# Sharpe Ratio biased upward?

In Schweser pg 36 of Alt Inv it says the annualized sharpe ratio is biased upward by the square root of 4. Can someone help me wrap my head around this? Doesn’t it all depend on the time period you are looking at? Why would the annual Sharpe be biased upward? Is it market convention to use quarterly returns for Sharpe?

1, This is a chapter of alternative investment. so qutaerly valuation is fair. GIPS: RE valued at least quarterly after 2008; PE valued at least annually.

2, Sharpe ratio is time dependent. Quaterly shape ratio is lower than annual sharpe ratio.

If you dissect Sharpe:

(Return-Rfr)/risk

for example, if you use monthly return and monthly standard deviation, you calculate monthly sharpe.

now if you want to calculate annual sharpe, you time return by 12, but you time standard deviation by square root of 12. so your numerator increases more than your denominitor.

effectively, when you lengthen your sharpe periord, you bias Sharpe upward.

thank you that clears it up!

Good explanation passme, thanks!