I've got the monthly standard deviation for a portfolio of stocks and I need the yearly value. Is it 'statistically allowed' to just multiply the monthly value by 12? For example:
monthly standard deviation = 5,
hence, yearly standard deviation = 60.
If not, how can I get the yearly standard deviation from the monthly value?
(I cannot recalculate because I do not have the source data).
2007-07-13 08:47:31 · 6 answers · asked by Tal0 1 in Science & Mathematics ➔ Mathematics
Actually, it is a core assumption for the portfolio that each month behaves the same.
Plus, I know that the year mean return does change and is higher due to compounding:
monthly mean return= 1%
yearly mean return= 12.68%
2007-07-13 11:09:43 · update #1
Actually you can guess the annual variance if you assume each of twelve months is exactly like the other eleven. Here's how...
Assume each month has variance sd^2 = sum(q - Q)^2/n; where q is a daily quote, Q is the average quote over n days in a month. (NB: use n, not n - 1 because this is not a sample of the month it is the whole month) Then the variance of a year is SD^2 = 12*sum(q - Q)^2/12*n, which is just sum(q - Q)^2/n, the monthly variance because the 12's cancel out.
SD^2 = 12*sum(q - Q)^2/12*n because the numerator is just the sum of square of deviations for twelve months of data points and 12 n = N the total number of data points in a year. In other words the SD^2 relationship is just the definition of a variance for the 12n days worth of quotes over the year. Q remains the same because the average of averages is the average.
Hence SD = sqrt[sum(q - Q)^2/n] = sd = 5, which was given; so your yearly standard deviation (SD) is the same as the monthly (sd) but if and only if you assume each month is exactly the same.
2007-07-13 10:08:41 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
No, you cannot multiply it by 12. Standard deviation is a measure of spread. There's actually a good chance that the yearly standard deviation would be very close to, if not equal to, 5 - assuming that the monthly data and yearly data are similar. You would need data to support this claim. If you don't have the data, you cannot have a standard deviation.
2007-07-13 08:53:03 · answer #2 · answered by whitesox09 7 · 0⤊ 0⤋
This question is actually a lot easier than it looks :) First you need to know that for normal distribution the expected value and the mean are the same thing. To answer this question: First you have to realise that he buys 9 seed packets, each containing 40 seeds. So it is : 9 x 40 = 360 Then the number of bad seeds is 9 x 4, as there are 4 bad in each packet. So this number is taken away from the 360 to get your mean: 360 - (9 x 4) = 324. (Of course if you find it easier you could also just do 9 x 36) I am unsure about the second part, I assume it is just 9 x sd, but I don't want to write anything just in case).
2016-03-19 06:26:54 · answer #3 · answered by Anonymous · 0⤊ 0⤋
That's interesting
2016-07-29 09:29:41 · answer #4 · answered by ? 3 · 0⤊ 0⤋
Need more information before I can give an answer
2016-09-20 03:40:37 · answer #5 · answered by patria 4 · 0⤊ 0⤋
thanks for all the answers.
2016-08-24 08:33:53 · answer #6 · answered by Anonymous · 0⤊ 0⤋