standard deviation

I am getting confused and need some help. In the AI reading, it says that if we lengthen the time interval that we calculate standard deviation from we will reduce standard deviation. But when we are calculating var if we use daily var we assume that the standard deviation is close to zero and thus we will have a lower var than if we use annual var. so in this case standard deviation is getting larger as we increase the time interval. What I am I not realizing? I am getting confused. I think I need a study break…

well just thinking about it qualitatively, i saw something (cant remember where) and they showed a bat flying up and down. Imagine if you could watch the bat fly up and down over a period of time. That’s your normal volatility and standard deviation. Now imagine if the bat flies into a tunnel and out the other side. You then measure the movement of the bat from the beginning of the tunnel (into the tunnel where there is no movement) and out of the tunnel. That’s your volatility and would reduce the standard deviation because you’ve essentially lengthen the time interval. I always think about it that way, especially for alternative assets that have understated std and understated correlations with other assets because their bat go through the tunnel…so we dont see all the volatility in between.

I can’t recall reading that by lengthening the time period you reduce the annualised I would have thought that for most assets it would be the opposite:- for assets with traded markets and daily prices (eg. listed shares, commodities, currencies) you generally get more accurate (generally HIGHER) annualised st.devs when you annualise st.devs from monthly or quarterly price data, than by annualising the from daily prices. This is because daily price moves often have significant serial correlation and this leads to artificially low annualised st.devs. So generally better to use annualised st.devs calculated form longer periods (eg annualised from monthly or quarterly data). But in the case of most alternative assets (RE, VC, HF, etc) - assuming you can get accurate (not smoothed) value data - the main problem with as a measure of risk is the skewness and kurtosis - esp asymetric risk of many HF strategies. Better to use measures like downside deviation, semi-deviation, drawdowns, etc. can’t help you beyond that, sorry…

hi … was looking for the bat illustration … i remember reading this up but am just not able to recall where in the L3 curriculum does it appear … just finished browsing through all the books of L3 2018 but haven’t yet located it.

Anyone here who can direct me to this illustration?

If we use daily VaR, daily mean return is assumed to be non material as zero. And daily mean return is calculated as Annual mean return/252 - no of trading days within year while standard deviation (volatility) in VaR equation is calculated as Annual StDev / SQRT of 252 and not assumed to be zero.

Thus, daily Normal VaR = Annual Mean Return / 252 or Zero - (conf.level Z Value) (Annual StDev / SQRT of 252)

You didn’t read that carefully.

And Yep, is getting larger as we are extending a time interval for StDev x SQRT Time interval.