Chapter 07 Flashcards
Market risk is also referred to as
systematic risk, nondiversifiable risk
Systematic risk is also referred to as
market risk, nondiversifiable risk
Nondiversifiable risk is also referred to as
systematic risk, market risk
Diversifiable risk is also referred to as
unique risk, firm-specific risk
Unique risk is also referred to ask
diversifiable risk, firm-specific risk
Firm-specific risk is also referred to as
diversifiable risk, unique risk
Nonsystematic risk is also referred to as
diversifiable risk, unique risk
The risk that can be diversified away is
firm specific risk
The risk that cannot be diversified away is
market risk
The variance of a portfolio of risk securities
is the weighted sum of the securities’ variances and covariances
The standard deviation of a portfolio of risky securities is
the square root of the weighted sum of the securities’ variances and covariances
The expected return of a portfolio of risky securities
is a weighted average of the securities’ returns
Other things equal, diversification is most effective when
securities’ returns are negatively correlated
The efficient frontier of risky assets is
the proportion of the investment opportunity set that lies above the global minimum variance portfolio
The capital allocation line provided by a risk-free security and N risky securities is
the line tangent to the efficient frontier of risky securities drawn the from the risk-free rate
Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always
equal to zero
Which of the following statement(s) are true regarding the variance of a portfolio of two risky securities?
I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II) There is a linear relationship between the securities’ coefficient of correlation and the portfolio variance
III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities
III only
Which of the following statement(s) are false regarding the variance of a portfolio of two risky securities?
I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II) There is a linear relationship between the securities’ coefficient of correlation and the portfolio variance
III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securitiesh of the
I and II
Efficient portfolios of N risky securities are portfolios that
have the highest rates of return for a given level of risk
Which of the following statement(s) is(are) true regarding the selection of a portfolio from those that lie on the capital allocation line?
I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors
II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors
III) Investors choose the portfolio that maximises their expected utility
II and III
Which of the following statement(s) is(are) false regarding the selection of a portfolio from those that lie on the capital allocation line?
I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors
II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors
III) Investors choose the portfolio that maximises their expected utility
I only
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
The expected rates of return of stocks A and B are … and …, respectively.
13.2%; 7.7%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
The standard deviation of stocks A and B are … and …, respecitvely
1.5%; 1.1%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
The variances of stocks A and B are … and …, respectively
2.2%; 1.2%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
The coefficient of correlation between A and B is
0.46
covA,B = 0.1(10-13.2)(8-7.7) + 0.2(13-13.2)(7-7.7) + 0.2(12-13.2)(6-7.7) + 0.3(14-13.2)(9-7.7) + 0.2(15-13.2)(8-7.7) = 0.76;
rA,B = 0.76 / [(1.1)(1.5)] = 0.46
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
If you invest 40% of your money in A and 60% in B, what would be your portfolio\s expected rate of return and standard deviation?
9.9%; 1.1%
E(R) = 0.4(13.2) + 0.6(7.7)
SD = [(0.4)^2(1.5)^2 + (0.6)^2(1.1)^2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]^0.5
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
Let G be the global minimum variance portfolio. The weights of A and B in G are … and …, respectively.
0.23; 0.77
W.A = [(1.1)^2-(1.5)(1.1)(0.46)]/(1.5)^2+(1.1)^2-2(1.5)(1.1)(0.46)] = 0.23
W.B = 1 - 0.23 = 0.77
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
The expected rate of return and standard deviation of the global minimum variance portfolio, G, are … and …, respectively.
8.97%; 1.05%
E(R) = 0.23(13.2) + 0.77(7.7)
SD = [(0.23)^2(1.5)^2 + (0.77)^2(1.1)^2 + 2(0.23)(0.77)(1.5)(0.46)]^0.5 v= 1.05%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.10 - 10% - 8%
2 - 0.20 - 13% - 7%
3 - 0.20 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 15% - 8%
Which of the following portfolio(s) is (are) on the efficient frontier?
A. The portfolio with 20% in A and 80% in B
B. The portfolio with 15% in A and 85% in B
C. The portfolio with 26% in A and 74% in B.
D. The portfolio wi9th 10% in A and 90% in B.
E. A and B are both on the efficient frontier
C. Portfolio with 26% in A and 74% in B
It has the greatest mean-variance criterion
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
The weights of A and B in the global minimum variance portfolio are … and …, respectively.
