Effects of Short Selling on Sharpe Ratio and Information Ratio

What are the effects of short selling the benchmark/ securities in the portfolio/ risk free asset on the Information ratio and Sharpe ratio?

Thank you in advance.

Sharpe ratio won’t change as it’s unaffected by cash or leverage.

On the other hand IR ratio is affected by cash and leverage. Therefore if you short the benchmark portfolio, you will invest the proceeds into an active portfolio which has higher active risk and return, so IR ratio would rise…

That’s my take on it, happy to be corrected.

I think IR will not change if you shift the weights from the benchmark portfolio towards the active portfolio. IR will still be active risk divided by st. deviation of active risk whether you have 20% or 120% invested into the active portfolio.

Yea you are correct there. IR ratio is not affected by active weights so short selling the benchmark shouldn’t do anything. Thanks!

Short position will improve information ratio. see 2021 CFA Level 3 Curriculum Reading 25