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Treynor Ratio

Hello everyone,

I would like to know if there's any correlation betweeen Treynor Ratio, Sharpe Ratio and Drawdown. As there's al algo for example with a DD of 12% and Sharpe 3.0 but a TR of -19. I would like an interpretation of this TR as this algo have a +200% Compounding Annual Return.

Thanks!

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My amateur intepretation of what Wikipedia says:

Treynor Ratio = E(r_i - r_f) / beta_i

Sharpe Ratio = E(r_i - r_f) / D(r_i - r_f)

r_i - r_f = Excess portfolio return (r_i is portfolio return, r_f is risk free return)

beta_i: Portfolio beta

E, D: expected value, standard deviation

A very (with benchmark) uncorrelated portfolio is going to have a large Treynor ratio, which is also proportional to expected excess portfolio return. E.g. |T.R| > 1000 not uncommon for intraday algos. Note that if your correlation with benchmark is negative, Treynor Ratio will be negative too (not necessarily a problem, only if your excess return is negative).

As for Sharpe Ratio relation to drawdowns, a single occurrence event can cause a huge drawdown but contribute moderately to volatility since it only happened once... That's why drawdown is an interesting number in its own right.

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Both Treynor Ratio and Sharpe Ratio are reward-to-volatility ratios. The difference is that Treynor uses beta while Sharpe uses standard deviation as a volatility measure. These measures are correlated because they take into account the asset volatility despite a different reference (the reference for beta is the market).

On the other hand, the drawdown impacts the volatility: the bigger the drawdowns, the higher the volatility is. Consequently, Treynor and Sharpe ratios are inversely proportional to the drawdown(s). 

Assuming that the risk free rate is zero, a return of 200% and a Treynor ratio of -20, we found that beta is -10. Negative beta means that we see a decline in the algorithm portfolio value when the market goes up.

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by QuantConnect. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. QuantConnect makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances. All investments involve risk, including loss of principal. You should consult with an investment professional before making any investment decisions.


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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by QuantConnect. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. QuantConnect makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances. All investments involve risk, including loss of principal. You should consult with an investment professional before making any investment decisions.


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