As I wrote three weeks ago and two week ago, by reading Ghislaine Idabouk's briliant dissertation on the mathematics of options pricing (Black, Scholes, Merton, etc) I have been inspired to do a weekly blog on philosophy of economics. This week I want to expand on one of her central points. Ghislaine nicely show how in the Fundamental Theorem of Asset Pricing, the assumption of No Arbitrage (about which more in the future), or risk-neutral investment, a martingale measure could be linked to the existence of a pricing function. A market without the possibility of arbitrage (and a few other non trivial assumptions) is a perfect market. Now last week I explored the weird modal nature of a martingale. This week I want to call attention to the importance of the risk-free asset in the modern capital asset pricing edifice.
Now a risk-free asset has a steady income flow and no risk of default (it is, hence, risk-free). In practice, a (US) treasury bill is treated as a risk-free asset. Recall that in my first installment of this series I called attention to the neglected Knight-ian distinction between uncertainty and risk. Knight tried to explain entrepreneurial profit as, in part, a consequence of uncertainty. He understood insurance as a way to reduce such uncertainty by trading away some part of future profit against the risk (if I may use that term) of uncertain losses. Interestingly, if an insurance market can operate smoothly, then according to Knight we are in the realm of risk. (Individual uncertainty can be turned into business risk.)
Amusingly, real agents don't treat US T-bills as a risk-free asset. For, it is possible to buy insurance against default of the US Federal Government. At the hight of credit crisis the price of so-called credit default swaps (CDS) hit record highs, that is, they became very popular among sophisticated investors. In the Eurozone, CDSs are the favorite vehicle to bet for and against default of particular European countries. This year Germany banned certain kinds of trading in CDSes (thus, making a smoothly operating insurance market illusory).
Moreover, the existence of insurance against default of so-called risk-free assets suggests that even deep (that is, extremely liquid) markets are by no means perfect. As M. Ali Khan taught me, A French economist, Malinvaud, was among the first general equilibrium theorists to grasp the significance of this in 1973. Malinvaud's approach has two nice features: 1. He obtains more economic realism (he gets insurance and doesn't need complete markets); 2. He has fewer modal assumptions (the balance between supply and demand is required to hold only in expected value across all states and no longer for each single state)!
The closing lines of Malinvaud's piece are still worth quoting: "To a large extent the theory [discussed in this piece--ES] could be transposed to a situation in which individuals would not know the true probabilities but would have subjective probabilities [that is, Knightian uncertainty--ES]. In order to save the symmetry of the problem it will suffice to assume that the subjective probabilities are formed in the same way by everybody and that any individual assigns the same probabilities to two social states w and w' in which he has the same individual state s and in which the distributions of others among individual states are the same. But, of course, such a situation will not lead to the preceding pleasant limit properties unless the subjective probabilities given to the various frequency distributions coincide with the objective probabilities. Perhaps still more interesting would be a generalization permitting individuals to progressively learn the probabilities. Even the insurance institutions 'could be involved in such a learning process. But adding this new dimension to the problem would obviously make it quite a bit harder." (Malinvaud, Econometrica, 408)
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