The present value relation says that, under certainty, the value of a capital good or financial asset equals the summed discounted value of the stream of revenues which that asset generates. Otherwise arbitrage would be possible. Under uncertainty, and if risk neutrality is assumed, the future payoffs are replaced by their conditional expectations. Under risk aversion either the natural probability measure under which expectations are taken must be replaced by a ‘risk-neutral measure’, or the discount factor must be modified by a factor that reflects risk. The present value relation leads to bubbles if a convergence condition is not satisfied.
KeywordsArbitrage Bubbles Capital asset pricing model Capital budgeting Capital market efficiency Excess volatility tests Fisher’s separation principle Martingales Present value Risk aversion Risk neutrality Risk premium Risk-neutral probabilities Speculative bubbles Uncertainty Wealth-maximization decision rule
- Gilles, C., and S. LeRoy. 1992a. Asset price bubbles. In The new Palgrave dictionary of money and finance, ed. J. Eatwell, M. Milgate, and P. Newman. London: Macmillan.Google Scholar
- LeRoy, S. 1989. Efficient capital markets and martingales. Journal of Economic Literature 27: 1583–1621.Google Scholar
- Samuelson, P. 1965. Proof that properly anticipated prices fluctuate randomly. Industrial Management Review 6: 41–49.Google Scholar
- Shiller, R. 1981. Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review 71: 421–436.Google Scholar