risk adjusted utility

CFA Level III
#1

In reading 26 (book 3 p 237) they give a formula for Utility as U = E® - .5*Risk Aversion*Volatility But in reading 32 (book 4 p 254) they give it as U = Expected Active Return - Risk Aversion * Volatility I’m fine with one focusing on active returns and the other on overall returns…but why the .5 multiplier in one but not the other? Anybody have an intuition for this? Maybe they`re just assigning “risk aversion” factors as twice as large in the formula from R26? Think its worth worrying about? Thanks, Ben

#2

Good observation. The standard is multiplying with .5. I would definitely not worry about it. They would give you the formula to use if they want you to calculate.

#3

Just another stuff-up from CFAI - the inconsistencies in the readings and the sample, mock and past exams is just appalling.

#4

Isn’t is 0.005 and not 0.5?

#5

Ashwin Wrote: ------------------------------------------------------- > Isn’t is 0.005 and not 0.5? Depends on how you express vol. If vol is whole numbers, ie std dev is 21 not .21, you use .005.

#6

CharterMePls Wrote: ------------------------------------------------------- > In reading 26 (book 3 p 237) they give a formula > for Utility as > > U = E® - .5*Risk Aversion*Volatility > > But in reading 32 (book 4 p 254) they give it as > > U = Expected Active Return - Risk Aversion * > Volatility > > I’m fine with one focusing on active returns and > the other on overall returns…but why the .5 > multiplier in one but not the other? Anybody have > an intuition for this? Maybe they`re just > assigning “risk aversion” factors as twice as > large in the formula from R26? Think its worth > worrying about? > > Thanks, > Ben It should be E®-0.5*risk_aversion_parameter*Variance®, not volatility

#7

You are only worried about the downside, not the upside vol. Therefore times 1/2

#8

1morelevel Wrote: ------------------------------------------------------- > You are only worried about the downside, not the > upside vol. Therefore times 1/2 That only seems reasonable but totally incorrect. If you consider constant risk aversion utility U(x)=-exp(-lambda*x) and then assume that x is normal with (mu, sigma^2), then EU(x)=mu-0.5*lambda*sigma^2 which has nothing to do with upside and downside volatility.