Theory of Capital Markets

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Presentation transcript:

Theory of Capital Markets Security Markets VI Miloslav S Vosvrda Theory of Capital Markets

The explanation of security prices One of the principal applications of security market theory is the explanation of security prices. The static Capital Asset Pricing Model or CAPM, begin with a set Y of random variables with finite variance on some probability space. Each y in Y corresponds to the random payoff of some security.

span(Y) The space of linear combination of elements of Y, meaning x is in L if and only if for some scalars and some in Y. The elements of L are portfolios. Some portfolio in L denoted 1 is riskless. The utility functional of each agent i is assumed to be strictly variance averse, meaning that whenever and .

The market portfolio The total endowment M of portfolios is the market portfolio, and is assumed to have non-zero variance. Suppose is a competitive equilibrium for this economy. The equilibrium price functional p is represented by a unique portfolio in L via the formula:

For the equilibrium choice of agent i, consider the least squares regression of on : where the residual term e has zero expectation and zero covariance with ; that is Since both 1 and are available portfolios, agent could have chosen the portfolio

We have implying that is budget feasible for agent i. Since and string variance aversion implies that . Since is optimal for agent i, it follows that e=0. For any portfolio , relation implies that

where k= and K= ,

Defining the return on any portfolio x with non- zero market value to be and denoting the expected return by and where which is known as the beta of portfolio x.

The Capital Asset Pricing Model is relation By words: The expected return on any portfolio in excess of the riskless rate of return is the beta of that portfolio multiplied by the excess expected return of the market portfolio.

the riskless expected rate of return. Consider the linear regression of on , where aby is any portfolio with non-zero variance. The solution is For the particular case of y=M, we have By taking expectations shows that This is a special property distinguishing the market portfolio. A portfolio whose return is uncorrelated with the market return has the riskless expected rate of return.