true or false, all else equal, lower the beta, higher the IR.
IR being information ratio???
IR = IC*sqrt(breath) if beta is lower, B = Corr*SDm*SDp/SDm^2 = Covariance/SDm^2…so if beta decreases the covariance decreases and the information coefficient would be lower so IR would be lower? False - that’s my guess…i have no idea though.
The beta of what is lower?
let me see how clueless I am: IR=alpha/std. of alpha. Alpha is not detminned by beta. My guess is that beta has nothing to do with IR.
Beta is lower -> Correlation with market is lower -> Higher tracking risk (?) - > Lower IR. Had to make an assumption at the (?). What’s interesting is where do you get these questions from?
a friend of mine is to graduate from his mba. he is having an interview today with GS. the question he got is. “two eqity managers with a same benchmark, one manager outperform bm by x% while his beta to bm is higher; another manager also outperforms bm by x% but beta is lower. in addition, one can’t assume the same vol for both portfolio. question is which manager has higher information ratio?” is it clear now? i post this cause i think it might be helpful to L3er’s like us.
Random, It’s a very interesting question (after June 7).
The one with lower beta would have a higher IR. To generate the same return with a lower beta, the manager has to make more independent investment decision.
ws Wrote: ------------------------------------------------------- > let me see how clueless I am: > > IR=alpha/std. of alpha. > > Alpha is not detminned by beta. > > My guess is that beta has nothing to do with IR. I like this analysis better.
ws is right. lower beta leads to higher ir. alpha = R - Rb, the same sig(R-Rb) = sqrt(cov(R,Rb)) = sqrt(beta * var(bm)) IR = alpha / sig(R-Rb) = (R-Rb) / sqrt(beta * var(bm))
rand0m Wrote: ------------------------------------------------------- > a friend of mine is to graduate from his mba. he > is having an interview today with GS. the > question he got is. > > “two eqity managers with a same benchmark, one > manager outperform bm by x% while his beta to bm > is higher; another manager also outperforms bm by > x% but beta is lower. in addition, one can’t > assume the same vol for both portfolio. question > is which manager has higher information ratio?” > > is it clear now? i post this cause i think it > might be helpful to L3er’s like us. I think the IR for the second manager would be higher BUT only because of misspecification of benchmark and NOt because of skill.
“two eqity managers with a same benchmark, one manager outperform bm by x% while his beta to bm is higher; another manager also outperforms bm by x% but beta is lower. in addition, one can’t assume the same vol for both portfolio. question is which manager has higher information ratio?” I’m going to say the manager with the Lower Beta will have the Higher IR for the fact that he has a lower Beta which suggests via CAPM that he should outperform the bench by
Bigwilly…read you post twice. GIVEN THE CONTEXT. I am confused. At beginning, you said that you think higer beta will produce higer IR, at the end, you wrote that lower beta manager outperformed MORE than he/she was “supposed” to according to CAPM. Well, isn’t that a good thing?==> outperform more than what he/she was “supposed” to? So, lower beta produce higer IR?
I got it - in simplier terms. IR = IC * sqrt (breadth) IC = forecasts - actual outcome; the closer they are the better the correlation. We know that the higher the correlation, the higher the beta, so if beta is lower, we can make the case that correlation is lower so IC would be lower. A lower IC a lower IR. from schweser: “The IC is measured by comparing hte investor’s forecasts against actual outcomes. the closer they are, the higher the correlation between them, and the greater the IC.”
ws, At the beginning, he said the lower beta would have the higher IR.
ws, you might have read it while i was editing it, i posted it, saw my mistake and fixed it, so it must have been during that 10 second time window 
Sorry!!! I am going home!!! Sorry!!!
With all else equal, a lower beta should result in a higher IR. Conceptually, beta is a proxy for market risk. For a lower beta, the _expected_ return of an asset is a lower magnitude (up or down) wrt the market benchmark. So if the actual return is constant, then the difference between the expected and actual return will be greater, leading to higher alpha. Alpha = Ra - Rf - beta(Rm-Rf) (Ra is the return of the asset, Rf, the risk-free asset) So the numerator increases in the IR equation IR= alpha/std(alpha). But the dispersion of the excess return doesn’t change, so the denominator stays constant. Thus, the IR increases. Just to clarrify a couple points: 1) alpha is indeed dependent on beta. 2) Beta is NOT a measure of an assets correlation with the market benchmark, that would be the R^2, or correlation coefficient. Beta is the slope of the correlation line, showing how sensitive the dependent variable (asset return) is to the independent variable (market return). Going beyond the scope of the CFA CBOK, if your R^2 is low (I use 0.80 as a threshold), then your beta becomes more and more meaningless because its becoming the slope of an increasingly weak correlation without statistical significance (probably). When our group is hiring managers and we’re setting the manager benchmark for an IPS, one of the first things I look for is a high R^2. I only look at beta wrt the risk tolerance of our client and the overall portfolio risk. And I always verify how alpha is calculated, making sure its beta-adjusted. Hope this helps the discussion!
^Thanks man!! Have a question. You 1) alpha is indeed dependent on beta. Using your equation Alpha = Ra - Rf - beta(Rm-Rf). I can see that. Is this in CAPM context, or in general? Can you please explain a little? When I said Alpha is not determined by beta, I was thinking in absolut terms. Thanks