Which of the Following Constants Can Be Added to X2 - 3x to Form a Perfect Square Trinomial?

A diversification benefit is a reduction in portfolio standard departure of return through diversification without an accompanying subtract in expected return. Portfolio diversification is afflicted by the number of assets in the portfolio and the correlation between these assets.

Correlation

The trade-off betwixt adventure and return for a portfolio depends not only on the expected asset returns and variances but also on the correlation of nugget returns. The correlation between two avails represents the degree to which avails are related.

The correlation is the engine that drives the whole theory of portfolio diversification. The following effigy illustrates minimum-variance frontier of a two-asset portfolio for 4 dissimilar correlations.

The endpoints (X and Y) for all the frontiers are the same, since at each endpoint the expected return and standard divergence are but the expected return and standard deviation of either asset.

A: correlation = i. This indicates a perfect linear relationship between the two assets. Diversification has no potential benefits.
B: correlation = 0.v. Portfolio diversification can be accomplished. The lower the correlation, the greater the diversification benefits.
C: correlation = 0. This indicates at that place is no linear relationship between the ii assets. More diversification can be achieved and so B.
D: correlation = -one. This indicates a perfect inverse linear relationship. Notice the minimum-variance frontier has ii linear segments: XZ and ZY. XZ (line D) is the efficient frontier. The risk of the portfolio tin can be reduced to zero if desired.

The determination: As the correlation between ii assets decreases, the diversification benefits increase.

Consequence of Number of Avails on Portfolio Diversification

For an equally-weighted portfolio, its variance is

σ^two-bar is the average variance of return across all stocks, and Cov-bar is the boilerplate covariance of all pairs of two stocks.

Note that if n gets large enough:

The first component becomes very small.
The second component gets shut to Cov-bar.

Therefore, the variance of an as-weighted portfolio approximately equals the average covariance as the number of assets becomes large.

Case

Assume portfolio A has 2 assets and portfolio B has xxx assets. They are both equally weighted. The average nugget 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/thirty 0.iii = 0.31.

Portfolio B which has more avails has a lower variance.

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

It takes less than xxx stocks to achieve 90% of the diversification benefit.
The higher the average correlation, the greater the number of stocks needed to attain a specified risk reduction.
If you add more stocks to the portfolio, the standard deviation of the portfolio volition eventually reach the level of the market place portfolio.

Practice Question 1

The greatest portfolio diversification is accomplished if the correlation between assets equals

A. -1.
B. 0.
C. 1.
D. - infinity.

Correct Reply: A

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

Practice Question 2

In large portfolios, ______ is the most important factor to determine the portfolio risk.

A. Individual asset risks.
B. Average individual asset variance.
C. Average covariance.
D. Market risk.

Correct Reply: C

The variance of a portfolio approaches the average covariance as the number of avails gets large.

Practice Question 3

It is Not possible to construct a portfolio with cipher variance of expected returns from assets whose expected returns have positive variance individually. True or false?

Correct Answer: Simulated

Do Question 4

Calculation another security to a portfolio of stocks will reduce the hazard of the portfolio if the additional security

A. has returns that are negatively correlated with the other stocks in the portfolio.
B. is from an industry that is not already represented in the portfolio.
C. has returns that are positively correlated with the largest holdings in that portfolio.

Correct Respond: A

Practice Question 5

Portfolio theory as described by Markowitz is most concerned with:

A. the identification of unsystematic adventure.
B. the elimination of systematic risk.
C. the effect of diversification on portfolio take a chance.

Correct Respond: C

Practise Question six

The correlation coefficient of Portfolio X'southward returns and the market place's returns is 0.95, and the correlation coefficient of Portfolio Y'southward returns and the market'south returns is 0.40. Which of the post-obit statements best describes the levels of portfolio diversification?

A. Both Portfolio X and Portfolio Y are poorly diversified.
B. Portfolio X is well diversified and Portfolio Y is poorly diversified.
C. Portfolio X is poorly diversified and Portfolio Y is well diversified.

Correct Answer: B

Practise Question seven

Assume that a risk-balky investor owning stock in White Corporation decides to add the stock of either Black or Dark-green Corporation to her portfolio. All three stocks offer the same expected return and total adventure. The covariance of returns between White and Blackness is -0.05 and between White and Green is +0.05. Portfolio risk is expected to:

A. refuse more by buying Black.
B. decline more than by ownership Green.
C. increase by buying either Blackness or Green.

Right Answer: A

Practice Question viii

If y'all want maximum diversification, you should search for stocks with a correlation coefficient equal to:

A. +i.0.
B. 0.0.
C. -1.0.

Correct Respond: C

Practice Question ix

Which statement is truthful?

I. The higher the boilerplate correlation, the fewer stocks we need to achieve a target risk reduction.
2. The variance of an every bit-weighted portfolio approaches the boilerplate variance equally n gets large.

Correct Answer: None of them

I: The lower the correlation, the greater the diversification benefits.
Ii: It approaches the average covariance.

Practice Question ten

Stocks A, B, and C each accept the same expected render and standard departure. Given the correlation coefficients between these stocks shown in the table below, which combination of these stocks will result in the everyman risk portfolio?

A. as invested in stocks A and B.
B. every bit invested in stocks B and C.
C. equally invested in stocks A and C.

Correct Answer: C

Everything else being equal, the portfolio that has the lowest correlation, or most negative, will have the lowest risk.

Practice Question eleven

To finer diversify a portfolio an investor wants stocks with _________ correlation coefficients, the consequence will be to ________ the standard deviation of the portfolio.

A. Negative; decrease
B. Negative; increase
C. Zippo; increase

Correct Answer: A

Diversification benefits: risk reduction through a diversification of investments. Investments that are negatively correlated or that have low positive correlation provide the best diversification benefits. Such benefits may be particularly evident in an internationally diversified portfolio.

Practise Question 12

For a ii-stock portfolio, what would be the preferred correlation coefficient betwixt the two stocks?

A. -ane.00
B. 0.00
C. i.00

Right Answer: A

Practice Question xiii

Which statement about portfolio diversification is correct?

A. Diversification reduces the portfolio'southward expected render because diversification reduces a portfolio's systematic risk.
B. Equally more securities are added to a portfolio, total risk typically would be expected to fall at a decreasing charge per unit.
C. The risk-reducing benefits of diversification do not occur meaningfully until at least thirty individual securities are included in the portfolio.

Correct Answer: B

Practice Question 14

Security A has an expected return of 18% and a standard divergence of twoscore%. Securities B and C each have expected returns of 12% and standard deviations of 20%. If the correlation between rates of return for A and B is 0.35, and for A and C is 0.85, then investors property only A:

A. who desire to reduce risk would be ameliorate off adding B to their portfolios.
B. who want to reduce risk would exist meliorate off adding C to their portfolios.
C. would need to know the correlation between rates of return for B and C to decide which security offers the best opportunity for risk reduction.

Right Reply: A

Since B and C have the aforementioned expected return and standard difference, the lower correlation of A and B will provide portfolios with superior opportunities to reduce risk.

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