returns based style analysis

I read the same thing in both Schweser and CFAI readings R^2 provides the amount of the investor’s return explained by the regression’s style indexes. It measures the STYLE DRIFT. One minus this amount indicates the amount unexplained by style and due to the manager SECURITY SELECTION. The error term in the regression, which is the difference between the portfolio return and the returns on the style indices, is refered to as the manager’s SELECTION RETURN ************************* My question: if R^2 = 70% and error = 5% Does it mean that based on the regression 30% of investor returns is explained by security selection which equals 5%

R^2 is 70% that means 70% of variation in dependent variable (portfolio return) is explained by variation in independent variable (benchmark return) I dont know what you mean by error = 5%? i

No. If Error = 5% then 5% of the returns are due to Selection Return, while 25% is due to Security Selection.

R^2 = 70% means that your regression (from the benchmark) explains the managers returns (his/her style) = Style Bet 1-R^2 = Selection Bet; means the difference between your regression and the manager’s returns is from the manager picking stocks that didn’t come from the benchmark (i.e. what you based your regression on) error = 5% means the manger not only picked stocks but he picked stocks that were able to generate a return in of 5% in excess of what the regression expected. i.e. “superior selection”

Are you guys referring to manager’s alpha as error here? In above context, 70% of the variation in the return is explained by manager’s style. The keyword here is variation. The other 30% of the observed variation must be attributable to whatever manager did (or perhaps misspecified factor model). 5% is manager’s alpha - that is return over and above that is attributable to style. Bigwilly, can you explain your response above?

I think a single error (5% or whatever) can not be compared or used with R^2 Actually R^2 is calculated according to the error observed for each observation (real return Vs expected return according to your regression model), I mean, you will have as many error terms as observations Doing some calculations (I don´t remember from level II), you will get that R^2 is 70% (or whatever), so 30% will not depend on your regression But substracting one of the error terms (5%, for example) to R^2 or to (1-R^2) does not make sense to me. What do you think? atpr, can you write the complete example, or tell us book and page? thx

Schweser-SS10-page 135-top of the page CFA Reading 31- page 116- in the middle of the page between the 2 examples

thx atpr I think that STYLE DRIFT = SECURITY SELECTION = (1-R^2) is obtained from a multiperiod analysis, and applies to your regression in general, while the error term comes from the last observation Is like trying to extrapolate deviation of returns by comparing the difference between last year return and average year return… can be whatever, but deviation is calculated using st deviation, which is calculated n years, not only last one In the exam, I guess we will not be given both R^2 and one error term. Again, not sure about this, but I think that they are not comparable, that is mathematically incorrect

hala_madrid Wrote: ------------------------------------------------------- > thx atpr > > I think that STYLE DRIFT = SECURITY SELECTION = > (1-R^2) is obtained from a multiperiod analysis, > and applies to your regression in general, while > the error term comes from the last observation > Agree, The R^2 is the style selection, (1-R^2) is the style drift, the 5% error is active return ( Actual return - Predeicted by the model).

mo34 Wrote: ------------------------------------------------------- > Agree, The R^2 is the style selection, (1-R^2) > is the style drift, the 5% error is active return > ( Actual return - Predeicted by the model). Active return = actual return - benchmark return, right? I mean, your formula (active return = actual return - predicted by the model return) is the right one if the benchmark is not a single index but a returns-based constructed benchmark, right? thx mo34

R^2 -fraction of RETURN VARIATION attributed to style 1-R^2-fraction of RETURN VARIATION attributed to selection error–manager selection return alpha->Actual return - Predeicted by the model.

the 5% error, yes, is like an alpha because it is comes from some place that we can’t explain. i.e. outside of our benchmark (that we used for the basis of our regression). therefore it would be like active management. but gang, I also think we need to state that RBSA Alone does not not identify style drift. that would be “Multiple” RBSA. in other words we need to look at RBSA over periods to see if there is a Style drift taking form. we don’t get that information from R^2 or the error or the alpha. Remember RBSA can NOT detect style drift. but RBSA observed over MANY periods can! Hala I don’t understand this relationship? STYLE DRIFT = SECURITY SELECTION = (1-R^2) is obtained from a multiperiod analysis how can that show me style drift? why would I look at this even in a multiperiod analysis? what will this show me? I just look at the coefficients to see if they have change or are consistant to see if a style drift has occured. Anybody else approach these questions in the same fashion?

You are correct - You have to run RBSA over multiple periods (e.g. rolling 1 year window) to catch style drift.

hala_madrid Wrote: ------------------------------------------------------- > mo34 Wrote: > -------------------------------------------------- > ----- > > > Agree, The R^2 is the style selection, > (1-R^2) > > is the style drift, the 5% error is active > return > > ( Actual return - Predeicted by the model). > > > Active return = actual return - benchmark return, > right? > > I mean, your formula (active return = actual > return - predicted by the model return) is the > right one if the benchmark is not a single index > but a returns-based constructed benchmark, right? > > thx mo34 If we assume that the regression used enough asset class indices that if it covers a good portion of the variation (high R^2), then 1-R^2 is the misfit-return (due to the fact that the model does not cover all of the variation) and the error term is the active return (actual - expected). I agree that we can’t dedect style drift with this method unless we have the variation of the coefficents over time.

I agree