The risk-return ratio is a measure of

return Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document or t ...

in terms of

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...

for a specific time period. The percentage return (R) for the time period is measured in a straightforward way: :

R=\frac

where

P_

and

P_

simply refer to the price by the start and end of the time period. The risk is measured as the percentage

maximum drawdown The drawdown is the measure of the decline from a historical peak in some variable (typically the cumulative profit or total open equity of a financial trading strategy). Somewhat more formally, if X(t), \; t \ge 0 is a stochastic process with X(0) ...

(MDD) for the specific period: :

\textit=\max_(DD_t)\textDD_t=\begin \displaystyle 1-(1-DD_)\frac&\textP_t-P_<0\\ 0&\text\end

where ''DD_t'', ''DD''_''t''-1, ''P_t'' and ''P''_''t''-1 refer the drawdown (''DD'') and prices (''P'') at a specific point in time, ''t'', or the time right before that, ''t''-1. The risk-return ratio is then defined and measured, for a specific time period, as: :

RRR=R/\textit

Note that dividing a percentage numerator by a percentage

denominator A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...

renders a single number. This RRR number is a measure of the return in terms of risk. It is fully comparable, i.e. it's possible to compare the RRR for one share with the RRR of another share, just as long as it's the same time period. The RRR as defined here is formally the same as the so-called MER ratio, and shares some similarities with the

Calmar ratio Calmar ratio (or Drawdown ratio) is a performance measurement used to evaluate Commodity Trading Advisors and hedge funds. It was created by Terry W. Young and first published in 1991 in the trade journal ''Futures''. Young owned California Mana ...

, the

Sterling ratio The Sterling ratio (SR) is a measure of the risk-adjusted return of an investment portfolio. While multiple definitions of the Sterling ratio exist, it measures return over average drawdown, versus the more commonly used max drawdown. While the ma ...

and the Burke ratio. However, the RRR can arguably be regarded as more general than the MER ratio since it can be used for any time interval even daily or intra-day prices, while the MER ratio seems to be confined to measuring only the risk and return of a fund since inception until the current date. It is also less ad hoc than the Calmar, the Sterling and the Burke ratios. The RRR was first defined and popularized by Dr. Richard CB Johnsson in his investment newsletter ('A Simple Risk-Return-Ratio', July 25, 2010).

References

{{reflist * Johnsson, Richard CB
A Simple Risk-Return-Ratio
Financial ratios Investment indicators