 # VAR and standard deviation relation to time

Yearly VAR = monthly VAR * square root 12

Yearly standard deviation = monthly standard deviation / square root 12

Whats the intuition?

Yearly Std Deviation = Monthly Std Deviation * Sqrt(12) not divided by as you have done …

Yearly should be higher that monthly.

Yearly Variance = Monthly Variance * 12

Take sqrt on both sides

Yearly stddev = monthly stddev * sqrt(12).

not sure… but not only know this but how it applies to hedge fund performance. Monthly performance is annualized x 12 and std deviation is x the square root of twelve. So sharpe can be gamed.

Also for daily figures use 270 days which is the # of trading days.

and pretty sure you have the first part WRONG - that Yearly VAR = Monthly VAR * sqrt(12).

You need to arrive at it as

Monthly Return = Yearly Return / 12

Monthly StdDev = Year StdDev / sqrt(12)

now for a 5% Monthly VAR: VAR Value = Monthly Return - 1.645 * Monthly StdDev

and calculate it.

# of trading days is 250 not 270. … for clarification.

My notes says, sharpe can be gamed by increasing the time interval of volatility calculation that actually reduces the volatility(standard deviation). The reason, sample size is 250 with daily returns Vs 12 with monthly returns when calculating the yearly standard deviation.

Not sure if comparison between VAR and std is even relavant.

yes 250, not 270.

cpk how was Omaha?

that is correct, you can move the time period out and smooth the volatility. Also can write call options to enhance return.

Yes, to derive yearly std from monthly std you divide it by square root 12. Using yearly std in place of monthly sharpe approximately goes up by square root twelve.

Yearly VAR = monthly VAR * square root of 12 if expected return in VAR calc is 0. Thats it. Page 236.