Wednesday 15 January 2020

CAPM and the risk free rate

In a recent post, I was musing about Sharpe and Lintner's decision to treat the risk free rate as an external fact about the world, and not endogenous to their model.  I noted that if you do this, then the curvy efficient frontier flattens down and becomes the capital market line.  Instead we have a set of risky assets and an additional tangent mechanism whereby the line running from the risk free (a.k.a. zero volatility) rate to the tangent point on the efficient frontier is introduced into the CAPM world.

I found out subsequently, re-reading the excellent Fischer Black biography that he considered it endogenous.   In his 1969 initial extension of CAPM, Black sees no role for the monetary authority, and models the risk free rate as the equilibrating rate which satisfies those timid investors who prefer to have larger fractions of their wealth in safe assets and who therefore want to lend all their money (via depositing it with the bank) to leveraged and more aggressive investors, who are happy to borrow that money and climb up past the tangency point on the CML.  

In this model, having a monetary authority messing with the risk free rate in order to stabilise the price level or even worse, to manipulate the economy, implied the system was in a non-equilibrium state, and hence had opportunities for profit.

There's something temptingly beautifully simple in this model of people having two choices for their wealth, and their changing distribution of animal spirits driving not only the price of money but also the price of risk.  It certainly doesn't much correspond to reality but then again nor did option prices much coalesce around the famous Black-Scholes formula pre-1973.  On the other hand, it says nothing about the origins of those animal spirits which stir up price discovery for the prices of money and risk.  Perhaps the only institution the libertarian radical markets theorist needs is human psychology.