# Does Sharpe Ratio change with Leverage?

Was reading page 481 of book 4 (curriculum) and came across this line:

“The information ratio and the Sharpe ratio will not always be degraded by a reasonable rise in active or absolute risk, and a reasonable level of leverage can increase expected compounded return. The appropriate tactics must be evaluated by the manager in the context of his investment approach and investors’ expectations.”

However, I remember reading somewhere that Sharpe Ratio does not change with leverage.

Don’t understand what I am missing here.

The Sharpe ratio does not change with leverage.

Same capital allocation line, same Sharpe ratio.

Thanks S2000 magician. In that case, I really don’t understand what the line in the text quoted above is referring to

Sharpe doesn’t change. Increased leverage increases return by taking more risk (as measured by vol) – there is a proportionate change in the numerator and denominator of the Sharpe.

A few things:

a) statement doesn’t say Sharpe ratio changes with leverage. It refers to degradation (changes presumably) with changes in active or absolute risk.

b) Saying Sharpe ratio doesn’t change with leverage assumes you can borrow (and lend) at the risk free rate. (go through the math to see this)

c) In real life, you (generally) can’t borrow at the risk free rate so Sharpe ratio does change. In fact the statement says a reasonable level of leverage can increase expected compound return. Note the use of the word reasonable. Thus, the statement appears to be based at least in part on a recognition that the rate of borrowing is not constant across all levels of borrowing (or said another way, across different levels of leverage). Thus, it might be alluding to the Sharpe ratio changing with leverage even though it doesn’t explicitly state that.

Or at least that’s my story and I’m sticking to it for now.