Editing Risk-free rate (section)

==Theoretical measurement==
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:

# Expected increases in the money supply should result in investors preferring current consumption to future income.
# Expected increases in productivity should result in investors preferring future income to current consumption.

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 [[James Tobin|Tobin]] makes on page 17 of his book ''Money, Credit and Capital''.<ref>{{cite book |last1=Tobin |first1=James |authorlink1=James Tobin |last2=Golub |first2=Stephen S. |title=Money, Credit and Capital |page=17 |date=1997 |isbn=978-0070653368 |publisher=McGraw-Hill Education}}</ref> 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.

An alternative (less well developed) interpretation is that the risk-free rate represents the time preference of a representative worker for a representative basket of consumption. Again, there are reasons to believe that in this situation the risk-free rate may not be directly observable.

A third (also less well developed) interpretation is that instead of maintaining pace with purchasing power, a representative investor may require a risk free investment to keep pace with wages.

Given the theoretical 'fog' around this issue, in practice most industry practitioners rely on some form of proxy for the risk-free rate, or use other forms of benchmark rate which are presupposed to incorporate the risk-free rate plus some risk of default.<ref>{{cite book |first=Malcolm |last=Kemp |title=Market Consistency: Model Calibration in Imperfect Markets |chapter=5}}</ref> However, there are also issues with this approach, which are discussed in the next section.

Further discussions on the concept of a 'stochastic discount rate' are available in ''The Econometrics of Financial Markets'' by Campbell, Lo and MacKinley.