John Dodson:hi there
 Peter:hi john.
 Holly Borgie:hello
 Sharon Linden:bless you
 Holly Borgie:gesundheit
 John Dodson:Let's use the UMConnect audio instead of the conference line for now.
 Fanda:yes
 Peter:yes.
 Sharon Linden:yes
 John Dodson:how is the homework going?
 Greg:I'm a bit lost.  I wish I had attended class in person during the case discussion.
 Peter:i'm a little stuck on how to represent expectation and variance with Beta. Any guidance here?
 Sharon Linden:Could you discuss how you arrived at the B* values in the discussion?
 John Dodson:With the two-step, in general you have $\alpha(\beta)=\alpha_{MV}+\beta(\alpha_{SR}-\alpha_{MV})$
 Peter:yes
 Holly Borgie:yes
 Fanda:yep
 Abdou Mouguiss Ba-Traore:yes
 John Dodson:S(\alpha) is generally a function of $E\Psi$ and $\var\Psi$
 John Dodson:$\Psi=\alpha'M$
 John Dodson:$E\Psi=\alpha'EM$
 John Dodson:$\var\Psi=\alpha'\cov M\alpha$
 John Dodson:$\max_{SR}\beta S(\alpha(\beta)))$
 John Dodson:$S$ is a scalar, $\beta$ is scalar, so the problem reduces to a single 1st-order condition: $S'(\beta)=0$
 Fanda:did you do the derivative in mathematica?
 John Dodson:Fanda, its a fairly simple function in this case, but you are welcome to use Mathematica is you need to.
 Sharon Linden:When we differentiate, should we use 2nd moment is variance
 John Dodson:I don't understand Sharon.
 Holly Borgie:I'm just confused because in the case where c=0, alpha_mv = 0, and you have this messy formula for alpha_sr (from slides).
 John Dodson:you are differeiating wrt $beta$
 Holly Borgie:when you plug that in, it's just kind of huge and confusing.  I guess I'm not sure how to take the derivative of that (don't judge me)
 John Dodson:but $\alpha_{SR}$ doesn't depend on $\beta$
 Holly Borgie:ok, yes that's true.
 John Dodson:You can probably leave your answer in terms of $\alpha_{SR}$
 Fanda:Hey John, is it correct that you want us to change the Cornish-Fisher to Arrow-Pratt as a new satisfaction index function?
 John Dodson:Yes, use Arrow-Pratt. Cornish-Fisher is only useful for VAR and ES
 Sharon Linden:$\alpha_{SR}$ involves expectation. I feel like the derivative of expectation is variance.
 John Dodson:Not in this case. We are differentiating wrt $\beta$
 Fanda:in Arrow-Pratt, we have this A(\psi) thing. when taking the derivative of it, are we supposed to simply leave it there and write down something like A\prime?
 John Dodson:Now, $E\Psi$ and $\var\Psi$ both depend on $\beta$ (see above), but $\alpha_{SR}$ does not.
 Fanda:of course chain rule might be used
 John Dodson:Fanda, there is a particular $A$ for this utility function.
 John Dodson:Yes, in a sense you are using the chain rule. Since $A()$ depends on $E\Psi$, which depends on $\beta$
 Fanda:I see the definition of that A(\psi). so gamma, zeta, eta are all parameters, right?
 John Dodson:Yes, although here only $\eta$ is relevant.
 Fanda:what do you mean \eta is relevant?
 John Dodson:for the assignment, we are using prospect theory utility.
 John Dodson:$u(\psi)=\erf(\psi)/\sqrt$
 Fanda:i am typing this whole thing. haha thanks
 John Dodson:oops. $u(\psi)=\erf(\psi/\sqrt)$
 Fanda:so that is the functional form of utility
 John Dodson:I will save the chat log when we are done.
 Fanda:so back to your case, how did you get the Cov thing on the second page?
 John Dodson:Fanda, that's a general property. You can prove it from the definitions of the MV and SR portfolios.
 Fanda:ok. i would just pretend if i do the FONC on that huge \beta^* carefully, i would end up the covariance equation
 John Dodson:Fanda, the zero covariance result is about the SR and MV portfolios, which define the efficient frontier. There is no direct connection with any satisfaction or beta in this result.
 John Dodson:$\Psi_{SR}=$
 John Dodson:sorry $\Psi_{SR}=\alpha_{SR}'M$ etc.
 Greg:John, have you said anything in the past half-hour?  It's been silent on my computer.
 Greg:Thanks
 Fanda:hey John, I see a lagrangian function on the slide. is that the place where the zero covriance is gotten by taking the FONCs?
 Fanda:page 8
 John Dodson:Fanda, that's probably right. It is appealing that the "cash" portfolio should be orthogonal to a "fully leveraged" portfolio.
 John Dodson:One would think that there would be a better portfolio out there if this were not so.
 John Dodson:by that, I mean that the outcomes are uncorrelated.
 Fanda:i see
 Fanda:thanks John
 Abdou Mouguiss Ba-Traore:Hi John, which function of AP should we use, bec i have seen different functions out there?
 John Dodson:Abdou, I cite the AP for prospect theory utility on slide 22.
 Abdou Mouguiss Ba-Traore:oh i see, thx!
 Abdou Mouguiss Ba-Traore:So the optimal beta should be in function of  alpha(sr) and 'nu' and some sort of variance?
 John Dodson:probably it is a function of both the expected value and the variance of $\Psi_{SR}$
 John Dodson:and the utility paramter $\nu$
 Abdou Mouguiss Ba-Traore:i meant the result?
 John Dodson:Abdou, you can write the result in terms of $E\Psi_{SR}$ and $\var\Psi_{SR}$
 John Dodson:and $\eta$ (not $\nu$)
 Abdou Mouguiss Ba-Traore:ok
 Abdou Mouguiss Ba-Traore:thx
 John Dodson:any questions?
 Abdou Mouguiss Ba-Traore:Thanx John and see u Wed.
 John Dodson:sure
 Abdou Mouguiss Ba-Traore:thanx John and see u Wed
 John Dodson:I am going to sign-off shortly.