An Analytic Derivation of the Efficient Portfolio Frontier

Cover An Analytic Derivation of the Efficient Portfolio Frontier
An Analytic Derivation of the Efficient Portfolio Frontier
Robert C Merton
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174). In W. Sharpe [8], Chapter 4, the figures appear to have R = ^ and a double tangency.
20 and (46) crl, ZlU'l^K ^T^i ^ ^i " ^>/(^ - ^^>* ^'^°°' (45) (Ofj^ - R)/(A - RC) and eliminating (A - RC) by combining (45) and (46), we derive (TkM (47) ^k " ^ = "^ (QfM - R), k = 1, . . . , m, which is the security market line.
21 References [1] F, Black, "Capital Market Equilibritjin with No Riskless Borrowing or Lending, " Financial Note 15A, unpublished, August, 1970, [2] D, Cass and J, Stiglitz, "T
...he Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds, " Cowles Founda- tion Paper, May, 1969, [3] E. Fama, "Risk, Return, and Equilibrium, " Report 6831, University of Chicago Graduate School of Business, June, 1968, [4] M, Jensen, "Risk, The Pricing of Capital Assets, and the Evalua- tion of Investment Portfolios, " Journal of Business. Vol, 42, i^ril, 1969, [5] J, Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, " Review of Economies and Statistics.

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