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Monday, April 20, 2009

Has Declining Mathematical Literacy in the U.S. Contributed to the Economic Crisis?

The idea that students in the U.S. are behind other major nations in math and science has been discussed widely, and it’s backed up with hard data. For example, a study by the Program for International Student Assessment (PISA), administered by the Organization for Economic Cooperation and Development (OECD), found that 15-year-olds in the U.S. ranked 24th among other countries in math literacy and 26th in problem solving.

It’s telling that the math and science performance of students in the U.S. seems to decline as they progress through school and as the expected skill-set advances with age group. Elementary students test about on par with international peers, but in middle school they fall behind, culminating in the troubling results for the 15-year-olds in the PISA study.

Talk of problems with math and science education in the U.S. is nothing new, having emerged as a topic of attention in the media at least as far back as the 1970s. As a long-term issue, it raises the question of what has happened as students with inadequate mathematical literacy and problem solving skills have advanced into college and on to professional life.

I don’t currently have data to back this up, but it would seem that the students who do come out of high school with a strong grounding in math would gravitate toward the more math-intensive subjects like science, engineering, and biomedicine. For the rest, that leaves the less mathematically rigorous majors like business and liberal arts, in which students can struggle through the most basic required college math courses and then move on to advanced coursework in their chosen majors.

By extension, this would mean that some graduates less skilled in mathematics may have moved on to careers in fields like financial services, which, in turn, is problematic when you consider the increasingly complex nature of the financial instruments that have emerged over the past 20-30 years.

One such instrument is the securitized pool of subprime mortgages, which, now infamously, investors were allowed to purchase at 30-to-1 leverage. What does this mean, mathematically, and what level of math does it take to understand it?

As one of my math professors was fond of saying, the best way to understand something is to take “the simplest example,” so that’s what we’ll do. Let’s say I have $10 to invest, and I am allowed to invest it at “30-to-1 leverage.” Leverage is really a euphemism for debt. If I can invest my $10 at 30-to-1 leverage, it means essentially that I can use my $10 as collateral to borrow $300.

So let’s say I do that, and I use the borrowed $300 to buy a security consisting of 300 $1 loans (as I said, this is a simple example). For each year it’s outstanding, simple interest of 5 percent is payable on each $1 loan. Thus, for the first year, I can expect a profit of $0.05 on each of the loans, or $15 -- a handsome return, made possible by 30-to-1 leverage, of 150 percent on the 10 dollars of my own cash that I put up as collateral. My budget for the year is based on that expected return, including payments on the $300 I borrowed to buy the security, along with any other expenses -- after which, hopefully, I will retain a decent profit margin.

However, let’s assume everything doesn’t go quite as planned. I receive my interest payments on 285 of those loans, for a return of $14.25. But 15 of the borrowers, or about 5 percent, default. Here are the consequences:

  • I’ve incurred a shortfall of $0.75, or 5 percent, on my budgeted revenue for the year, from which my expenses and profit margin were to have been derived.
  • I’m now on the hook for the $15.00 in bad debt. If I can’t collect, the first $14.25 of that loss eats up the interest revenue I received, and the other 75 cents adds to the loss on my original $10.00 cash -- now 7.5 percent -- and that’s before paying my expenses, including the payments on the $300 I borrowed to buy the security.
  • I would now do my best to mitigate this devastating loss, laying off staff and cutting other expenses, and filing claims with any company that may have insured me against losses. And so the cycle of crisis begins, with losses passed through the system from one stakeholder to the next.

This is a very simple model of what happened in the subprime mortgage crisis, and it illustrates how leverage has as much power to magnify losses when things go wrong as it does to magnify profits when things go right.

For the current discussion, it’s noteworthy that the math I used here is very simple -- using ratios and percentages to calculate expected interest, returns, etc. No advanced math is required -- no algebra, certainly no calculus. It’s elementary-school or at most middle-school stuff. It’s the sort of math that the cohort of fifteen-year-olds in the PISA study should have mastered well.

So how could this crisis have been allowed to happen? Did too many people in the financial community -- not to mention the grass-roots consumers who were taking out mortgages, negotiating home prices, and investing in the stock of banks that were issuing risky mortgages -- lack the math skills to comprehend the possible consequences? Or were they blinded to the magnitude of danger by the lure of potential profit?

While only simple math is required to see the inherently questionable risk in such a highly leveraged investment, there are other factors to consider when evaluating an investment, such as:

  • How accurate are the valuations of the assets underlying the security -- the accuracy and stability of home prices, in this case
  • How accurate are the assessments of the ability of the borrowers to repay, and of their default probability
These two considerations require somewhat more complicated math. Analyzing valuation accuracy, risk of loss, and default probabilities enters the realm of actuarial science and is highly vulnerable to any flawed assumptions or inaccuracies in the input data (garbage in, garbage out). Among such data flaws could be widespread misrepresentation of borrowers about their incomes, or prices that have been distorted by a speculative bubble. The results of an actuarial analysis should price the level of risk into the cost of the security and measure the risk, in terms of factors like expected default rates, against the expected return. But any inaccuracies in the original data or assumptions can lead to a misinformed decision.

If we look in this context at how the subprime mortgage crisis could have been allowed to occur, we see only a couple of explanations: (1) not enough people understood the math well enough to see what could go wrong, and/or (2) those who saw the potential for disaster (and, yes--there were a few lonely, expert voices crying in the wilderness) didn’t speak up loudly enough or act decisively enough.

Or, perhaps more plausibly, the explanation could lie in some combination of the two factors. If so, the level of math literacy throughout society is even more important. If enough everyday homeowners, mortgage underwriters, investment bankers, and others throughout the population of stakeholders understand the math, they are more likely to make better decisions that would counteract the impact of those who may be capable of understanding the danger but, out of whatever motivation, are at best in denial or at worst deliberately ignoring it.

This is why it’s good to see that math and science education are among the priorities of the Obama administration. Combined with the greater public attention the crisis is generating to finance and economics, an increased level of mathematical sophistication throughout the country could lead to a future of better financial decisions by all stakeholders, from the boardrooms of the financial sector to grass roots consumers on Main street. This would make future crises of this magnitude far less likely. Sphere: Related Content

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