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Paathshaala : Treynor and Sharpe Ratio

Treynor 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:

Treynor 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.

Sharpe Ratio

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.

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