The market price of risk

A mean-variance equilibrium model is tested against data from the Italian bond market. General equilibrium models under uncertainty were first constructed by Allais [1] and Arrow [2]. The model tested is of the class formulated by Borch [3], on the basis of works by Markowitz [8] and Tobin [18], and developed further by Sharpe [17], Lintner [6] and Mossin [10]. The bonds used in the test are annuity bonds. These are bearer bonds in loans, where the loan is repaid by a constant amount per period in cover of repayment of capital and interest on the loan. A lottery is arranged before each payment date, in order to determine which bonds shall be redeemed by the forthcoming repayment of capital. The bonds not drawn for redemption then participate in the next lottery, which is held one period later. A sequence of such lotteries is arranged, until all bonds in the loan have been redeemed, and the full amount of capital in the loan has been repaid. An annuity bond thus has an uncertain maturity. Its probability of redemption on a future date is given by the repayment plan for the capital of the loan. The certainty alternative which is considered relevant to the investors is investment in Government bonds. With the market for Government bonds assumed to be in equilibrium, this property is used to take account of the time dimension of investment in the annuity bonds. The investors are then assumed to behave in accordance with the von Neumann and Morgenstern theory [11], and establish preferences over probability distributions of present wealth. Such a behavioural assumption was tested earlier in an experiment [15], and gives a reasonable description of investor behaviour. Italian data were chosen, because investors paid no taxes on income from capital gains and interest payments during the period studied.