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A diversification benefit is a reduction in portfolio typical deviation of return with diversification without an accompanying decrease in intended return. Portfolio diversification is impacted by the variety of assets in the portfolio and also the correlation in between these assets.

Correlation

The trade-off between hazard and also rerevolve for a portfolio depends not just on the supposed asset retransforms and also variances but additionally on the correlation of ascollection returns. The correlation between 2 assets represents the level to which assets are related.

The correlation is the engine that drives the entirety concept of portfolio diversification. The following number illustprices minimum-variance frontier of a two-asset portfolio for 4 various correlationships. The endpoints (X and Y) for all the frontiers are the exact same, considering that at each endpoint the supposed return and conventional deviation are ssuggest the meant return and also conventional deviation of either asset.

A: correlation = 1. This indicates a perfect direct connection between the two assets. Diversification has actually no potential benefits.B: correlation = 0.5. Portfolio diversification deserve to be achieved. The reduced the correlation, the greater the diversification benefits.C: correlation = 0. This suggests tright here is no direct connection in between the two assets. More diversification deserve to be completed then B.D: correlation = -1. This indicates a perfect inverse linear partnership. Notice the minimum-variance frontier has actually 2 straight segments: XZ and also ZY. XZ (line D) is the efficient frontier. The threat of the portfolio have the right to be diminished to zero if wanted.

The conclusion: As the correlation between 2 assets decreases, the diversification benefits increase.

Effect of Number of Assets on Portfolio Diversification

For an equally-weighted portfolio, its variance is σ2-bar is the average variance of rerotate across all stocks, and also Cov-bar is the average covariance of all pairs of two stocks.

Note that if n gets large enough:

The first component becomes incredibly little.The second component gets cshed to Cov-bar.

Because of this, the variance of an equally-weighted portfolio about equals the average covariance as the variety of assets becomes huge.

Example

Assume portfolio A has 2 assets and portfolio B has 30 assets. They are both equally weighted. The average ascollection variance is 0.5 and the average covariance is 0.3.

The variance of A is 1/2 0.5 + 1/2 0.3 = 0.4.The variance of B is 1/30 0.5 + 29/30 0.3 = 0.31.

Portfolio B which has actually more assets has actually a reduced variance.

In general, as the variety of stocks increases, the variance of the portfolio will certainly decrease.

It takes less than 30 stocks to accomplish 90% of the diversification benefit.The better the average correlation, the greater the number of stocks essential to achieve a specified danger reduction.If you include even more stocks to the portfolio, the traditional deviation of the portfolio will certainly ultimately reach the level of the sector portfolio.

Practice Concern 1The greatest portfolio diversification is accomplished if the correlation between assets equalsA. -1.B. 0.C. 1.D. - infinity.

Correlation is a number in between -1 and +1. The reduced the correlation, the bigger the diversification benefits.

Practice Question 2In big portfolios, ______ is the most important element to recognize the portfolio hazard.A. Individual asset threats.B. Average individual ascollection variance.C. Mean covariance.D. Market hazard.

The variance of a portfolio ideologies the average covariance as the variety of assets gets big.

Practice Inquiry 3It is NOT feasible to construct a portfolio with zero variance of meant returns from assets whose meant retransforms have actually positive variance individually. True or false?

Practice Question 4Adding one more defense to a portfolio of stocks will certainly alleviate the hazard of the portfolio if the additional securityA. has retransforms that are negatively associated via the other stocks in the portfolio.B. is from an industry that is not already represented in the portfolio.C. has actually retransforms that are positively correlated via the biggest holdings in that portfolio.

Practice Question 5Portfolio concept as defined by Markowitz is a lot of concerned with:A. the identification of unorganized threat.B. the elimicountry of systematic hazard.C. the result of diversification on portfolio risk.

Practice Inquiry 6The correlation coeffective of Portfolio X"s retransforms and the market"s retransforms is 0.95, and also the correlation coefficient of Portfolio Y"s retransforms and the market"s returns is 0.40. Which of the adhering to statements finest describes the levels of portfolio diversification?A. Both Portfolio X and also Portfolio Y are poorly diversified.B. Portfolio X is well diversified and also Portfolio Y is poorly diversified.C. Portfolio X is poorly diversified and Portfolio Y is well diversified.

Practice Question 7Assume that a risk-averse investor owning stock in White Corporation decides to add the stock of either Babsence or Green Corporation to her portfolio. All three stocks market the very same expected rerevolve and also complete risk. The covariance of returns between White and Babsence is -0.05 and between White and Eco-friendly is +0.05. Portfolio danger is supposed to:A. decrease even more by buying Black.B. decline more by buying Green.C. boost by buying either Black or Green.

Practice Concern 8If you desire maximum diversification, you must search for stocks with a correlation coefficient equal to:A. +1.0.B. 0.0.C. -1.0.

Practice Question 9Which statement is true?I. The better the average correlation, the fewer stocks we must achieve a targain threat reduction. II. The variance of an equally-weighted portfolio approaches the average variance as n gets big.

I: The lower the correlation, the greater the diversification benefits.II: It viewpoints the average covariance.

Practice Question 10Stocks A, B, and C each have the very same supposed return and also traditional deviation. Given the correlation coefficients in between these stocks shown in the table below, which combination of these stocks will certainly lead to the lowest risk portfolio? A. equally invested in stocks A and B.B. equally invested in stocks B and also C.C. equally invested in stocks A and C.Correct Answer: C

Everypoint else being equal, the portfolio that has actually the lowest correlation, or the majority of negative, will have actually the lowest threat.

Practice Concern 11To efficiently diversify a portfolio an investor desires stocks through _________ correlation coefficients, the effect will certainly be to ________ the traditional deviation of the portfolio.

A. Negative; decreaseB. Negative; increaseC. Zero; increaseCorrect Answer: A

Diversification benefits: risk reduction through a diversification of investments. Investments that are negatively correlated or that have actually low positive correlation carry out the finest diversification benefits. Such benefits might be specifically apparent in an globally diversified portfolio.

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Practice Concern 12For a two-stock portfolio, what would certainly be the desired correlation coreliable between the two stocks?

A. -1.00B. 0.00C. 1.00Correct Answer: A

Practice Question 13Which statement about portfolio diversification is correct?

A. Diversification reduces the portfolio"s intended rerotate bereason diversification reduces a portfolio"s organized risk.B. As more securities are included to a portfolio, full danger generally would be supposed to loss at a decreasing price.C. The risk-reducing benefits of diversification perform not happen meaningcompletely till at leastern 30 individual securities are consisted of in the portfolio.Correct Answer: B

Practice Question 14Security A has an intended return of 18% and also a conventional deviation of 40%. Securities B and C each have expected returns of 12% and also standard deviations of 20%. If the correlation in between prices of return for A and B is 0.35, and for A and also C is 0.85, then investors holding just A:

A. who want to reduce risk would be better off including B to their portfolios.B. who desire to alleviate hazard would be better off adding C to their portfolios.C. would certainly need to recognize the correlation in between prices of return for B and C to identify which protection uses the finest opportunity for risk reduction.Correct Answer: A

Because B and also C have the same intended return and also conventional deviation, the lower correlation of A and also B will administer portfolios through remarkable methods to mitigate risk.