Thoughts on the riskfree rate

Early in my blogging life, September 20, 2008, to be precise, I posted my thoughts on riskfree rates generally and about using the US treasury bond rate as a riskfree rate, in particular. With the turmoil sweeping through the European sovereign bond market right now, the time may be ripe to revisit the topic.

Let us start by stating the obvious. Knowing what you can make on a riskfree investment is a prerequisite for any type of corporate financial analysis or valuation. In most textbooks on finance, though, the riskfree rate is taken as a given.

Backing up a bit, consider the three conditions that have to be met for an investment to have a guaranteed return over its life. First, the cash flows have to be specified up front; this essentially rules out any residual cash flow investment (equity) and puts into play investments where the cash flows are contractually defined (fixed income). Second, there can be no default risk in the entity promising the cash flows; a corporate bond rate can never be a riskfree rate. Third, there can be no reinvestment risk; a six-month treasury bill is not riskfree for a five year cash flow, since the rates in the future can change. The bottom line is that we generally try to find a long-term, default-free rate to use as a riskfree rate.

Given this premise, it is not surprising that most books suggest using the US treasury rate (ten or thirty year) as the risk free rate in US dollars. Implicit in this practice is the assumption that the US treasury is default free. One troubling story from last week related to Moody's potentially downgrading the US from Aaa (and thus introducing the possibility of default into the equation).
http://abcnews.go.com/Technology/wireStory?id=9732868

Now, let's think about a Euro riskfree rate. There are a dozen European governments that issue ten-year bonds and the link below provides rates as of last Friday.
http://markets.ft.com/markets/bonds.asp
Note that the rates vary from 3.11% for Germany to 6.66% for Greece. Since the bonds are all in one currency (Euros), the differences have to be due to default risk. Thus, the German Euro bond rate is likely to be closer to the riskfree rate in Euros than any of the other bonds; in fact, the true riskfree rate is probably a little bit lower than the German bond rate.

Let's now look at an even more complex scenario. Assume that you want a riskfree rate in Indian rupees. At the start of the year, the Indian government ten-year bond rate (denominated in rupees) had an interest rate of 7%. If we accept Moody's rating for India of Ba2 and estimate a default spread of 2.5% for Ba2 rated bonds, the riskfree rate in Indian rupees is 4.5%:
Rupee riskfree rate = 7% - 2.5% = 4.5%

One last rung of complexity. In some emerging markets, there are no long term government bonds in the local currency. Here, the choices are either to do the analysis in a different currency or in real terms.

Ultimately, if riskfree rates in different currencies are measured right, differences between rates should be entirely due to expected inflation. Once that is accomplished, valuations will become currency neutral (as they should be).

In summary, estimating riskfree rates is not always easy. I have a paper on the topic that examines the estimation of riskfree rates in more detail:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1317436
I hope you find it useful.