Fall 2020 CAS Exam 9 Thread

Bodie chapter 10, under “Executing Arbitrage”

I mean, the market beta is 1, so if you have another portfolio with a positive alpha and beta = beta_p, then the weights you need to get a beta of 0 are just the weights from the formulas above. You can easily get that by solving 2 equations and 2 unknowns (w_p+w_M = 1 and w_p*beta_p+w_M = 0). No need to memorize those equations.

Do you guys want to share problems that use this technique?

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I don’t know if I’ve seen a specific problem with it, but I’ve only done the 2011-2015 exams so far. The concept is pretty simple though.

If you have a well-diversified portfolio it should have no firm-specific risk. If this portfolio has a positive alpha, then if you’re able to create a portfolio combining it and the market portfolio, you will have an arbitrage opportunity. Select weights in your positive alpha portfolio and the market portfolio so that the total beta is zero (no systematic risk) and that the weights add up to 1.

Thanks - until your posts, I didn’t quite get that arbitrage portfolios seek beta=1.

act123 - this was just one of the flashcards that you passed on to me.

They seek beta = 0, not 1. If beta is zero that means there’s no systematic risk.

what page is this? I can’t seem to find it.

You want beta zero and weights to be equal to 1.

But your doing this with a market portfolio. Normally, they give you a new portfolio lets say Z and stocks A, B, C and you need to create portfolio Q to offset it.

In my book, it’s on page 332. The second to last section of 10.2.

That is funny. They took it out of the 11th edition, but it is in the 10th edition. I wonder why…

No wonder why I didn’t see it.

Found this on reddit

When I’m doing old exams, how can I check if the question is outdated or not? I’m only using Rising Fellow for this sitting which doesn’t have any info regarding old exams as far as I’m aware.

I believe Crystal has a list and TIA has a list… I don’t recall seeing RF having a list.

So I am not sure… Unless someone compiles it for you.

See the following link from RF: link

Also, for anyone that’s done practice exams already, any thoughts on the difficulty of them? I just finished taking all past exam + RF exams, and I’m trying to gauge the relative difficulty. I thought RF exams weren’t at all representative of the exam, way too straightforward. Past exams didn’t seem bad at all, with the exception of 2018 which for some reason I thought was more tricky.

RF the problems were to calculation intensive. Overall straightforward.

Crystal Clear exams are mad hard. Do you have the 2014 exam in Excel? I am looking for it.

Thank you! This is extremely helpful! Where did you find that? I can’t seem to see it in my RF material.

Edit: Never mind, I found it on the RF resources page. Apparently you don’t need to pay for RF to view the previous exam questions chart.

I saved the CC for last cause I heard they were hard too so I’ll be doing those this weekend. Hope I don’t get destroyed. I don’t have the older exams in excel though sorry.

I had typed up a ton of problems from CC&RF in excel before and was planning to do the exams, but it’s such a chore and TIA had up to 2015 so I’ve just been using theirs.

Also, anyone up for discussing different arbitrage scenarios in BKM just to talk through it? I think arbitrage gets asked almost every sitting in some way, either related to index models, CAPM, multi-factor models, or even bonds. I think I have most of them straight, but sometimes get confused about how to structure the arbitrage opportunity for equities (i.e. borrow at risk-free rate to fund an investment or not).

Sure.

Additional topics I would like to discuss:

  1. Bodoff - vertical/horizontal continuous questions/exponential, how to do it when its allocated by event versus by lob/peril.
  2. Kreps - I have read this paper so many times but they still haven’t really tested it.

The CC exams are in Excel at least the first two.

She also uploaded the third one in excel on her drive.

For Bodoff, I think if they give you a continuous distribution you’d have to first allocate the capital to each event/loss using the typical AC(x) formula with the limits being defined typically from 0 to the loss or the VaR scenario (depending on which is smaller). The issue is afterwards, you have to re-integrate but with respect to x and limits of layers of capital (similar to what’s done in the discrete case). The main thing that tripped me up here was for losses > VaR, AC(X) may change so you have to change the formulation and the integral would be from the VaR to infinity. This is vertical then horizontal which I think ties better to the discrete case, but you could do it reversed too.

Kreps – I’m not sure of this one either. I can find risk loads, allocate capital based on those, test reinsurance, but that’s pretty much all I feel like this paper is. I feel like most test writers would be as confused as we are by it, the question on 2019 was extremely straightforward for example. I think if it gets asked this year, it’s probably going to be reinsurance evaluation related.

For arbitrage, I think there are a couple scenarios:

  1. Index Model -> A portfolio has a positive alpha and a beta, B. To create risk-free profit, create a tracking portfolio by mimicking beta. If B>1, you’d borrow at the risk-free rate to fund an investment in a portfolio that tracks the beta of the positive alpha (created via the market index). If B<1, lend at the risk-free rate (with weight 1-B).

  2. CAPM -> Same process as index model, but instead of the market index it’d be the market portfolio?

  3. APT -> Match systematic component of portfolio that has arbitrage. I think in this case, there’s no borrowing since the systematic components are the same so you could theoretically sell one portfolio to fund an investment in another?

  4. Markowitz -> Create a zero variance portfolio. You’d have to borrow at the risk-free rate to fund the investment and your net profit is the excess return on the zero variance portfolio.

CC exam 2 has a kreps question that I have never seen before…