Ratio (Reward to Variability Ratio)
Developed by Jack Treynor, Treynor ratio is
a measurement of the returns earned in excess
of that which could have been earned on a riskless
investment (i.e. Treasury Bill) (per each unit
of market risk assumed).
Treynor Ratio is a ratio of return generated
by the fund over and above risk free rate of return
(generally taken to be the return on securities
backed by the government, as there is no credit
risk associated), during a given period and systematic
risk associated with it.
Symbolically, it can be represented as:
Ratio (T) = (R i - R f) / ß i.
Ri : Portfolio Return
Rf : Riskfree Return
ßi : Portfolio Beta
All risk-averse investors would like to maximize
this value. While a high and positive Treynor
Ratio shows a superior risk-adjusted performance
of a fund, a low and negative Treynor Ratio is
an indication of unfavorable performance. T does
not quantify the value added of active portfolio
management. It is a ranking criterion only. However,
it can be expected that portfolio managers, which
possess private information, will have a higher
T than the T of the uninformed market strategy.
A ranking of portfolios based on T measure is
only useful if the funds under consideration are
sub funds of a broader, fully diversified portfolio.
If this is not the case, portfolios with identical
systematic risk, but different total risk, will
be rated the same. But the portfolio with a higher
total risk is less diversified and therefore has
a higher unsystematic risk which is not priced
in the market.
Performance of a fund is also evaluated on the
basis of Sharpe Ratio, which is a ratio of returns
generated by the fund over and above risk free
rate of return and the total risk associated with
it. According to Sharpe, it is the total risk
of the fund that the investors are concerned about.
So, the model evaluates funds on the basis of
reward per unit of total risk. Symbolically, it
can be written as:
Sharpe ratio (Si) = (Ri - Rf)/Si
Where, Si is standard deviation of the fund.