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Gain, Loss, and Two-State Modeling

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  • O'Connor, Philip
  • Rozeff, Michael S

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, risky 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. Copyright 2002 by Kluwer Academic Publishers

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  • O'Connor, Philip & Rozeff, Michael S, 2002. "Gain, Loss, and Two-State Modeling," Review of Quantitative Finance and Accounting, Springer, vol. 18(1), pages 39-58, January.
    • Handle: RePEc:kap:rqfnac:v:18:y:2002:i:1:p:39-58
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