# The Substantial Gain-Loss Ratio

The Substantial Gain-Loss Ratio is a generalization of the Gainâ€“Loss-Ratio, proposed by Bernardo and Ledoit (2000). It can either be used as a performance measure on a market with known prices or to derive price intervals in incomplete markets. For both applications, it overcomes theoretical drawbacks of the original Gain-Loss-Ratio, which e.g. reaches infinity for nontrivial cases in many standard models with continuous probability space. The Substantial Gain-Loss Ratio includes the original Gainâ€“Loss-Ratio as a limit case and is applicable in case of continuous probabilities. Additionally, in its function as a performance measure it helps illuminate the source of out-performance that a portfolio reveals. The article can be found over ScienceDirect.

## Publications:

Published in Finance Research Letters Vol. 12C, Pages 58-66:

Weakening the Gain-Loss Ratio measure to make it stronger

If you have any questions or are interested in code or graphics, please contact me!

## Calculation

The calculation of the SGLR in general cases is not trivial and can be very time consuming.
Under the following link you can download Matlab-code for the calculation of the SGLR for historic data on return and SDF.
The code uses GPU and CPU parallelization and the NAG toolbox for the optimization step.
The theoretical background to this code is described in a working paper by Sebastian Mentemeier and me.

For a risk-neutral benchmark investor the calculation is more easy. You can download Matlab-code and an example here.