2013 CFA mock - Portfolio

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FrankCFA

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The question is asking if below statment is correct or not. Seems makes sense. But the answer said it’s not correct… Anyone knows why? Thanks.
As the average correlation between securities in a portfolio increases, the risk reduction benefits of diversification decrease. Furthermore, as average correlation between securities in a portfolio rises, the number of securities in the portfolio must be increased in order to achieve the same percentage of portfolio risk reduction when the average correlation between securities is lower.
 
it also appears in 2014 mock march. The answer in that is more detail.
CFA recycles questions from 2012 - 2013 mocks…
 
The lower the correlation between stocks, the greater the potential diversification benefits, but the greater number of stocks required to achieve those benefits. Best to refer back to the text for the formulae that will give you a sense of why this is the case.
 
Hi Frank… I had the same problem with this (and still do). I still dont, to this day, understand why when stocks are uncorrelated, you need more stocks to achieve the benefits. Imagine, if you have a portfolio of 3 gems, all uncorrelated with each other, vs 3 gems that are positively correlated with each other… If you add an uncorrelated gem to an existing portfolio, it should quickly enhance that portfolio.. So I dont get why that rule exists.. If you add a correlated stock (say80%), you should add more to get those benefits! This part bugs me but i have resorted to memorizing.
 
I was stunned reading the “correct answer”.
Please help us understand this question. Thx
 
Carbolic, i think the only person who can answer this is the Magician.. Magician, wherever you are, we need your help here.
I’ve posted this inquiry before bot got no responses.
 
Is it possible that this results because(referring to the formula for a portfolio’s variance) when you have uncorrelated stocks, the variance of the portfolio is only a function of the weights and individual variances? So to reduce the portfolio variance one needs to increase the number of stocks to decrease the weights or one needs to get securities with lower variances into the portfolio.
Then, in the case of negatively correlated stocks, we can reduce the portfolio variance more quickly since we are subtracting 2*weights*covariance?
Portfolio variance = (weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight(2)*covariance(1,2)
Does the text or answer key specify that this is for any (pos/neg) correlation, or is it possible this is what they are referring to? Any thoughts on this?
 
I can remember “The lower the correlation between stocks, the greater the potential diversification benefits, but the greater number of stocks required to achieve those benefits.”
But it’s not easy to understand why…
 
I’d suggest following the forumla in the text as a good starting point.
 
If I remember correctly, that question required you to use the formula for the variance of a portfolio that went something like:
variance of the portfolio = variance [ { ( 1 - p ) / n } + p ]
Where p = correlation.
This formula indicates that as ‘n’ increases, portfolio variance drops rapidly.
 
Yes, the formula says that, but it doesn’t make sense theoretically. I can plug those numbers in, but I still won’t be able to explain it to my grandmother.
 
Firstly, I don’t think the expectation should be that college level stats is explainable to your grandmother!
Really this is about achieving the maximum possible diversification benefit, on a relative basis.
Try entering the formula into excel and messing around with it.
For instance, let’s say you have two 50 stock portfolios, portfolio 1 has a correlation of 0.3 and portfolio 2 has as a correlation of 0.5.
In the first portfolio, your max achievable diversification is 0.3 of individual stock variance. With 50 stocks, the actual portfolio variance is 0.3140 of individual stock variance (or, you’ve achieved 95.5% of max diversification).
In the second portfolio, your max achievable diversification is 0.5 of individual stock variance, with 50 stocks, actual portfolio variance is 0.5100 of individual stock variance (or, you’ve achieved 98.0% of max diversification).
So, here you can see that correlation increased, and with the same number of stocks, you’ve achieved more of your relative achievable diversification benefits.
 
Let’s say you had a portfolio with a correlation of 1, so it moves with the market. Now, you are talking to your financial advisor, and he suggests you add stocks that are uncorrelated to the existing portfolio to improve it. if you add a stock that is perfectly correlated to that portfolio, the diversification benefits of that one stock doesn’t impact the portfolio, because there are none! now if you add one stock that is perfectly negatively correlated (of the same value) you are saying that the benefits of that one stock won’t be reflected as much as the 1st stock? Would you as a prudent investor do that? I am still confused about this and I apologize if I am not getting you.. There has to be another way to explain this.
 
This is about acheivable diversification. In a portfolio of perfectly correlated stocks, the best diversficiation you can achieve within that portfolio, is perfect correlation. So you don’t need to add any more stocks, since you’ve already achieved the maximum diversification. This is in line with the idea that: The lower the correlation between stocks, the greater the potential diversification benefits, but the greater number of stocks required to achieve those benefits.
In your negatively correlated stock example, this is also consistent. This will lower the portfolio correlation, which will increase the diversification benefit, but you had to add a stock to get there.
 
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