John Dodson:hi there Sharon Linden:hi john John Dodson:how is the assignment going? Sharon Linden:I am still a bit confused about it John Dodson:Are you doing it numerically or analytically? John Dodson:Do you know now to set-up 'P' and 'v' for Black-Litterman? John Dodson:Btw, the picks matrix 'P' is different from the price vector 'P_\tau'! John Dodson:or rather, $P_{t+\tau}$ Sharon Linden:Right John Dodson:eq 9.39 and succeeding Holly Borgie:What does our picks matrix look like in this case? Is it just a row vector, since we only have one view? John Dodson:yes, it is just a single row with a single non-zero entry. Fanda:Hey John, so in the P in our homework, does the place of entry 1 indicate the which market variable will be pick up? John Dodson:yes, Fanda. John Dodson:It says your "pick" is a portfolio consisting of a single share in a single asset. Fanda:I am looking at euqation 9.39. could you explain more about what the area of expertise g(x) is? Fanda:or how does it work with the concept of view John Dodson:The rows of the picks matrix 'P' represent combinations of assets -- portfolios actually. The components of the view vector 'v' are the corresponding target outcomes -- like values of the objective '\Psi'. Fanda:So in the case of our homework, would the view expressed as Px = +0.05? John Dodson:Well, the 'x' in 9.39 is a generic variable. I would rather say your 'v' is a vector of one component and its value is 0.05 Fanda:something like this: v = (...,0.05,...)' in muti-dimensional case? John Dodson:no, Fanda. 'v' corresponds to 'P'/ John Dodson:so there is a component to 'v' for each row of 'P' -- a "view" for each "pick" Fanda:do you mean, if P = (0,1,0), then v = (0,0.05,0)? John Dodson:Fanda, how many rows does 'P' have in your case? Peter:Can you help me start out the second part of the problem? For the second part: What fraction of the SRportfolio’s initial value should be invested in this component? Can we just plug in what we got from the first part into alpha_SR as in lecture 2, slide 8? Will that be the answer there or are there more steps? John Dodson:That should be fine, Peter. John Dodson:By the way, Peter, how many assets are in your investible universe for this problem? John Dodson:You should be fine as long as there are enough. Fanda:i see. each row of P corresponds to an entry in view. Peter:I thought that M was the market and P is a subset of M. We would use both of these as the investible univers. So for that ratio (in part 2) I'm getting a lot of cancellation for that and I think d=1. Does that sound right? John Dodson:Correct, Fanda. And each row of 'P' has to have an entry for each asset in the investible universe (even if most are zero). John Dodson:Peter, what is the length of 'M' in your case? Peter:Well I am trying to solve it for the general case, but when I'm writing it out as an example to help me understand I'm just using 3 different assets...for simplification and that's what it looks like's done in the book: he uses 3 indexes: Spanish, Canadian, and German. John Dodson:right. For the numerical version, you will probably need at least twenty assets. For the general case, you need to look for patterns in lower-dimensional versions (such as three) and consider how to take the limit as $\dim M\to\infty$ Fanda:Hey John, for the second part, is it right as Peter mentioned that we plug in what we have for part 1 and find out what the value of the entry of the compent the manager has the view on is? Fanda:sorry i messed up the dimention Fanda:dimension John Dodson:Fanda, the second part is about the mean and variance of the component, conditional on the view. John Dodson:no sorry, that's the first part John Dodson:the second part relates to the SR portfolio. John Dodson:you need to solve for this portfolio, then report what the weight is for this component. Fanda:do you mean the beta of the analytical solution? John Dodson:no, there's no beta here. John Dodson:just the SR portfolio John Dodson:beta would come in if you had a satisfaction to optimize, but you don't have that here. John Dodson:Any other questions? John Dodson:By the way, I think the project outlines look good. I will send a few comments, but nothing that should push anyone off course. Peter:not really. still working on it Peter:sorry, i copy-pasted that into the wrong chat. Xiaowen:in the exercise we did in class last Wednesday, you had set zeta to be 1*e8. Should we assume zeta to be a value or how do we calculate that? John Dodson:Xiaowen, this is tricky. Since this normal markets - exponential utility approach has an unconstrained optimum, the result is effectively paramterized by the risk aversion of the representative agent. Generally, you will have to assume some reasonable level for this. Xiaowen:I guess I don't fully understand "zeta0=alphaCap'*covP*alphaCap/(p'*alphaCap)". Xiaowen:ok John Dodson:This was a draft, based on the idea that maybe you know a reasonable level for $E\Psi_{\alpha_0}$, which you can use to calibrate $\zeta_0$ Xiaowen:ok Xiaowen:and another thing is Xiaowen:in the quadprog, the first constraint, -EM'/min(ret,max(EM./p)-eps), I assume it is for positive profit? I am confused by the -eps. John Dodson:Xiaowen, I put in the 'eps' to avoid complaints from quadprog from reducing the feasible set to a single point. John Dodson:if the target return is set near its maximum value, the solution will consist of a 100% weight in the highest returning asset. If it is set to high, there is no solution. Xiaowen:I see. Xiaowen:Is there a concern if the returns are all negative? John Dodson:yes! In that case, the optimal portfolio would be all cash, right? Xiaowen:yes, I agree. Xiaowen:but the min would still be negative, right? John Dodson:I suppose so. But the problem is to minimize the variance given a return at least this great, so the result would be zero allocations. Xiaowen:ok that make sense. John Dodson:Any other questions? Xiaowen:Thank you, have a good night. John Dodson:ok, good night everyone.