Unexpectedly Intriguing!
February 7, 2013

Barry Ritholtz' points to an outstanding post by Chris Arnade at Scientific American, with the irresistible title "The Real, and Simple, Equation that Killed Wall Street". Here's a sample, but read the whole thing!:

"If it weren't for those meddling kids!" That was the punch line for every Scooby Doo episode. It also is the overly simple narrative that many in the media have spun about the last financial crisis. Smart meddling kids armed with math hoodwinked us all.

One article, from the March 2009 Wired magazine, even pinpointed an equation and a mathematician. The article "Recipe for Disaster: The Formula That Killed Wall Street," accused the Gaussian Copula Function.

It was not the first piece that made this type of argument, but it was the most aggressive. Since then it has been a common theme in the media that mathematics, especially obscure advanced mathematics, is largely responsible for the catastrophe that doomed the world to the last five years of recession and slow growth.

This theme plays on the fallacy that danger always comes from complexity. It's a fabrication that obscures the real causes, that makes it easier to say, "Hey, it wasn't my fault, I was blinded by science."

The reality is much simpler and less sexy. Wall Street killed itself in a time-honored fashion: Cheap money, excessive borrowing, and greed. And yes, there is an equation one can point to and blame. This equation, however, requires nothing more than middle school algebra to understand and is taught to every new Wall Street employee. It is leveraged return.


The equation, though simple, reveals one dangerous truth that investors love to exploit. If you can find an asset that returns more than the cost to borrow money then any return is possible with enough leverage.

The simple equation incorporates the following elements to calculate the effective rate of return for an investment made with borrowed money:

  • The Nominal Rate of Return - what the rate of return is on the whole amount invested, which is the prospective gain for the investor.
  • The Cost of Borrowing - the interest rate charged by the lender.
  • The Percentage of Your Down Payment - the percentage of the whole amount made up by money out of the investor's own pocket.

We've built a tool to calculated the leveraged rate of return for an investment that takes these factors into account, but we've added an extra wrinkle - the tax rate that might apply for the return on the investment, which is also something that can greatly affect the investor's choice of investment and can definitely affect their returns!

Leveraged Investment Data
Input Data Values
Nominal Rate of Return [%]
Cost of Borrowing (Lender's Interest Rate) [%]
Percentage of Money Down (Investor's Own Money in Investment) [%]
Tax Rate on Return [%]

Leveraged Rate of Return
Calculated Results Values
After Tax Rate of Return [%]

The default numbers in our tool above are taken from Chris Arnade's example in his post, but the 23.8% tax rate we've entered corresponds to the capital gains tax rate that took effect on 1 January 2013 (assuming this were an investment to which this tax rate would apply).

In Arnade's example, which assumed a tax-free nominal rate of return (or an after-tax rate of return), the leveraged rate of return was 15%. Imposing a tax rate of 23.8% as in our example reduces the effective rate of return of the leveraged investment to 6.67%.

But, if the investor didn't leverage the investment, putting 100% of their own money into it, the after tax rate of return would be 5.53%.

So there's still an advantage for an investor seeking to leverage their investment by borrowing a large portion of the total funds they will invest, but the taxes take a large portion of the leveraged gains out of the picture for the investor.

But we can certainly see the huge incentive that an investor would have for leveraging their investment if it were not subject to taxes, much as many municipal bonds are.

Could the same kind of leveraged bubble that led to the collapse of the financial industry in 2008 be at work in the municipal bond market today? ETF Trend's John Spence summarizes the growing concerns:

"Investors are looking for ways that they can pick up yield, especially munis, which have the tax advantage on the income," said Matthew Tucker, head of iShares fixed-income strategy, in the report. [Muni Bond ETF Rally]

Yet the muni bond rally has raised concerns the asset class has "gotten pricey and risky at the same time," reports Jason Zweig at The Wall Street Journal.

If there is indeed a bubble developing in the markets for municipal bonds, that would make the argument for doing away with their tax-exempt status much stronger.

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