I’m trying to wrap my ahead around how leverage affects the information ratio (but not sharpe)? I understand the how cash affects it but not leverage. Could someone give a simple scenario?
thanks
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Because…that’s honestly the best answer I can give just one of those things I am memorizing.
When you change the aggressiveness of the portfolio, IR is unchanged because an increase or decrease in the benchmark % both the numerator and the denominator change and balance out IR. When you simply change cash (adding, remove, or borrowing) , the change in the numerator and denominator arent balanced. So by adding cash, your IR goes down and removing cash, your IR goes up.
For Sharpe Ratio, adding and removing cash doesnt change the SR because SR is based off the Risk Free Rate. (Rp - Rr) / STDp . So adding or removing cash cause the numerator and denominator to balance out so that the ratio is exactly the same.
Think of adding/removing cash in the SR as the same as adding and removing benchmark in the IR. Risk free rate is the same as the benchmark. If your IR is benchmarked against the Risk Free Rate, IR = SR.
what about for leverage in regards to IR though?
your numerator goes up 2x because you borrowed money and doubled down on some stock… your denominator should also go up 2x cause your risk is doubled from being leveraged… no?
The denominator is relative to the benchmark, not the risk free rate.