Gosh, maybe I just need to brush up on my hypothesis testing and confidence intervals (or perhaps it’s just late), but can someone explain why it means the manager added value with trading strategies if her value added return falls above and outside the 95% confidence interval? Why does that mean her return had nothing to do with chance?
Many Thanks. B
can’t remember from the books but I would assume you’re testing whether the manager simply ‘got it lucky’ by measuring the likelihood of them achieving those returns through luck.
if there’s only a small chance (eg 5%) that the results were down to luck, you can reject the null and conclude that it must have been down to skill.
Yeah. It is just a normal confidence interval. If the manager is 2 standard deviations above the benchmark, it means that there is just 5 % chance that his value adding skill is nada.
But why does that mean there’s only a 5% change of the manager’s results occuring due to luck ? Doesn’t it just mean that those results will only occur 5% of the time?
And why does that mean if his results fall within the confidence interval that they are the result of chance?
Missing the tie in with luck.
Thanks for your help
…
-2sigma mean +2sigma
rej rej
outside – reject the hypothesis that the manager’s performance is not luck.
inside - accept.
we’re talking probabilities of returns falling in the upper tail . If the manager creates enough +ve excess returns , he is relying on something other than luck.
Hypothesis H0 is that he has no skill .Alternative is he has skills that deliver +ve alpha. test statistic is mean excess return .if mean excess return is +ve at the 5% probability ( 95% confidnce ) , the hypothesis H0 would be rejected .
There is not enough evidence to prove the manager relies only on luck to generate alpha.
_ No, no, no, no, no! _
(You never _ accept _ the null hypothesis: you merely fail to reject it.)
oops you’re right , I should have said fail to reject . Thanks for correction
The book says that the Null hypothesis is that the manager earns 0 value-added excess returns, so H0 = 0. What does the ensuing hypothesis test / confidence interval have to do with luck then ? And why does falling within the confidence interval imply that his return is lucky?
if return is within the bands, we fail to reject H0. No conclusion can be made. That’s it. End of story.
I’m not sure where in the CFAI text that you read his return is lucky. That is only one of the possibilities. The other possibility is that he is indeed skillful but from the available data over the period, we cannot classify him unambigously.
it does give examples that the return is lucky.
say a manager has a 80% band of -5.12% to 5.12% and his return is 5.9%.
QC chart would indicate that he is skilful. (he is outside the band).
but there is a 10% chance (luck) involved that he fell in that band.
Agreed, but this is not the same issue.
The question just above my post concerning the case where the return is within bands.
When the return is outside the bands, we need to deal with confidence level, type I and type II error… The luck factor is the Type I error then.