Gain, Loss, and Two-State Modeling

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 Samp;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 Samp;P 500's expected gain is about three times its expected loss