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Efficient Portfolios in a Market with a Risk-Free Asset

In: Mathematical Financial Economics

Author

Listed:
  • Igor V. Evstigneev

    (University of Manchester)

  • Thorsten Hens

    (University of Zurich)

  • Klaus Reiner Schenk-Hoppé

    (University of Manchester)

Abstract

The chapter continues the study of a financial market with a risk-free asset. It provides formulas for the expected return and the variance of the return on an efficient portfolio and shows how to represent the efficient frontier for the market with a risk-free asset through equations in the $∖sigma$-$m$ plane and in the $∖sigmaˆ{2}$-$m$ plane. The chapter introduces the notion of the tangency portfolio, examines conditions under which it exists and derives a formula for it. A discussion of the properties of the tangency portfolio is followed by a geometric illustration explaining the term “tangency.” The highlight of the chapter is the notion of the Sharpe ratio and the evaluation of the Sharpe ratio for the tangency portfolio. The chapter concludes with Tobin’s mutual fund theorem, which is formulated and proved.

Suggested Citation

  • Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2015. "Efficient Portfolios in a Market with a Risk-Free Asset," Springer Texts in Business and Economics, in: Mathematical Financial Economics, edition 127, chapter 6, pages 43-51, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-16571-4_6
    DOI: 10.1007/978-3-319-16571-4_6
    as

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