A new financial risk ratio

Randomness in financial markets has been recognized for over a century: Bachelier (1900), Cowles (1932), Kendall (1953), and Samuelson (1959). Risk thus enters into efficient portfolio design: Fisher (1906), Williams (1936), Working (1948), Markowitz (1952). Reward versus risk decisions then depend upon utility to the investor: Bernoulli (1738), Kelly (1956), Sharpe (1964), and Modigliani (1997). Returns of a portfolio adjusted to risk are measured by a number of ratios: Treynor, Sharpe, Sortino, M2, among others. I will propose a refinement of such ratios. This possibility was mentioned in my recent book: Antieigenvalue analysis, World-Scientific (2011). The result is a new set of growth-to-return risk-based financial ratios of ratios.