William F. Sharpe, Bank Capital Adequacy, Deposit Insurance and Security Values, The Journal of Financial and Quantitative Analysis, Vol. 13, No. 4, Proceedings of Thirteenth Annual Conference of the Western Finance Association, June 20-26, 1978 (Nov., 1978), pp. 701-718

The normative procedures of Markowitz [4], Sharpe [6], and others can be utilized to determine an optimal portfolio (set of security holdings) given estimates of risk, relevant constraints, and expected returns on securities. Building on these foundations, the positive models of Sharpe [7], Lintner [3], Mossin [5], and others assume that investors form portfolios as if they were following such procedures. We observe considerable differences in portfolio composition, some of which undoubtedly stem from differences in expectations. Yet the predictions of most investors are either made implicitly or, if made explicitly, are jealously guarded and hence cannot be observed by outsiders.

Almost twenty years ago, Markowitz [4] first suggested that portfolio selection be regarded as a parametric quadratic programming problem. Risk is stated in terms of the predicted variance of portfolio return — a function that is quadratic in the decision variables (the proportions of the portfolio invested in various securities). All other functions (e.g., expected return) and constraints are assumed to be linear. The objective is to find the set of efficient feasible portfolios. A portfolio is feasible if it satisfies a set of relevant linear constraints; it is efficient if it provides (1) less variance than any other feasible portfolio with the same expected return and (2) more expected return than any other feasible portfolio with the same variance.

This paper describes ways in which computers can be used to help teach elementary college economics. Most of the methods can be implemented with present-day equipment; the rest will prove feasible within a few years. Examples given here are not intended to provide a full or even a representative menu for a beginning course; they simply illustrate some of the more interesting possibilities.

What policy should a corporation adopt concerning the funding of a defined-benefit pension plan and the investment of the assets held in trust for the plan? Until recently, pension plans did not have to be insured, and some risk could be borne by intended beneficiaries. Federal legislation has now mandated such coverage. This paper analyzes corporate policy under three conditions which correspond, roughly, to the earlier situation (‘uninsure’ loans), the current situation (‘partially insured’ loans), and the situation required by law to be implemented in the future (‘completely insured’ plans). We show that if insurance premiums are set correctly, corporate policy in this area may not matter; otherwise the optimal policy may simply be that which maximizes the difference between the value of the insurance and its cost.