I sent the below to a schweser instructor last week and received the answer below. i’m not sure if this makes sense to me. someone want to translate? thanks: Lower correlation between assets means greater diversificaton benefits: understood. However, the notes also say: higer the average correlation, the fewer stocks it takes to achieve a specified risk reduction. . This seems like a contradicton to me. Am I thinking about this the wrong way? Thank you. Regards, then they replied: Thank you for choosing Schweser. This is a funny little optimization problem, isn’t it? Imagine you were arranging angry dogs in a room. The closer any two get, the more likely it is they will fight. How do you minimize the number of fights? If you only have two, you put them as far from each other as possible. If you add a third, you have to move the other two slightly closer to each other the keep them equidistant. Beyond 4 dogs, you have to start thinking in multiple dimensions…3 then…4 and so on. Now, portfolio optimization is doing the same deal, but in many, many dimensions. The only optimal solution is if they are all the same distance apart.
it probably makes sense and i’m not getting it? like when daniel-san was painting mr miyagi’s fence and not understanding that he was really learning karate?
Look like an interesting problem. I remember that picture in level 1 book. If there are 2 equities have correlation -1, then you can completely remove the risk. This seems to be in sync with that explanation.
i would think of it more like this way- say you just had MSFT in your portfolio. Adding IBM is going to reduce your risk. Adding GOOG from there reduces it more. But if these stocks are all highly correlated, then as they say above as the goal of “specific” risk reduction probably you take care of when you buy 1/3rd of all 3 intead of now buying 1/10th of those plus DELL plus HP plus AAPL, etc. If your goal there was to have a diverse little tech fund, then maybe 5 stocks or 10 stocks gets about as much unsystematic risk as you can out of there seeing as they’re all tech stocks and therefore highly correlated to begin with. i started PM tonight… i’m about 10 pgs in. going to stop in a few, though, b/c i have a soccer game in at 9!
and what a weird little dog analogy. i guess it makes sense in this context… um, kind of? wax on ron mexico… wax off…
It doesn’t make sense except in some weird mean-variance space. Sigh. Higher average correlation only helps if you can short stocks.
Kerry1 found this below post for me re: this topic, and it made the most sense to me… certainly more than the pissed off dogs. does it pass muster? yanke10, All the book is really saying is that if your average correlation is already low, it will be that much harder to reduce it by adding further stocks to the portfolio. If the average correlation was high it wouldn’t take much to reduce it - think “diminishing marginal returns”. Start with a portfolio with a high average correlation. Add one stock - average correlation drops, say, by 50%. Start with a portfolio with a low average correlation. Add one stock - average correlation would only drop by 5%. Therefore in a portfolio with low average correlation you need more stocks to achieve the same amount of “diversification”. Good question!
My take on it (aside from the bit about the dogs fighting) is this: The answer talks about a risk reduction, so I am assuming that you are starting with a portfolio with a certain level of correlation/diversification benefit. You want to add a few stocks to make correlation to go down by x%. If average correlation is very high then existing diversification benefits will be low. If you add one more stock, chances are pretty good that correlation will decrease by a goodly amount and benefits will increase. Conversely, if average correlation is already very low then adding one more stock is much less likely to reduce correlation further. Adding 20 stocks may not make much difference. Example 1. Two stocks are perfectly correlated. You add one more stock (assumed not to be perfectly correlated with the first two) then overall correlation will come down substantially. Benefits go up. Good. Example 2. Two stocks are perfectly uncorrelated. You add one more stock (assumed not to be perfectly uncorrelated with the first two) then overall correlation will increase. Benefits go down. Bad. So, the higher the correlation for an existing portfolio, the fewer additional stocks are required to make it go down. My argument is going around in circles much like the fighting dogs, but hopefully you catch my drift.
DBlA. that was perfect. thanks. now if you can mix in a dog analogy that would be awesome. jk. thanks. it just wasn’t presented that clearly, in my opinion, in the text or schweser…
JoeyDVivre Wrote: ------------------------------------------------------- > It doesn’t make sense except in some weird > mean-variance space. Sigh. > > Higher average correlation only helps if you can > short stocks. Can you short dogs though?
I think Michael Vick was short dogs.
I suppose if you can buy ham and cattle futures, there’s no reason why Korea might not have a futures market in dogs.
for you bloomberg users out there: type in COKPMON Index (GO). it is an index of Monthly Kidnappings in Colombia… however it is subject to a one month lag!
wow. i just looked it up. how do we trade it? that is hilarious! ok, maybe kidnapping isn’t hilarious.
Hmm. I wonder what market manipulation might take place if people were seriously long…