QUANT CH 12 FRM PART 1

[mhkpayel20]

Hi,
Suppose that observations on an exchange rate at the end of the past 11 days have been 0.7000, 0.7010, 0.7070, 0.6999, 0.6970, 0.7003, 0.6951, 0.6953, 0.6934, 0.6923, and 0.6922. Estimate the daily volatility using both approaches in Section 10.5

1. what is the standard formula of SD here? is it sqrt{[Xi-avg(Xi)]^2/n}
2. Can anyone please explain this one elaborately?

 

[David Harper CFA FRM]

Hi @mhkpayel20 See below; XLS is here https://www.dropbox.com/s/9tuaflaknmgj0je/052720-hull-10-5-volatility.xlsx?dl=0 There are a few ways to calculate daily volatility (as the question says). Here

• The daily prices (yellow cell) inputs inform the daily returns, u(i); I could have used LN[P(i)/P(i-1] instead
• A proper variance squares the deviation from the mean daily return (-0.0011) but as daily is short, it's okay to assume mean = zero before squaring (the final column.
• The MLE (i.e., biased) variance is the average squared return (0.53006% to match the answer), but the unbiased variance has (n-1) in the divisor. Hope that helps,

 

[mhkpayel20]

Thanks for clarifying and explaining elaborately