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Standard Deviation Query

  • #1
  • First Post: Jul 9, 2010 3:50am Jul 9, 2010 3:50am
Hi
I'm hoping that some kind person can help me with a question regarding the calculation of standard deviation;

-after calculating the initial deviation figures, some of them are negative. When squaring up a negative figure, do you ignore the negatives? Or, do you observe it and therefore diminish the number further?

For instance, with a deviation of -5.95, would you multiply -5.95 x -5.95, or 5.95 x 5.95, or even -5.95 x 5.95?

I know that this is, in all probability, an amazingly stupid question, but do you know the feeling when you've been staring at something for 4 hours...........

Thanks, in hope!
  • #2
  • Jul 9, 2010 4:09am Jul 9, 2010 4:09am
Quoting Interceptor
Hi
I'm hoping that some kind person can help me with a question regarding the calculation of standard deviation;

-after calculating the initial deviation figures, some of them are negative. When squaring up a negative figure, do you ignore the negatives? Or, do you observe it and therefore diminish the number further?

For instance, with a deviation of -5.95, would you multiply -5.95 x -5.95, or 5.95 x 5.95, or even -5.95 x 5.95?

I know that this is, in all probability, an amazingly stupid question, but do you know the feeling when you've...
Variance = StDev^2, therefore it is always positive.
  • #3
  • Jul 9, 2010 5:36am Jul 9, 2010 5:36am
Could you run that past me again?
My brain hurts!
  • #4
  • Jul 9, 2010 5:45am Jul 9, 2010 5:45am
Yes, squaring negatives results in positives, and thats what has to be done in the Stdev calculation.
The nail that sticks out gets hammered back in
  • #5
  • Jul 9, 2010 5:46am Jul 9, 2010 5:46am
Quoting Interceptor
Could you run that past me again?
My brain hurts!
http://upload.wikimedia.org/math/8/3...353af56596.png

A standard deviation is always positive. If you get a negative standard deviation, you have already done something wrong.
  • #6
  • Jul 9, 2010 5:55am Jul 9, 2010 5:55am
If I understand your question correctly, I think you mean you get a negative value when calculate the xi − m(X). No problem after you square it as in the formula above, the result has to be positive. and then you will no have any negative terms to see.
  • #7
  • Jul 9, 2010 6:23am Jul 9, 2010 6:23am
First, as said before, squaring something then taking the square
root has become a standard way of getting the absolute value.

The standard deviation formula here is the "bias corrected"
version, there's the population deviation formula too that's
slightly different.

None of your stdevs should be negative. If they are, you're not
doign them right. If you have access to excel or oo calc, use
that.

If you're planning to use this in forex trading, you might
want to study up on statistics. While it works fine w/ returns
data, it isn't so useful in price data.
  • #8
  • Jul 9, 2010 6:29am Jul 9, 2010 6:29am
Thanks for the replies thus far.
I'm going to be a real ballache, now.
Looking at the data, below, could somebody tell me where I'm going wrong?

Pips........£1,000,000 (Opening) .......Deviation (from 5.95%) .........Squared

 +292 .....£1,116,800 (+11.68%) .................5.73 ........................32.83
 +432 .....£1,309,783 (+17.28%) ................11.33 ..................... 128.37
 +263..... £1,447,572 (+10.52%) ................. 4.57 ...................... 20.88
 +120..... £1,517,055 (+ 4.8%) ...................-1.15 ........................1.32
 +479..... £1,807,722 (+19.16%) .................13.21 .....................174.50
 +194..... £1,948,000 (+ 7.76%) .................. 1.81 ....................... 3.27
 +75 .......£2,006,440 (+ 3.00%) ................ -2.95 ........................8.70
 +61....... £2,055,397 (+ 2.44%) ................ -3.51...................... 12.32
 +205 ..... £2,223,939 (+ 8.12%).................. 2.17 ...................... 4.71
 +329 ..... £2,516,609 (+ 13.16%)................ 7.21 ......................51.98
 +157...... £2,674,652 (+ 6.28%).................. 0.33....................... 0.11
 0 ...........£2,674,652 (+ 0.00%) ................ -5.95 .................... 35.40
 -28 ....... £2,644,695 (- 1.12%) ................ -7.07 ......................49.98
 -38........ £2,604,495 (- 1.52%)................. -7.47 ......................55.80
 +209 ..... £2,822,230 (+ 8.36%).................. 2.41 ........................5.81
 - 42 .......£2,774,816 (- 1.68%) .................-7.63 ...................... 58.21
 +245 ..... £3,046,747 (+ 9.80%) ..................3.85 ...................... 14.82
 -200 .......£2,803,007 (- 8.00%) ...............-13.95 .................... 194.60
 +300 ......£3,139,367(+ 12.00%) ..................6.05 ..................... 36.60
 +149 .......£3,326,473(+ 5.96%)................... 0.01.......................... 00
 +370 ...... £3,818,791(+ 14.80%)................. 8.85........................ 7.52
 -73 .........£3,707,282(- 2.92%) ..................-8.87 ......................78.67
 -7 ...........£3,696,901(- 0.28%) ................ -6.23 .......................38.81
 +137 ...... £3,899,491(+ 5.48%).................. 0.47 .........................0.22
 +92 .........£4,042,992(+ 3.68%) ............... -2.27......................... 5.15


