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Its shouldn’t be. How did you arrive at that conclusion? To get monthly st form weekly you multiply by 52^0.5/12^0.5
.Have a look at a stock price chart for a day and then have a look at a price chart for a quarter. Notice that the movement for a stock during a single session is a lot noisier than it is for a quarter (which will often exhibit an up or down trend depending on fundamentals and prevailing market conditions). This example of daily vs. quarterly is a little more extreme than weekly vs. monthly, but you get the picture.
In the alternative investments reading, CFAI discusses the effect on the sharpe ratio of lengthening the measurement interval for standard deviation. The conclusion is that lengthening the interval will reduce volatility, resulting in an overstated risk-adjusted return.
The formla for changing time length of the standard deviation for a Sharpe ratio is the same as it is for calculating VAR. If I recall correctly the issue with the Sharpe ratio for hedge funds is that you multiply the numerator by a number and the denominator by the square root of that number. that’s why the risk adjusted returns for longer perids is overstated.
coggttuso8190, can you point to which page are you referring to?
CFAI Reading 26, page 83 - last bullet (ways to game the Sharpe) #1: “Lengthening the measurement interval. This will result in a lower estimate of volatility; for example, the annualized standard deviation of daily returns is generally higher than the weekly, which is, in turn, higher than the monthly.”
My understanding was that its not necessarily the length of measurement interval that lowers volatility, but rather estimating std. dev for longer time frame using shorter period inputs, like annualizing std. dev using daily std dev. Is that correct?
thanks
you multiply periodic STDEV by the sqrt of TIME. So, if square root of time is 12 (monthly) it’s less than square root of time (250) daily.