CFA Practice Question

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CFA Practice Question

The correlation coefficient of Portfolio X's returns and the market's returns is 0.95, and the correlation coefficient of Portfolio Y's returns and the market's returns is 0.40. Which of the following statements best describes the levels of portfolio diversification?

A. Both Portfolio X and Portfolio Y are well-diversified.
B. Both Portfolio X and Portfolio Y are poorly diversified.
C. Portfolio X is well-diversified and Portfolio Y is poorly diversified.
Correct Answer: C

User Contributed Comments 24

User Comment
leoo why?
Gina r=1 is perfect correlation, that means that the assets behave like one.
the hypothetical market portfolio is the best diversified portfolio, with zero variance and assumed to lie on the CML. if the returns of portfolio X are highly correlated with those of the optimal market portfolio, X must be well diversified.
svetla well done Gina!
jerrycane I think it's wrong, r=-1 makes zero variance. If assets behave like one, it's perfect correlated.
haarlemmer 1. Market is well diversified
2. Largely correlated with the market leads to the conclusion of B
victor1911 to have a better diversification, the best should not be -1?
modol market portfolio has variance. There is no correlation without variance.
Nikita huh?
Nightsurfer Gina's right. Correlation to the mkt portfolio implies high diversification.
bdaguy The volatility associated with the market is referred to as systematic risk, the risk that you can't eliminate through portfolio diversification. Within that marketplace, that's the lowest risk level you can obtain for that particular return.

The more that you can diversify a portfolio, the lower the amount of diversifiable risk...although at a cost which brings the portfolio return closer to the market return.

Once a certain level of diversification is reached, the portfolio effectively has the same risk/return characteristics as the market. When this occurs, it becomes highly correlated with the market.

This in effect is the essence of portfolio management ==> diversification of a portfolio to effectively emulate the risk/return characteristics of the marketplace.

You can try to achieve a return higher than the market but can only be done at a higher level of risk. The less that your portfolio emulates the market, the less it's correlated with the market and the less it's diversification.
AnhDoUM Correlation of -1 is between stocks in the portfolio, not between portfolio and market.
Farina If you're investing in a specific market, you cannot diversify any further than owning every single asset within that market (i.e., every single stock in a major index). This minimises unsystematic (company/asset specific) risk but maximises systematic risk (market) risk.
dobrekone Just to make clear we are tlaking about the "Beta" of the portfolio here.
B is of course the correct answer.
However, the correlation of -1 means the same level of diversification as would the correlation of 1 . You could achieve a correlation of the portfolio with the market of -1 by having the "short" version of the market portfolio (i.e. in your portfolio you would have negative weights of the same assets as in the market portfolio)
eb2568 While I understand the concept, I don't understand why anyone would consider a portfolio that essentially tracks the market returns as "diversified". Who cares about that type of diversification when the market falls 30%? Do people simply say, oh well, I'm diversified and watch their portfoios go down? I'm not advocating ST trading or anything like that, but tracking the market returns hardly seems like a true diversification strategy.
HenryQ You guys are mixing diversification with market neutral. Market portfolio is definitely the most diversified portfolio as it totally eliminates unsystematic risks. However that does mean the portfolio can't have negative returns. If you have a portfolio of 0, it does not move with the market, but it does not mean it always have positive returns.
Phlipsen very good question
tkwangju Gina is right
magicchip A good tricky question. Assume always that market is the ultimate in diversification.
kickeli Good point HenryQ
Zahid04 The answer is right. I agree with HenryQ.
moneyguy Very tricky as we have been concentrating on correlation between securities within one portfolio. This is a market comparison question!! Watch out for this kind of "misdirection" on exam day.
johntan1979 The question asked about level of portfolio diversification, NOT level of returns.

Which portfolio is more diversified than the market itself, consisting of EVERY asset out there?

Think before you argue.
NOBAN the justification of the answer here is in considering the stocks' returns with the optimum / market return. considering the answer from this persepective gives it meaning and it makes sense. A good question!
mikus Spot on Gina
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