standard deviation question Please help

after working some problems in the stalla cd, I worked a few portfolio SD questions. Here is my problem. In the calculation do you use the SD of the individual assets as the same notation as the data. FOr example what is the SD of a two asset class portfolio. If the expected return is in percents. Woudn’t the SD also be in Percents. example: variance= w1^2(SD1^2)+w2^2(SD2^2 … if the data is in percents for example the E® = 3.5% the stalla CD is telling me this: In the calculation such as a SD1^2 = 3.5% variance= (w1^2) (3.5)^2 NOTE:you do not hit the percent button, instead you square the 3.5 which gives you 12.25 or would it instead be w1^2 (.0350)^2 which gives you .0012 these are two totally different answers. because you have to add them together. THE cfa books shows to use it as a percent of .0350 but the stalla is showing the 3.5 and then squaring it. anyone know why?

There is a difference of a factor of 10000, because 3.5/0.035=100, and if you are squaring the 3.5%, the difference will be a factor of 100^2=10000. variance= (w1^2) (3.5)^2 NOTE:you do not hit the percent button, instead you square the 3.5 which gives you 12.25 --> So if you are doing this you need to divide 12.25 by 10000, and you’d get the answer mentioned in the CFAI book. I am most comfortable with working using the method listed in tthe CFAI book, and you’d get the answer 0.001225, = 0.1225%. It appears to me that the stuff in the stalla cd is WRONG. you need to divide 3.5 by a hundred to get the correct answer. By the way did the Stalla CD choose the option with 12.25%?? I certainly hope not!

I would bet my life that the Stalla CD calculates sd correctly. What’s the problem here, anyway? S1: w = 0.3 sd = 3.5% S2: w= 0.7 sd = 4.5% Var§ = 0.3^2*3.5^2 + 0,7^2*4.5^2 = 11.025 => Sd§ = Sqrt(11.025) = 3.32% or Var§ = 0.3^2*(0.035)^2 + 0.7^2*(0.045)^2 = 0.0011025 => sd§ = Sqrt( 0.0011025) = 0.0332 = 3.32% Same.

Joey, my suspicion is that he is confused by the factor of 10000 thing,since what he did showed only the variance part [using waht you did, if you did not press the % sign, the answer you get is 100^2 X that the figure you get if you punched the % button]. My mistake above when I said that the Stalla CD was wrong because I thought it said that the variance was 12.25%. btw5555, variance= (w1^2) (3.5)^2 NOTE:you do not hit the percent button, instead you square the 3.5 which gives you 12.25 --> All you need to do here is to divide 12.25 by 10k, then take the square root of that number.

let me give the exact problem. And you tell me what you think. Sample Problem::::::: Let me give two exact problems although it seems to me they are worked two different ways when it come to hitting the % key being hit. Example 1 - while hitting the % key for the SD Rhondre Hall, CFA, works for a private wealth management firm. To assess the risk and expected return of his client’s combined equity and bond positions, Rhondre has used past return data to develop the following estimates for his client’s holdings: Item Amount Equity Portfolio: Expected Return: E(RE) 8% Equity Portfolio: Standard Deviation: 22% Bond Portfolio: Expected Return: E(RB) 4% Bond Portfolio: Standard Deviation: 12% Correlation between Equity and Bond Portfolios: .16 Rhondre’s client has $6,000,000 invested in the equity portfolio and $12,000,000 invested in the bond portfolio. Based on this information, what are the expected return and standard deviation of his client’s portfolio? answer is: expected return 5.33% and SD 11.68% solution: variance = (.333)^2 (.22)^2 + (.667)^2 (.12)^2 + 2(.333)(.667)(.22)(.12)(.16) Example 2 — with out hitting the % key for the SD Mo Howard, CFA, intends to create a two-stock portfolio comprising Larry Corporation and Curly International. The possible returns of the two stocks are the following: Larry Curly Return (“R”) Probability (“P®”) Return (“R”) Probability (“P®”) -5% 0.3 -35% 0.3 5% 0.4 35% 0.4 10% 0.3 40% 0.3 The risk-free rate (“rf”) is 3%, and the standard deviation of the market index (“óM”) is 25%. In addition, Larry’s returns are approximately 75% correlated with the market overall (i.e., ñLARRY,M = 75%), whereas Curly’s returns are approximately 45% correlated with the market (i.e., ñCURLY,M = 45%). The covariance between Larry and Curly is 188.25. The standard deviation of a portfolio that is 2/3 of Larry and 1/3 of Curly is closest to: answer is: SD is 14.9% Variance = (.6667)^2 (5.9)^2 + (.3333)^2 (33.1)^2 + 2(.6667)(.3333)(188.25) Note as you can see when doing the second problem is you hit the 5.9 then % which the SD should be in a percent since the data is in %. any solutions:

I noticed that too. They seem to treat percentages as regular numbers. For example, in calculating the error number in an ANOVA table they square the solution for (Y1 - Y^) which was .32% (or .0032) and derive .1024. Shouldn’t it be .00001024??? The SEE works out to .042695 but the book has 4.27.

On the first problem – even if you did consistently 22 and 12 everywhere – and then hit sqrt you get 11.68. .333^2 * 22^2 + .667^2 * 12^2 + 2 (.333) ( .667) (22)(12) (.16) = 136.4982293 sqrt = 11.68 So you can do the problem calculation either way, and you NEED to be consistent. That is all there is to it. CP

as a follow up: mean is measured in the unit of the measurements. e.g. % if all the measurements are in %. Std Dev is also measured in the unit of the measurements. Variance is in the (UNit of measurements) squared. CP

BUt what if the question asks for the variance not the SD. you are right you still get the same SD but not the Variance.

For the variance you might get to see either of the following answers: 136 %^2 or .00136