 (148.76/25 = 5.95% weekly)

 Risk free rate = 0.5% per annum (UK bank rate), therefore 0.25% for 25 weeks

 Average return 5.95% - risk free return 0.25% = 5.70%

 Sum of deviation squares = 1020.58

 Divided by one less than total weeks (24) = 1020.58/24 = 42.52

 Square root of 42.52 = 6.52

 6.52 is the Standard deviation

 5.95 divided by 6.52 = 0.91
  • #9
  • Jul 9, 2010 7:00am Jul 9, 2010 7:00am
Have a look at my results (sharpe of 1.12)
Attached Image (click to enlarge)
Click to Enlarge Name: sharpe.png Size: 34 KB
The nail that sticks out gets hammered back in
  • #10
  • Jul 9, 2010 7:05am Jul 9, 2010 7:05am
1. Riskfree interest calc not correct. .25% per half year is .01% per week.
2. Better leave it out for the time being marginal influence and takes attention away from the real important stuff.
3. Dividing by 24 is not necessary. Not much influence however.
4. Roughly 20% chance on a negative week, so 5 in average, you have 6 nothing to worry about.
  • #11
  • Jul 9, 2010 7:20am Jul 9, 2010 7:20am
Quoting Noloqy
Have a look at my results (sharpe of 1.12)
Thanks for this.
The thing that's confusing the hell out of me, and the reason why I feel I must be doing something wrong with my calcs, is the 'low' Sharpe figure such as the 1.12 which you have kindly worked up.
I read that a Sharpe of 2 is very good, and 3 and upwards is excellent.
My trading figures show an account which, at the end of 6 months, is 4 times the starting size. And this ends up with a low/average Sharpe!
I need a lie down.............
  • #12
  • Jul 9, 2010 7:21am Jul 9, 2010 7:21am
Quoting Rik
1. Riskfree interest calc not correct. .25% per half year is .01% per week.
2. Better leave it out for the time being marginal influence and takes attention away from the real important stuff.
3. Dividing by 24 is not necessary. Not much influence however.
4. Roughly 20% chance on a negative week, so 5 in average, you have 6 nothing to worry about.
Thank you.
So, forget all about the risk free return figure?
  • #13
  • Jul 9, 2010 10:54am Jul 9, 2010 10:54am
I would not use a deduction for riskfree in this case. First of all BOTH your average as well the week's result should be adjusted, leading to the same outcome only with a more difficult calculation. Second even if it would have to be deducted only from one yor StDev would be something like 6.51 (or 6.53) hardly relevant (less than .2%).
So making things more difficult without any real advantage.
  • #14
  • Last Post: Jul 9, 2010 11:49am Jul 9, 2010 11:49am
BTW I would not use a formula with N-1 (in your case 25-1).
First most ST Dev formulas donot use it (only sometimes when not all info is available, but you got everything).
Second it is more difficult again.
Third calculation results hardly change anyway.

Keep it as simple possible till you understand the basic calculation than start to add things. Otherwise you only increase the chance of mistakes if you donot work with a standard package/program. And anyway only add things if they really add something not only more complicated calc.'s.
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