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The Risk-Free Rate And Default Risk

Aug 4, 2011 Marc Odo

Over the last half-century, many of the developments and models used in finance assume the presence of a “risk-free rate”. This rate of return is used as a reference point or springboard for a vast array of analysis, including:

  1. Forecasts of future capital market and asset class returns, as forward-looking analysis often uses a “risk-premium” above and beyond an assumed risk-free return.
  2. Performance analysis of individual investments. Metrics like the Sharpe ratio evaluate the additional-return vs. additional-risk tradeoff of particular investments, using the risk-free rate as the baseline.
  3. Company specific valuations, as the risk-free rate is factored into the cost of capital and is used to discount future cash flows.
  4. Estimation of public and private pension liability values, as future cash outlays are discounted back to present value terms.
  5. Pricing for most all other forms of debt.

Historically U.S. Treasury debt was almost universally accepted as the risk-free investment. There might have been debate about the rate of inflation or the appropriateness of matching investment time horizons with the appropriate spot on the yield curve, but the possibility of default was never seriously questioned. However, with the recent political brinkmanship in Washington D.C. regarding the extension of the federal debt ceiling, many are wondering how the possibility of a default on U.S. Treasuries would impact financial analysis.

Realizing we are venturing into somewhat unchartered waters here, it seems to me there are a few ways one can approach the question.

  1. Assume the models are still valid, but tweak the inputs to incorporate the possibility of a default.
  2. Seek out new or different inputs to the same models.
  3. Scrap the models entirely.

Let’s start with the simplest solution, to assume the models and formulas are still valid and that the only thing we need to do is tweak the inputs. Although the yield on U.S. Treasuries was almost always used as the risk-free rate, “risk-free” is a bit of a misnomer. After all, inflation is a very real economic risk, and re-investment risk is an additional risk. Those risks have always been factored into prices and yields of debt. Assuming U.S. Treasuries are bought and sold on open, free, and liquid markets, the buyers and sellers will determine the appropriate “price” of the inflation and reinvestment risks. An efficient market way of thinking would simply assume that markets will start to price in the possibility of default risk.

After all, if you want to think of things at a 30,000 foot level, inflation risk and default risk are essentially the same thing: a reduction in future purchasing power. Inflation is a high probability of a gradual diminishment in future value, while default risk is a low probability of a large diminishment of future value. If you think open markets are the best way of discovering the price of risk, you can likely to continue to use the yield on U.S. Treasuries as your risk-free rate in your models and calculations, realizing the rates are likely to be higher than they have been historically now that they will start to incorporate the possibility of default.

The second possibility is to assume that the models will need new inputs entirely in order to remain valid. In this scenario, we can no longer assume U.S. Treasuries are risk-free and would need to be replaced. What would make a valid replacement? In my opinion, the most promising candidate would be U.S. Treasury-Inflation Protected Securities (TIPS). Over the last decade and a half the federal government has tried to remove inflation risk from their debt by offering TIPS, where the principal of the debt is adjusted by CPI. However, as liabilities of the U.S. government, TIPS would still be subject to default risk. If you’re looking for an isolated market estimate of default risk, I think TIPS would give you that. This well-written paper by Aswath Damodaran of NYU provides insight.

The final option would be to throw out all the long-established models entirely, but this seems a bit too extreme. As a recent article in The Economist points out, there aren’t really any viable pricing models or alternative investment options that could take the place of U.S. Treasury debt in its central role in the financial system, at least in the short term. Thankfully a self-inflicted crisis was avoided at the 11th hour, but certainly the questions raised during the stalemate will linger and people’s definitions and/or perceptions of what is meant by the “risk-free rate” have permanently changed.

These additional links in The Financial Times and The Economist also provide useful food for thought.

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