized value of the asset increases if expected future cash flows increase, or if the discount rate decreases. Of course there is a lot of noise in those expectations, so we expected capitalized values of assets with noisy information to be at least somewhat volatile.

A price bubble is defined as a price increase that is not generated by changes in expectations of future cash flows or the discount rate. In other words, it is a price increase that is not connected to the fundamentals of the asset. The trouble with identifying a bubble is that market participants can have legitimate (i.e. based on sound research and reasoning) differences in their expectations of the future cash flow that an asset will generate. Further, people can have a different personal discount rate and attitude toward risk, which leads to differences in discount rates.

Now, in stock/bond pricing, discount rates should not deviate much across investors, since the required return is priced by the marginal investor. That means the only thing driving discount rate differences should be risk factors. But, for things like education, I think the story is different.

With education the asset being purchased is predominantly a signal, with some human capital development. It’s not clear at all that the human capital development can only be done through higher education, but that’s another topic. The point is, the expected cash flow generated from the asset is the so-called education premium. In other words, the student is purchasing a higher expected salary. These expectation differ by degree level (Bachelor’s, Master’s, Ph.D.) and by type (Business, Engineering, Arts, etc.).  

The premium of the typical bachelor’s degree over high school is $20,000/year (data here). Now that includes degrees of all types. I don’t have data for different majors. Using data on average tuition from here, the average state school costs is $33,000 for all four years for an in-state student. But wait one minute! Not only is there tuition, there is the opportunity cost of not working full time while in college. Let’s assume the full-time student won’t work, so we’ll add four years of high-school earnings to the investment. That’s $112,000.

Let’s see what the implied capitalization rate is. Take the average degree premium as the dividend and the total investment as the price, we find the implied capitalization rate is 13.7% in this case. This is an enormous discount. The lower the capitalization rate, the higher is the price relative to the dividend. Implied discount rates for out-of-state students are 12.3%, and for private schools it’s 9%.

At first blush I would say there is little evidence of a bubble in higher education. The problem is coming from bad combinations of tuition and degree (major). If your major does not promise greater than $28,000/year in earnings, on average, the college degree you’re getting is (guaranteed) not worth it.

Now, if you go to an in-state school, in order to get a 5% return on your money, you need a salary premium of $7300/year, after tax. That’s $10,400 before tax, assuming an average tax rate of 30% (federal and state). So if you want to score a job that pays off your education, you need to earn around $40,000/year. If you go with a 10% return, you need closer to $50,000/year. This is reasonable for engineering and some science jobs, and some (not many) business majors. You won’t be getting anywhere close to this with a humanities or social science degree.

My argument is that the average college degree pays off the degree holder. But within that are some very bad choices. In the end, the individual must make careful, informed decisions. 


  1. Do you imply that everyone should go to college - because of the expected payoff? You say that the average college degree pays off, but clearly, some folk don't need no college.

    I also wonder how the ivy league and other "upper crust" schools play into the equation. Does graduating from Yale guarantee you a better job, just because your degree says Yale? Or do other factors play a role. Like you, I think it depends on your major.

    My neighbor graduated from Yale Law school and he likes to think that sets him apart, but he can't land a super job right now. I've read where the supply of lawyers outstrips demand right now, creating underemployment. (and heaven knows we don't need any more lawyers!)

    I do like your straight-forward analysis, and I will definitely apply that to my kiddos. We may even utilize community colleges for gen ed stuff, and even the first two years. Community colleges are a fantastic way to stretch your hard earned dollar.

  2. I definitely think that not everyone should go to college. In fact, I think something with such a high required investment should be carefully thought out. Appropriate decisions regarding the meshing of personal interests and future income must be made. But that's a very individual sort of thing.

    No my main point is to question the existence of a bubble. Using average investment and payoffs, I don't see it. At the same time, it doesn't appear that there is a great return here, unless one attends a wicked cheap school.

    The problem is I have no data on price of degree/income relationships. State schools might be in the lower half of income, and private schools might be in the upper half. I doubt that is the case, but it is possible. Although that would just have the effect of making returns more equal, and they wouldn't go up very much.

    I also think we see a lot of expensive and bad choices being made. Law school is a great example. Way more lawyers exist than are needed, and way more law schools exist than are needed.

    I think the idea of CC is excellent. In addition to the benefits you suggest, it also introduces the student to the higher learning environment so that one may test the waters cheaply and decide if they want to pursue further education.

  3. Btw, I love James Altucher's blog. Here is a very interesting commentary about what can be done post-high school instead of college:

  4. Anecdotally, I've read where many folks who graduated during the recent recession, decided to ride it out in graduate school, with hopes of landing a good job after graduating, only to find that that good job didn't exist but their loan payments certainly did.

    You say you have no info on degree/income relationships, but they publish average salaries for accountants, lawyers, doctors, etc. You can also determine what those degrees cost (roughly), no?

  5. I don't have that data right now. If I dug around I could probably get it.