We consider an economy as in Campbell and Cochrane (1999), with time-varying risk free rates, and monetary asset holdings entering the utility function.
If there exists a risk free asset providing monetary services, its risk free rate obeys:
Unlike Campbell and Cochrane (1999), we allow for a time-varying risk free rate.
However, the Euro Area crisis led to changes in the monetary policy transmission mechanism and affected the determination of the risk free rates and bank funding costs leading to substantial heterogeneity in funding costs across Euro Area countries.
Developments in supposedly risk free rates are important as they affect banks' refinancing costs (Rottmann and Wollmershauser (2013).
In defining a credit crunch we aim to distinguish 'normal' shifts in loan supply (due for instance to changes in the risk free rate from a monetary policy decision) from excessive contractions in credit.
Risk free rates
are the rates governments borrow in the market, which other entities use to price from so, the risk free rate
with an extra amount on top to take account of the extra risk investors are taking on.
This would lead to rising liabilities (mitigated by deterioration in one's own credit standing if that is considered in the fair value model), just as many asset values were being pushed down by spreads and default estimates that overwhelmed the reduction of the risk free rates
Expected risk free rates
are allowed to vary freely over time, constrained only by the fact that they are equal across (risk-adjusted) assets.
In the CAPM, asset i's equilibrium expected return is Ki = Rf + iM [RPM], where Rf is risk free rate of interest, iM is the systematic risk (beta) of the asset I relative to the market portfolio, and RPM is the market risk premium.
The Global CAPM uses US treasury rates for risk free rate (Rf), and MSCI World Index is used as a proxy for market return.
The risk-free rate Rf$ used in equation (1) is for an asset that is risk free rate in US dollars.