Risk-free rate

The risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss, over a given period of time.

Since the risk-free rate can be obtained with no risk, any other investment having some risk will have to have a higher rate of return in order to induce any investors to hold it.

In practice, to infer the risk-free interest rate in a particular situation, a risk-free bond is usually chosen—that is, one issued by a government or agency whose risks of default are so low as to be negligible.

Risks that may be included are default risk, currency risk, and inflation risk.

As stated by Malcolm Kemp in Chapter five of his book Market Consistency: Model Calibration in Imperfect Markets, the risk-free rate means different things to different people and there is no consensus on how to go about a direct measurement of it.

One interpretation of the theoretical risk-free rate is aligned to Irving Fisher's concept of inflationary expectations, described in his treatise The Theory of Interest (1930), which is based on the theoretical costs and benefits of holding currency. In Fisher’s model, these are described by two potentially offsetting movements:

The correct interpretation is that the risk-free rate could be either positive or negative and in practice the sign of the expected risk-free rate is an institutional convention – this is analogous to the argument that Tobin makes on page 17 of his book Money, Credit and Capital. In a system with endogenous money creation and where production decisions and outcomes are decentralized and potentially intractable to forecasting, this analysis provides support to the concept that the risk-free rate may not be directly observable.

However, it is commonly observed that for people applying this interpretation, the value of supplying currency is normally perceived as being positive. It is not clear what is the true basis for this perception, but it may be related to the practical necessity of some form of (credit?) currency to support the specialization of labour, the perceived benefits of which were detailed by Adam Smith in The Wealth of Nations. However, Smith did not provide an 'upper limit' to the desirable level of the specialization of labour and did not fully address issues of how this should be organised at the national or international level.

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