Correlation coefficient

[fwvagabond]

Correlation coefficient of portfolio X and market is 0.95, correlation coefficient of portfolio Y and market is 0.60. Which portfolio is better diversified?

 

[JoeyDVivre]

c) Impossible to tell from given information.

If the portfolio just consists of stocks, then X is pretty well diversified but has lots of equity risk. Y could either be 1 stock (i.e., not well-diversified) or a portfolio consisting of the S&P 500, real estate, hedge funds, and other rsiky assets (i.e., well-diversified).

A portfolio is well-diversified if it is not vulnerable to security-specific risks. It has little to do with correlation to the market.

 

[CFAHouston]

Y - lower correlation - more diversified. Granted, there are other factors, but the cardinal rule is lower correlation, more diversified.

Joey, I'm not sure if X would me more diversified since it has close to perfect correlation.

Fwva - I'm guessing this is a made up questions

 

[lev]

I agree with JoeyDVivre. It's impossible to tell. Diversification measures how close portfolio's unsystematic risk is to zero.

In this case what you are given are two Betas, measures of systematic risk.



Edited 1 time(s). Last edit at Thursday, May 4, 2006 at 09:44AM by lev.

 

[jamespucyk]

According to Markowitz (Assuming a diversified portfolio) X would be a more diversified portfolio; a higher correlation would imply that it is closer to the market porfolio. Additional to that a portfolio becomes adequatly diversified after adding about 30 securities to it (unsystematic risk is reduced), but only fully diversified after the portfolio contains all risky assets (the market portfolio); put another way as unystematic risk is.

All of what Joe is saying is true and valid, but if this is a Markowitz PM (CML) question here. I will add though that by adding portfolio Y to porfolio X you will actually gain from further diversification if the weighed average SD of that portfolio does not detract from the diversificiation benefits of the correlation.

As a comment, if Y consisted of energy stocks (positively correlated to the market but not closely), and X was a diversified stock porftolio, with a few bonds and other assets, then, it would be X, but as Joe pointed out you really can't generalize too much based upon the information.

Also it's not only a function of the correlation, but of the portfolio's standard deviation, so you can't say that it's Y because it has a lower correlation. In theory then according to what you just said just holding gold would be a more "diversified portfolio" because it has a negative market correlation. You can also make that arguement on the from of stdev (but not expected return).

Bottomline, you can't determine, you have to look at correlation & portfolio expected return and stdev.



Edited 1 time(s). Last edit at Thursday, May 4, 2006 at 09:55AM by jamespucyk.

 

[vir_vict]

Just an argument

Assume both portfolio's have say 30 different securities.

If a portfolio has a coefficient of 1 with market portfolio, then it means its prices will follow exactly same trend as the market portfolio. Market portfolio is completely diversified. So if a portfolio higher correlation coefficient with market portfolio then it is indeed responding to only systematic factors, in the other words, unsystematic risks have been diversified.

Put in another way, say another portfolio has a coefficient of 1. We know the std dev of market portfolio.

Correlation coeff = Cov /(std dev1 * std dev2)

If Cov changes, then std dev2 has to change to maintain correlation coefficient of 1.

So higher correlation with market portfolio more diversified it is.

 

[jamespucyk]

Basically that's similar to the way I am looking at it, if a portfolio move lock and step with the market, it's a safe leap to assume in some capacity that it is very close to the market portfolio and therefore diversified.

However you can have a case where you have a portfolio (A) with a r= .8 STDEVport = .3 E(R)= .1 and another (B) r=.6 SD = .2 E(R) = .08, in this case the second portfolio has a lower risk adjusted return and would be closer to the efficient frontier. In this case correlation doesn't make as much of difference and a Markowitz investor would choose the second portfolio.

 

[fwvagabond]

Actually this is not a made-up question. This is #109 from CFAI 1998 Sample Exam (Part II). According to the key, the portfolio with the higher correlation coefficient is better diversified than the one with the lower measure.

I answered it wrong because I misunderstood the quesiton. I kept thinking the porfolio (X or Y) contains a market porfolio (don't know where I got that from the question text). But I have to agree with James. The higher the correlation coefficient, the closer the portfolio mimics the market, the lower the unsystematic risk, the better diversified it is.

Thanks all.

 

[jamespucyk]

That's the problem with multiple choice, you can't talk your way through the question.

 

[CFAHouston]

I know i'm going to complain about level 3 not being MC (if I ever get that far)

 

[JoeyDVivre]

The problem with lots of this is assuming that the market portfolio is the perfectly diversified portfolio and then assuming it is the S&P 500 or something. The perfectly diversified portfolio is one which invests proportionally in all the world's wealth. Unfortunately, the world's wealth consists of lots of uninvestable or marginally investable things including land (most of which is not for sale) and human capital (only a small fraction utilized).

This is a really dumb question, actually. Diversification can't be just a correlation coefficient.

 

[jamespucyk]

Actually when they say the market portfolio, they mean all risky assets, including land and precious metal and art, etc.

 

[vir_vict]

Why does it matter how you get the perfect market portfolio. If you are given a perfectly diversified market portfolio and then you are given portfolio with a correlation coefficient of 1 with market portfolio, why would it have any undiversified risk.

 

[JoeyDVivre]

I agree with that if there is such a thing, but that is very fanciful (how did it do yesterday and if I can't find out how do I calculate a correlation coefficient?)