It is well known that present institutional arrangements do not permit investors to use the proceeds of short sales to finance the purchase of other stocks. On the contrary, investors must place the proceeds of short sales in escrow, and they must also affirmatively invest (deposit) an additional amount equal to margin requirements (which may be as much as 100 percent) of the “proceeds” of the short sales. These escrowing and depositing requirements together will be referred to as “short-sales escrowing requirements.” These escrowing requirements not only involve forced or “by-product” holdings of the (nominally) riskless asset, they also change the structure of the investor's wealth constraint by requiring the substitution of absolute values for the natural number of shares when short sales are made.

John Lintner, The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets, The Journal of Financial and Quantitative Analysis, Vol. 4, No. 4 (Dec., 1969), pp. 347-400

Introduction, 49. — I. Some important definitions and building-blocks, 53. — II. The cost of capital and optimal dividends and growth under certainty, 58. — III. Simple stochastic unlevered growth, 65. — IV. Optimal (expectationally) steady growth, capital budgets, dividends and retentions, when σ2pt increases with futurity, 76. — V. Summary of conclusions, 91.

Where G is the geometric mean rate of return on the individual's net worth. W,k is the kth individual's initial wealth. Using this approximation, the market price of risk, 4)-1, is equal to HaIM. The inclividual investor's risk aversion is W11,-1, E(1 R1,) _ W*1,k, and HaIM (I W*1k)l. k Under the assumption that expected future prices are independent of current prices, the market price It may be noted that the Bernoulli utility function, unlike the quadratic and exponential utility of risk is unaffected by changes in the number of investors.

A PREVIOUS paper [9] developed a model of the structure of equilibrium prices for risk assets in a purely competitive in which a set of individually risk averse investors optimize their respective portfolios of risk assets in terms of common expectations and risk assessments with respect to a common horizon. When there is a riskless asset available for holding or borrowing at a fixed interest return and all probability assessments are normal (Gaussian) it was shown that in equilibrium a purely competitive will place an aggregate value on all the outstanding stock of any company V0j equal to the discounted value at the riskless rate r* of the certainty equivalent of -the distribution of its uncertain end-of-period aggregate value. This in turn is less than the statistical expectations V1* by the product of the market price of dollar

John Lintner, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, The Review of Economics and Statistics, Vol. 47, No. 1 (Feb., 1965), pp. 13-37