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Conic Portfolio Theory

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  • DILIP B. MADAN

    (Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA)

Abstract

Portfolios are designed to maximize a conservative market value or bid price for the portfolio. Theoretically this bid price is modeled as reflecting a convex cone of acceptable risks supporting an arbitrage free equilibrium of a two price economy. When risk acceptability is completely defined by the risk distribution function and bid prices are additive for comonotone risks, then these prices may be evaluated by a distorted expectation. The concavity of the distortion calibrates market risk attitudes. Procedures are outlined for observing the economic magnitudes for diversification benefits reflected in conservative valuation schemes. Optimal portfolios are formed for long only, long short and volatility constrained portfolios. Comparison with mean variance portfolios reflects lower concentration in conic portfolios that have comparable out of sample upside performance coupled with higher downside outcomes. Additionally the optimization problems are robust, employing directionally sensitive risk measures that are in the same units as the rewards. A further contribution is the ability to construct volatility constrained portfolios that attractively combine other dimensions of risk with rewards.

Suggested Citation

  • Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:03:n:s0219024916500199
    DOI: 10.1142/S0219024916500199
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    References listed on IDEAS

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    Cited by:

    1. Carr, Peter & Madan, Dilip B. & Melamed, Michael & Schoutens, Wim, 2016. "Hedging insurance books," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 364-372.
    2. Dilip B. Madan & King Wang, 2023. "Measuring Dependence in a Set of Asset Returns," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 363-385, June.
    3. Dilip B. Madan, 2016. "Adapted hedging," Annals of Finance, Springer, vol. 12(3), pages 305-334, December.
    4. Argimiro Arratia & Henryk Gzyl, 2020. "Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 929-952, December.
    5. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.

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