Fischer Black Capital Market Equilibrium with Restricted Borrowing INTRODUCTION Several authors have contributed to the development of a model describ ing the pricing of capital assets under conditions of market equilibrium The model states that under certain assumptions the expected return on any capital asset for a single period will satisfy E(R)=R1+BE(Rm)一R The in equation(1)are defined as follows: R, is the return or le period and is equal to the change in the price of the asset, plu vidends, interest, or other distributions, divided pri of the asset at the start of the period; Rm is the return on the market portfolio of all assets taken together; R, is the return on a riskless asset for the period; B is the"market sensitivity"of asset i and is equal to the slope of the regression line relating R, and Rm The market sensitivity B: of asset i is defined algebraically by B=cov(R, Rm)/var(Rm) (2) are as follows: (a)All investors have the same opinions about the poso: motions that ly used in deriving eq bilities of various end-of-period values for all assets. They have a com- mon joint probability distribution for the returns on the available assets (b) The common probability distribution describing the possible returns on the available assets is joint normal (or joint stable with a single char acteristic exponent).(c) Investors choose portfolios that maximize their expected end-of-period utility of wealth, and all investors are risk averse.( Every investor's utility function on end-of-period wealth in- creases at a decreasing rate as his wealth increases. )(d) An investor may take a long or short position of any size in any asset, including the riskless asset. Any investor may borrow or lend any amount he wants at the riskless rate of interest The length of the period for which the model applies is not specified The assumptions of the model make sense, however, only if the period is taken to be infinitesimal. For any finite period, the distribution of pos- sible returns on an asset is likely to be closer to lognormal than normal Graduate School of Business, University of Chicago Some of the basic ideas in this paper, and many helpful comments, wer rovided ugene Fama, Michael Jensen, John Lintner John Long, Robert Merton, Myron Scholes, william Sharpe, Jack Treynor, and Oldrich Vasicek. This ork was supported in part by Wells Fargo Bank and the Ford Foundation 1. A summary william F. Sharpe, Portfe eory and Capital Markets(New York: McGraw-Hill Book Co,1970) 44 his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 46: 59 AM All use subject to JSTOR Terms and ConditionsFischer Black* Capital Market Equilibrium with Restricted Borrowingt I N T R O D U C T I O N Several authors have contributed to the development of a model describ￾ing the pricing of capital assets under conditions of market equilibrium.1 The model states that under certain assumptions the expected return on any capital asset for a single period will satisfy E(AJ = Rf + /3JE(Rm) -Rf]. The symbols in equation (1) are defined as follows: Ai is the return on asset i for the period and is equal to the change in the price of the asset, plus any dividends, interest, or other distributions, divided by the price of the asset at the start of the period; Rm is the return on the market portfolio of all assets taken together; Rf is the return on a riskless asset for the period; fli is the "market sensitivity" of asset i and is equal to the slope of the regression line relating Rk and Rm. The market sensitivity /3i of asset i is defined algebraically by A - cov(Ai, Am)/var(Rm). (2) The assumptions that are generally used in deriving equation (1) are as follows: (a) All investors have the same opinions about the possi￾bilities of various end-of-period values for all assets. They have a com￾mon joint probability distribution for the returns on the available assets. (b) The common probability distribution describing the possible returns on the available assets is joint normal (or joint stable with a single char￾acteristic exponent). (c) Investors choose portfolios that maximize their expected end-of-period utility of wealth, and all investors are risk averse. (Every investor's utility function on end-of-period wealth in￾creases at a decreasing rate as his wealth increases.) (d) An investor may take a long or short position of any size in any asset, including the riskless asset. Any investor may borrow or lend any amount he wants at the riskless rate of interest. The length of the period for which the model applies is not specified. The assumptions of the model make sense, however, only if the period is taken to be infinitesimal. For any finite period, the distribution of pos￾sible returns on an asset is likely to be closer to lognormal than normal; * Graduate School of Business, University of Chicago. t Some of the basic ideas in this paper, and many helpful comments, were provided by Eugene Fama, Michael Jensen, John Lintner, John Long, Robert Merton, Myron Scholes, William Sharpe, Jack Treynor, and Oldrich Vasicek. This work was supported in part by Wells Fargo Bank and the Ford Foundation. 1. A summary of the development of the model may be found in William F. Sharpe, Portfolio Theory and Capital Markets (New York: McGraw-Hill Book Co., 1970). 444 This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:46:59 AM All use subject to JSTOR Terms and Conditions