Gain, Loss, and Two-State Modeling

20 Pages Posted: 18 Oct 2005

See all articles by Philip F. O'Connor

Philip F. O'Connor

University of Auckland - Department of Accounting and Finance; University of Waikato - Management School

Michael S. Rozeff

SUNY at Buffalo - Department of Financial & Managerial Economics

Abstract

Gain and loss, calculated from the upside and downside portions of return distributions, play a pivotal role in the two-state model. A two-state economy possesses a universal gain-loss ratio (G/L) for all assets that is related to the ratio of state prices and to the familiar risk-neutral probabilities. This paper derives many asset pricing properties in a two-state context and shows the role of gain and loss. Applied to bonds, for example, the debt yields depend directly on both G/L and a bond's potential loss. Using S&P 500 data over a 72-year period, the market has priced an Arrow-Debreu security in the gain state at approximately $0.36, while the Arrow-Debreu security in the loss state has been priced at $0.61. Historically, the S&P 500's expected gain is about three times its expected loss.

Keywords: gain, loss, state prices, asset pricing

JEL Classification: G12

Suggested Citation

O'Connor, Philip F. and Rozeff, Michael S., Gain, Loss, and Two-State Modeling. Review of Quantitative Finance and Accounting, Vol. 18, pp. 39-58, 2002. Available at SSRN: https://ssrn.com/abstract=819944

Philip F. O'Connor

University of Auckland - Department of Accounting and Finance ( email )

Private Bag 92019
Auckland 1001
New Zealand
+649-923-9431 (Phone)

University of Waikato - Management School ( email )

Hamilton
New Zealand
+64 7 838 4466 (Phone)

Michael S. Rozeff (Contact Author)

SUNY at Buffalo - Department of Financial & Managerial Economics ( email )

Buffalo, NY 14260
United States

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