Equilibrium Prices and the Capital Asset Pricing Model

Market prices are determined by supply and demand. At any one time, the supply of shares of a stock is fixed, so supply is vertical at 5,000,000 shares of BU in Figure 9.2 and 4,000,000 shares of TD in Figure 9.3. Market demand is obtained by "horizontal aggregation," that is, for each price we add up the quantity demanded by all investors. You can examine the horizontal aggregation of the demand curves of Sigma and Index in Figures 9.2 and 9.3. The equilibrium prices are at the intersection of supply and demand.

However, the prices shown in Figures 9.2 and 9.3 will likely not persist for more than an instant. The reason is that the equilibrium price of BU ($40.85) was generated by demand curves derived by assuming that the price of TD was $39. Similarly, the equilibrium price of TD ($38.41) is an equilibrium price only when BU is at $39, which also is not the case. A full equilibrium would require that the demand curves derived for each stock be consistent with the actual prices of all other stocks. Thus, our model is only a beginning. But it does illustrate the important link between security analysis and the process by which portfolio demands, market prices, and expected returns are jointly determined.

One might wonder why we originally posited that Sigma expects BU's share price to increase only by year-end when we have just argued that the adjustment to the new equilibrium price ought to be instantaneous. The reason is that when Sigma observes a market price of $39, it must assume that this is an equilibrium price based on investor beliefs at the time. Sigma believes that the market will catch up to its (presumably) superior estimate of intrinsic value of the firm by year-end, when its better assessment about the firm becomes widely adopted. In our simple example, Sigma is the only active manager, so its demand for "low-priced" BU stock would move the price immediately. But more realistically, since Sigma would be a small player compared to the entire stock market, the stock price would barely move in response to Sigma's demand, and the price would remain around $39 until Sigma's assessment was adopted by the average investor.

In the next section we will introduce the capital asset pricing model, which treats the problem of finding a set of mutually consistent equilibrium prices and expected rates of return across all stocks. When we argue there that market expected returns adjust to demand pressures, you will understand the process that underlies this adjustment.

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