4.5 Summary
In this chapter, the FSD and SSD stochastic dominance rules were formulated in terms of the distribution quantiles. The advantage of the stochastic dominance rules based on the quantile formulation is that they can be extended relatively easily to the case where lending and borrowing at the riskless interest rate is allowed. A mix of the riskless asset with the risky asset, xα, is given by xα=(1−α) r+α x whose cumulative distribution is Fα. If there is an α>0 such that Fα dominates G by FSD, SSD or TSD, then we can safely conclude that for any mix of G with the riskless asset there will be a mix of F with the riskless asset which dominates it by these rules, respectively. Thus, if FαDG for one positive value α, then the set Fα will dominate the set Gβ. Such dominance is called Stochastic Dominance with a Riskless Asset (SDR). For U∈U1, we developed FSD with a riskless asset denoted by FSDR. Similarly, for U∈U2 we presented SSDR. Finally, we established stochastic dominance rules with a riskless asset in the more realistic case where the borrowing rate rb is higher than the lending rate rl. The quantile framework is also more convenient for developing an algorithm for FSD and SSD (as will be seen in the next chapter), but not allowed to be employed instead of the cumulative distributions for TSD and higher degree SD rules.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
See H.M. Markowitz, “Portfolio Selection”, Journal of Finance, 1952.
See W.F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk”, Journal of Finance, 1964.
See J. Lintner, “Security Prices, Risk and Maximal Gains From Diversification”, Journal of Finance, 1965.
For detailed proofs, see Levy, H., and Kroll, Y., “Stochastic Dominance with a Riskless Asset: An Imperfect Market,” Journal of Financial and Quantitative Analysis, 1980.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
(2006). Stochastic Dominance: The Quantile. In: Stochastic Dominance. Studies in Risk and Uncertainty, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29311-6_4
Download citation
DOI: https://doi.org/10.1007/0-387-29311-6_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29302-8
Online ISBN: 978-0-387-29311-0
eBook Packages: Business and EconomicsEconomics and Finance (R0)