Risk-free Interest Rate - Theoretical Measurement of The Risk Free Rate

Theoretical Measurement of The Risk Free Rate

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.

However, perhaps the most common interpretation is aligned to 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:

i) Expected increases in the money supply should result in investors preferring current consumption to future income. ii) 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 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 holding 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 currency to support the specialization of labour, the perceived benefits of which were detailed by Adam Smith in The Wealth of Nations. However it should be observed that Adam 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.

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. (Again refer to Chapter Five of Malcolm Kemp's book, 'Market Consistency: Model Calibration in Imperfect Markets.') 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.