0.43; 0.57
W.A = 12/(16+12)
W.B = 1-0.4286
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
Weights in global minimum variance portfolio are 0.43 and 0.57
8.9%
E(R) = 0.43(10%) + 0.57(8%)
Given an optimal risky portfolio with expected return of 6% and standard deviation of 23% and a risk free rate of 3%, what is the slope of the best feasible CAL?
0.13
(6-3)/23
An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the capital allocation line must
borrow some money at the risk-free rate and invest in the optimal risky portfolio and invest only in risky securities
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
Portfolio - Expected Return - SD
W - 9% - 21%
X - 5% - 7%
Y - 15% - 36%
Z - 12% - 15%
Only portfolio W cannot lie on the efficient frontier.
It lies below the efficient frontier. It has a higher SD than Z with a lower expected return
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
Portfolio - Expected Return - SD
A - 10% - 12%
B - 5% - 7%
C - 15% - 20%
D - 12% - 25%
Only portfolio D cannot lie on the efficient frontier.
Only D lies below the efficient frontier. It has a higher standard deviation than C with a lower expected return.
Portfolio theory as described by Markowitz is most concerned with
the effect of diversification on portfolio risk
The measure of risk in a Markowitz efficient frontier is
standard deviation of returns
A statistic that measures how the returns of two risky assets move together is
covariance and correlation
The unsystematic risk of a specific security
results from factors unique to the firm
Which statement about portfolio diversification is correct?
Typically, as more securities are added to a portfolio, total risk would be expected to decrease at a decreasing rate.
The individual investor’s optimal portfolio is designated by
The point of tangency with the indifference curve and the capital allocation line
For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?
-1.00
Maximises diversification benefits
In a two-security minimum variance portfolio where the correlation between securities is greater than -1.0
the security with the higher standard deviation will be weighted less heavily
Which of the following is not a source of systematic risk?
Personnel changes
The global minimum variance portfolio formed from two risky securities will be diskless when the correlation coefficient between the two securities is
-1.0
Security X has expected return of 12% and standard deviation of 18%. Security Y has expected return of 15% and standard deviation of 26%. If the two securities have a correlation coefficient of 0.7, what is their covariance?
0.033
Cov = (0.7)(0.18)(0.26)
When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio,
the portfolio standard deviation will be less than the weighted average of the individual security standard deviations
The line representing all combinations of portfolio expected returns and standard deviation that can be constructed from two available assets is called the
portfolio opportunity set
Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 5%, what is the slope of the best feasible CAL?
0.27
(12-5)/26
Given an optimal risky portfolio with expected return of 20% and standard deviation of 24% and a risk free rate of 7%, what is the slope of the best feasible CAL?
0.54
(20-7)/24
The risk that can be diversified away in a portfolio is referred to as …
I) diversifiable risk
II) unique risk
III) systematic risk
IV) firm-specific risk
I, II and IV
As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?
It decreases at a decreasing rate
In words, the covariance considers the probability of each scenario happening and the interaction between
securities’ returns relative to their mean returns
The standard deviation of a two-asset portfolio is a linear function of the assets’ weights when
the assets have a correlation coefficient equal to one
A two-asset portfolio with a standard deviation of zero can be formed when
the assets have a correlation coefficient equal to negative one
When borrowing and lending at a risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier?
I) The one with the highest reward-to-volatility ratio
II) The one that will maximise his utility
III) The one with the steepest slope
IV) The one with the lowest slope
I, II and III
Given an optimal risky portfolio with expected return of 13% and standard deviation of 26% and a risk free rate of 5%, what is the slope of the best feasible CAL?
0.31
(13-5)/26
The separation property refers to the conclusion that
the determination of the best risky portfolio is objective and the choice of the best complete portfolio is subjective
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.15 - 8% - 8%
2 - 0.20 - 113% - 7%
3 - 0.15 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 16% - 11%
The expected rates of return on stocks A and B are … and …, respectively.
13%; 8.4%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.15 - 8% - 8%
2 - 0.20 - 113% - 7%
3 - 0.15 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 16% - 11%
The standard deviation of stocks A and B are … and …, respectively.
