Time horizon and information ratio

CFA Level II
#1

I feel like the below statemetn is contradicting… i don’t understand it.

"unlike leve of aggressiveness, time horizon does impact a managers information ratio. the informationr ratio will increase with the square root of time . this implies that a quarterly IR will be half as large as the annual information ratio.

4^2 = 2. why are they saying will be half as large.

#2

Imagine make 1 bet each quarter, so it is a total of 4 bets each year.

=> Yearly IR = IC x 4 ^ 0.5 = 2 x IC

Now the forecast horizon is lower to one quarter only

=> Quarterly IR = IC x 1 ^ 0.5 = 1 x IC

=> Yearly IR = 2 x Quarterly IR

Or Quarterly IR = 1/2 x Yearly IR

:smiley:

#3

Can you please help me understand what they mean by this.

Increasing the time horizon will increase your annualized IR ratio.

Is this the same as forecast horizon? looks like if i shorten the time period my IR should decrease…

#4

"Increasing the time horizon will increase your annualized IR ratio’’

Sounds weird to me.

If you increase the forecast horizon, from quarterly to semi-annually. Then the total number of bets each year would decrease from 4 to 2 . Which means your BR will be lowered by half and IR be lowered by square root of 2?

This may be an issue of how I interpret the word “time horizon”

But I think understanding the bottom line idea is sufficient:

  • You can improve your IR by making more bets (increasing BR) using the same level of skill for each bet (same IC, meaning not losing your forecast accuracy as you make more forecasts!!!)

Please tell me if I’m confusing you :smiley: Perhaps we should wait for s2000magician to clarify these terms.