Hello everyone, in a mock exam, i found this sentence : “The information ratio of an unconstrained portfolio is unaffected by the aggressiveness of the active weights”
I can’t believe this to be right…! if i can’t change my active weights (my unique power) in my portfolio in order to improve my IR, how can i get a positive IR ???
Thanks very much
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In a unconstrained portfolio, the actual active weights will not differ from the optimal active weights. i.e. unconstrained portfolio = optimal portfolio.
As such, the Transfer coefficient (correlation between actual weight and optimal weight) would be = 1 and as such formula wise, IR always remains the same.
If active weights were to increase in an unconstrained portfolio, the active risk would increase as well leaving the IR unchanged.
Think this way
For sharp ratio, however the weights you short or long risk-free rate, the sharp ratio doesn’t change.
so here, IR consists of long portfolio and short benchmark divided by standard deviation(fund, benchmark)
no matter how much you change the active weight, portfolio% and (1-%)benchmark, IR doesn’t change
(but sharp ratio of the combined portfolio, benchmark & uncombined portfolio, is changed, which is ur objective to improve)
I understand that if i have 50% invested in benchmark and 50% invested in my portfolio (whose stocks are from the benchmark), change the weight to 40/60 won’t change the IR (but will change the SR as it is compared to risk free rate).
But if in my portfolio i change the weight for each stocks compared to benchmark (active weights), my IR will change (no ?)
CFAI says : “The information ratio of an unconstrained portfolio is unaffected by the aggressiveness of the active weights”
And in an other mock, CFAI says : the manager must overweight securities for which he has forecasted the best relative returns in order to generate positive relative returns (transfer coefficient).
What is the difference between both ? Thank you !
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if you increase allocation on the active portolio, your active return goes up but so does your active risk, leaving IR constant.
The key here is to unconstrained, as there is a difference between unconstrained and constrained when it comes to this.
The formula to remember is: IR = TC * IC * Sqr.root(BR)
IR = Information ration TC = Transfer coefficient IC = Information coefficient BR = Breadth
The TC plays an important role in this case. The TC is the correlation between the optimal active weights and the actual active weights that we can have (basically dreamer versus reality).
Constrained portfolio (you cant always get what you want): As we increase our active weights, for an constrained portfolio, the risk (remember: we dream big) the more we will have the reality chasing us saying “stop there, you are getting way to risky now…” => decrease in correlation between the optimal active weights and the weights that we can actually take (thus TC decreases).
What happen to IR if TC decrease? Well it drops, thus it is affected by our aggressiveness of the active weights, as we are constrained. We simply cannot transfer our ability to forecast active return into actual active weights, we are restricted.
Unconstrained portfolio (you always get what you want): Unaffected by the aggressiveness of the active weights. Forget the whole reality chasing you, you are free as a bird. Go ahead and make that dream come true!
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