2.45%; 1.66%
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.15 - 8% - 8%
2 - 0.20 - 113% - 7%
3 - 0.15 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 16% - 11%
The coefficient of correlation between A and B is
0.590
Cov = 0.15(8-13)(8-8.4) + 0.2(13-13)(7-8.4) + 0.15(12-13)(6-8.4) + 0.3(14-13)(9-8.4) + 0.2(16-13)(11-8.4) = 2.40
2.40 / [(2.45)(1.66)] = 0.590
Consider the following probability distribution for stocks A and B:
State - Probability - Return on Stock A - Return on Stock B
1 - 0.15 - 8% - 8%
2 - 0.20 - 113% - 7%
3 - 0.15 - 12% - 6%
4 - 0.30 - 14% - 9%
5 - 0.20 - 16% - 11%
If you invest 35% of your money in A and 65% in B, what would be your portfolio’s expected rate of return and standard deviation?
10%; 1.7%
E(R) = 0.35(13%) + 0.65(8.4) = 10.01
SD = [(0.35)^2(2.45%)^2+(0.65)^2(1.66)^2 + 2(0.35)(0.65)(2.45)(0.590)]^0.5 = 1.7%
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The weights of A and B in the global minimum variance portfolio are … and …, respectively.
0.45; 0.55
W.A = 14/(17+14) = 0.45
W.B = 1-0.45
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The risk-free portfolio that can be formed with the two securities will earn … rate of return.
10.4%
E(R) = 0.45(12%) + 0.55(9%) = 10.35%
Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and standard deviation of 28%. If the two securities have a correlation coefficient of 90.8, what is their covariance?
0.049
Cov = (0.8)(0.22)(0.28)
Given an optimal risky portfolio with expected return of 16% and standard deviation of 20% and a risk-free rate of 4%. What is the slope of the best feasible CAL?
0.60
(16-4)/20
Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 3%, what is the slope of the best feasible CAL?
0.35
(12-3)/26
Consider the following probability distribution for stocks C and D:
State - Probability - Return on Stock C - Return on Stock D
1 - 0.30 - 7% - -9%
2 - 0.50 - 11% - 14%
3 - 0.20 - -16% - 26%
The expected rates of return of stocks C and D are … and … respectively.
4.4% and 9.5%
Consider the following probability distribution for stocks C and D:
State - Probability - Return on Stock C - Return on Stock D
1 - 0.30 - 7% - -9%
2 - 0.50 - 11% - 14%
3 - 0.20 - -16% - 26%
The standard deviation of stocks C and D are … and …, respectively.
10.35% and 12.93%
Consider the following probability distribution for stocks C and D:
State - Probability - Return on Stock C - Return on Stock D
1 - 0.30 - 7% - -9%
2 - 0.50 - 11% - 14%
3 - 0.20 - -16% - 26%
The coefficient of correlation between C and D is
-0.50
CovC,D = 0.30(7% - 4.4%)(-9% - 9.5%) + 0.50(11% - 4.4%)(14% - 9.5%) + 0.20(-16% - 4.4%)(26% - 9.5%) = -66.9; ρA,B = -66.90/[(10.35)(12.93)] = -0.50.
Consider the following probability distribution for stocks C and D:
State - Probability - Return on Stock C - Return on Stock D
1 - 0.30 - 7% - -9%
2 - 0.50 - 11% - 14%
3 - 0.20 - -16% - 26%
If you invest 25% of your money in C and 75% in D, what would be your portfolio’s expected rate of return and standard deviation?
8.225% and 8.70%
E(R.P) = 0.25(4.4%) + 0.75(9.5%) = 8.225%;
s.P = [(0.25)2(10.35)2 + (0.75)2(12.93)2 + 2(0.25)(0.75)(10.35)(12.93)(-0.50)]1/2 = 8.70%.
Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%.
The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.
0.46; 0.54
w.K = 1 - 0.54 = 0.46
w.L = 19/(19+16)
Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%.
The risk-free portfolio that can be formed with the two securities will earn … rate of return
11.4%
E(R) = 0.46(13%) + 0.54(10%) = 11.38%
Security M has expected return of 17% and standard deviation of 32%. Security S has expected return of 13% and standard deviation of 19%. If the two securities have a correlation coefficient of 0.78, what is their covariance?
0.047
Cov = (0.78)(0.32)(0.19)
Security X has expected return of 7% and standard deviation of 14%. Security Y has expected return of 11% and standard deviation of 22%. If the two securities have a correlation coefficient of -0.45, what is their covariance?
-0.0139
Cov = (-0.45)(0.14)(0.22)
