Finance / econometrics question

farrelb1 · November 1st, 2010, 11:38 am

Hi everyone,I am having trouble with the below question, any help would be much appreciated:The daily volatility of a stock price is 2%. Assuming the normal distribution with zero mean for daily price changes what is an approximate 99% confidence interval for the percentage price change in 10 days?Thanks,

amit7ul · November 1st, 2010, 12:47 pm

i guess the answer to your question is (NormalInverse(0.005), NormalInverse(.995))

eh · November 1st, 2010, 2:09 pm

If the returns are independent and the vol is constant, the 10 day return is N(0,10*0.02^2). You can work it out from that.P.S. 2% is very low for a stock vol!

Anthis · November 1st, 2010, 4:04 pm

QuoteOriginally posted by: farrelb1Hi everyone,I am having trouble with the below question, any help would be much appreciated:The daily volatility of a stock price is 2%. Assuming the normal distribution with zero mean for daily price changes what is an approximate 99% confidence interval for the percentage price change in 10 days?Thanks,+/- 2.81 times the 10 day vol.If returns are iid, then use the square root of time rule to get to the 10 day vol.

farrelb1 · November 2nd, 2010, 12:23 am

Thanks for the replies,Where did you get the +/-2.81 from?I thought it may be worked out using 0+/-(95% critical value)*sigma/root(n)...however i don't get the right answerBy the way...the three options are [-2.57%,2.57%] or [-16.25%,16.25%] or none of the above.

Anthis · November 2nd, 2010, 6:44 am

Apologies, 2.5758 is the correct value. 2.81 was the next line value, for 99.5% confidence interval in the table.

farrelb1 · November 2nd, 2010, 10:12 am

Awesome thanks so much for your help.FYI i ended up getting the correct answer i.e. 2.57% * root(10) * 2 = 16.25%