A Reinterpretation of the Optimal Demand for Risky Assets in Fund Separation Theorems

Romain Deguest (), Lionel Martellini () and Vincent Milhau ()
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Romain Deguest: Fundvisory, 75010 Paris, France
Lionel Martellini: EDHEC-Risk Institute, 06202 Nice Cedex 3, France
Vincent Milhau: EDHEC-Risk Institute, 06202 Nice Cedex 3, France

Management Science, 2018, vol. 64, issue 9, 4333-4347

Abstract: In a continuous-time portfolio selection model with N risky assets and K state variables driving their risk and return parameters, we derive simple expressions for the allocation to each asset in the K + 1 risky funds of the ( K + 2)-fund separation theorem. We show that the allocation to any given risky asset in each fund can be written in terms of the parameters of a regression of the excess returns of this asset on those of the N − 1 remaining assets. We also use these parameters to provide quantitative measures of the increase in Sharpe ratio of the speculative demand, or in the maximum correlation of each hedging demand with respect to the corresponding risk factor, associated with the introduction of a new asset in the investment universe. Finally, we show that in a multiperiod setting, an asset is “spanned” by others if and only if it improves neither the maximum Sharpe ratio of the speculative demand nor the maximum correlations of the hedging demands with the risk factors.

Keywords: intertemporal hedging; utility maximization; optimal portfolio (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:64:y:2018:i:9:p:4333-4347

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