Risk free rate

The risk free rate of return is the best rate that does not involve taking a risk. Both the return of the original capital and the payment of interest are completely certain.

The risk free rate for a given period is taken to be the return on government bonds over the period. This is because a government cannot run out of its own currency, as it is able to create more as necessary.

Any other investment should produce greater returns than the risk free rate. The extra return (the risk premium) reflects the extra risk involved.

The risk free rate is used by the CAPM and other valuation models.

Euro risk free rates

The risk free rate for the euro present a problem because the currency is issued by the European Central Bank, so only the ECB could print its way out of default, and the ECB does not issue bonds.

The bonds issued by national governments are not risk free because those goverments cannot print euros. There bonds therefore have a non-zero default risk.

The usual work around is to use the lowest risk euro bonds—i.e. those with the lowest interest rates. The rate will be slightly too high, but usually the error caused is not significant in the context of the other uncretainties of valuation.

An alternative is to use ECB's yield curve

It may be possible to estimate the risk premium on the bonds used to calculate either of the above (e.g. by comparison with other AAA rated bonds) and subtract it to get a true risk free rate, but it will not usually be worth it.

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