adding leverage to aportfoilio could have twin effects bcz it can increase the return and also a threat to portfolio thus, increase the risk (standard deviation)
isn’t it true that the effect is uncertain??
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Jai you seem to be ok with property 2 so let’s talk about property 1,
Sharpe ratio is unaffected by addition of cash or leverage because with use of leverage/cash return of your portfolio increases/decreases & at the same time even the sd of your portfolio shoots up/down & therefore, the effect gets nullified.
I hope the above explanation helps you in understanding the concept. Thank you!