 |
| Gain-to-Loss Ratio |
The gain-to-loss ratio is the ratio of the expected gain divided by the expected loss in a certain measurement period. The term “gain” refers to the expected excess returns that are above the risk-free rate and the term “loss” is the negative of expected excess returns that are below the risk-free rate.
The approach is intuitively appealing, in as much as gain conceptualizes a profit and a loss as its antonym. A gain-to-loss ratio greater than one means the expected gain exceeds the expected loss.
In this concept, expected gain and expected loss serve as an alternative to mean and variance, which are more commonly used in finance. In terms of a gain-to-loss ratio, this appears to be especially valuable when return distributions are not normally distributed.
    |
This is particularly the case in options markets, bond markets, insurance markets, and equity markets. For example, suppose an asset is selling for $100 and an investor assumes a 0.60 chance that the asset could appreciate to $140 within 1 year and a 0.40 chance that it could decline to $90.
Given a risk-free rate of 5%, the expected gain is 0.60[(140/100) – 1.05] = 0.21. The expected loss is 0.40[1.05 – (90/100)] = 0.06. The gain-to-loss ratio is 0.21/0.06 = 3.50. This compares favorably with the average S&P 500 long-term ratio which O’Connor and Rozeff (2002) estimate to be 3.0 for the period 1926–1997.
