Will the level of risk have any impact on the managers ratio of risk and return. Dude says" No! the ratio of risk to return remain unchange and equal to the informationr ratio even as risk changes.
Answers says teh statement is correct and adds… " as long as their is a corresponding change in alpha"
this is correct but i can’t see why.
There is a relationship between risk and return. As you take more residual risk, your alpha will also increase. But if alpha and residual risk increase to the same extent (for example both increase by 10%), the ratio of IR will remain the same.
The opposite: you take less residual risk, your alpha will also decrease and the IR will also remain the same.
So you cant make your IR better or worse simply by taking less or more residual risk.
How can you improve your IR? Remember IR = IC x BR ^ 0.5. You can either:
Increase the number of independent bets of alpha returns, which is breadth
Increase your skills, which is IC (the correlation between actual and forecast)
So if I increase my residual risk (denominator) by 10%, this will automatically increase my alpha by 10%?
To add to your last comment, will increase of time increase my IR too?
Yes your IR will remain the same because you’re just being more aggressive, so alpha return will increase to the same extent as the residual risk.
Imagine if you are more skillful now. As you take more residual risk, alpha return would increase more than the increase in residual risk => Your IR is improved.