Saturday, February 6, 2010

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).

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.
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:
I hope you find it useful.


Mahesh Sethuraman said...

I have a doubt with calculating rf as 7% - 2.5% = 4.5%. How is this different from deducting the CDS spread from a corporate bond's yield and call it the rf? Lets assume for now the CDS market is just as efficient at estimating the default spreads as the credit rating agencies.

I always thought of rf as investment in a domestic govt bond coz govt had the sovereign power to print money and therefore no risk. (of course there is a real risk but lets leave that aside for now). Moody's rating of Ba2 for India is from an external perspective isn't it?

Aswath Damodaran said...

That is pretty much it. The only problem with the CDS market is that there is some counter party risk but a CDS effectively insures you against default.
While your assumption about domestic government bonds not defaulting (because the government can print money) seems reasonable, it flies in the face of history. Governments have defaulted before and they will default again.

stock valuation said...


understanding that risk free rates around the world are dicey now due to the amount of government debt, how does this issue impact implied equity risk premiums?

Thank you for your extraordinary work.


Sanjeev said...

Hi Proff,

I am a new bee to your website and it seems phenomenal source of understanding. Thanks!

I had a query whether there is any data of historic World risk free rates . The reason I am looking for this data is I believe that there could be some corelation between risk free rate and market risk premium. I would love to hear your thoughts on this.

Looking forward to your guidance.


Unknown said...

@ Sanjeev,

You can get the historical bond yields (from the FED) in the US which would be your risk free rate for the US market.

Hope this helps.

Aswath Damodaran said...

If you want current riskfree rates in different currencies, you have to draw on a mix of data. I start with the Financial Times and then move online to look for riskfree rates in other currencies.

Unknown said...

An interesting and instructive post. But I fear we are missing one important part of the equation: investors care about real returns, not nominal returns (especially over the long term, when these two can diverge substantially). So surely the "risk-free" rate is not just free of cashflow, default and reinvestment risk but also inflation risk. If governments print money to pay interest on their bonds then they fulfill the contract (which is in nominal terms) but the investor's real return is reduced by inflation.

In contrast, equities have cashflow and default risk, but their cashflow is likely to increase roughly in line with economic growth (or rather, the growth in the profit share of output) and is thus to some extent insured against inflation.

Perhaps the true risk-free rate is the rate on inflation protected (index-linked) government bonds? (Always assuming that the index is an honest reflection of inflation, of course....)

Aswath Damodaran said...

If you want a real risk free rate, use the inflation index bond rate. But how many analysis and how much data in the real world is in real terms? Like it or not, we live in a nominal (currency based) world, where our cash flows are in nominal terms, our taxes are based on nominal earnings and our riskfree rates therefore have to be nominal as well.

Fabian said...

Dear Professor

I am pretty shure you have noticed that the itraxx Sovereign western europe is currently higher than the itraxx europe, which means that governments are more likely to default than corporates (of course, greece influences the index a lot). what does this mean for modern finance theory? what are the consequences for pension funds?

Ankit said...

Dear Sir,

I am a big fan of your books , Just one question . In case my time horizon for analyzing any investment is just 5 year shall I still take 10 year or 20 year sovereign interest rate as risk free rate ?..

Anonymous said...

What are the implications of a changing risk-free rate of return? Since it is used in so many valuation calculations, I'm imaging it would be fairly far reaching ultimately implying greater volatility in asset classes but I defer here for a more educated discussion.

seth_dhanraj said...

any 1 who has difficulty understanding the post ....or hav doubts.......should listen to the prof's lecture on .....risk free rate

which can be found at ..webcasts -> spring 2010 corporate finance - > lecture 6 dated 10th feb....

intial 15 mins should b gud...

Sergei Cheremushkin said...

And what to do, if the rate on national government bond is systematically less than the rate of inflation? In Russia the interest rate on bonds is around 7-8%, while the rate of inflation is 11-12%.

Dhaval Trivedi said...

Can we use RBI Treasury Bills coupon rate, without deducting CDS of country as Risk free rate?

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Natalie said...

what about a country like Egypt where gains on T bills are taxed at 20% while dividends and capital gains on equity are not? do we use the RFR as yield on T bills post or pre tax?
its intuitive to think its post-tax, but its not discussed in any text book...

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