Chapter 06 Flashcards
Which of the following statements regarding risk-averse investors is true?
They only accept risky investments that offer risk premiums over the risk-free rate
Which of the following statements is(are) true?
I) Risk-averse investors reject investments that are fair games.
II) Risk-neutral investors judge risky investments only by the expected returns
III) Risk-averse investors judge investments only by their riskiness
IV) Risk-loving investors will not engage in fair games
I and II only
Which of the following statements is(are) false?
I) Risk-averse investors reject investments that are fair games.
II) Risk-neutral investors judge risky investments only by the expected returns
III) Risk-averse investors judge investments only by their riskiness
IV) Risk-loving investors will not engage in fair gamesthe
III and IV only
In the mean-standard deviation graph and indifference curve has a … slope
Positive
In the mean-standard deviation graph, which one of the following statements is true regarding the indifference curve of a risk-averse investor?
It is the locus of portfolios that offer the same utility according to returns and standard deviations
In a return-standard deviation space, which of the following statements is(are) true for risk-averse investors? (The vertical and horizontal lines are referred to as the expected return-axis and the standard deviation-axis, respectively.)
I) An investor’s own indifference curves might intersect
II) Indifference curves have negative slopes
III) In a set of indifference curves, the highest offers the greatest utility.
IV) Indifference curves of two investors might intersect
III and IV only
Elias is a risk-averse investor. David is a less risk-averse investor than Elias. Therefore,
for the same return, David tolerates higher risk than Elias
When an investment advisor attempts to determine an investor’s risk tolerance, which factor would they be least likely to assess?
The level of return the investor prefers
Assume an investor with the following utility function: U = E(r) - 3/2(s^2)
To maximise her expected utility, she would choose the asset with an expected rate of return of … and a standard deviation of …, respectively.
A. 12%; 20%
B. 10%; 15%
C. 10%; 10%
D. 8%; 10%
10%; 10%
U = 0.10 - 3/2(0.10^2) = 8.5% highest utility of choices
A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6%. An investor has the following utility function: U = E(r) - (A/2)s^2. Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset?
8
0.06 = 0.15 - A/2(0.15)^2
According to the mean-variance criterion, which one of the following investments dominates all others?
A. E(r) = 0.15; Variance = 0.20
B. E(r) = 0.10; Variance = 0.20
C. E(r) = 0.10; Variance = 0.25
D. E(r) = 0.15; Variance = 0.25
A
Gives the highest return with the least risk; return per unit of risk is 0.75
Consider a risky portfolio, A, with an expected rate of return of 0.15 and a standard deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve?
A. E(r) = 0.15; SD = 0.20
B. E(r) = 0.15; SD = 0.10
C. E(r) = 0.10; SD = 0.10
D. E(r) = 0.20; SD = 0.15
E. E(r) = 0.10; SD = 0.20
Portfolio C is the only choice with the same risk-return trade-off of 1.0
Investment - E(r) - SD
1 - 0.12 0 0.3
2 - 0.15 - 0.5
3 - 0.21 - 0.16
4 - 0.24 - 0.21
U = E(r) - (A/2)s^2, where A = 4.0
Based on the utility function above, which investment would you select?
3
U(c) = 0.21 - 4/2(0.16)^2 = 15.88
Investment - E(r) - SD
1 - 0.12 0 0.3
2 - 0.15 - 0.5
3 - 0.21 - 0.16
4 - 0.24 - 0.21
U = E(r) - (A/2)s^2, where A = 4.0
Which investment would you select if you were risk neutral?
4
If you are risk neutral, your only concern is with return, not risk
Investment - E(r) - SD
1 - 0.12 0 0.3
2 - 0.15 - 0.5
3 - 0.21 - 0.16
4 - 0.24 - 0.21
U = E(r) - (A/2)s^2, where A = 4.0
The variable (A) in the utility function represents the
investor’s aversion to risk
The exact indifference curves of different investors
cannot be known with perfect certainty and although not known with perfect certainty, do allow the advisor to create more suitable portfolios for the client
The riskiness of individual assets
should be considered in the context of the effect on overall portfolio volatility and should be combined with the riskiness of other individual assets in the proportions these assets constitute the entire portfolio
A fair game
will not be undertaken by a risk-averse investor and is a risky investment with a zero-risk premium
The presence of risk means that
more than one outcome is possible
The utility score an investor assigns to a particular portfolio, other things equal,
will increase as the rate of return increases
The certainty equivalent rate of a portfolio is
the rate that a risk-free investment would need to offer with certainty to be considered equally attractive as the risky portfolio
According to the mean-variance criterion, which of the statements below is correct?
Investment - E(r) - Standard Deviation
A - 105 - 5%
B - 21% - 11%
C - 18% - 23%
D - 24% - 16%
A. Investment B dominates Investment A
B. Investment B dominates Investment C
C. Investment D dominates all of the other investments
D. Investment D dominates only Investment B
E. Investment C dominates Investment A
Investment B dominates investment C because investment B has a higher return and a lower standard deviation (risk) than investment C
Steve is more risk-averse than Edie. On a graph that shows Steve and Edie’s indifference curves, which of the following is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis.
I) Steve and Edie’s indifference curves might intersect
II) Steve’s indifference curves will have flatter slopes than Edie’s
III) Steve’s indifference curves will have steeper slopes than Edie’s
IV) Steve and Edie’s indifference curves will not intersect
V) Steve’s indifference curves will be downward sloping and Edie’s will be upward sloping
I and III
The capital allocation line can be described as the
investment opportunity set formed with a risky asset and a risk-free asset
Which of the following statements regarding the capital allocation line (CAL) is false?
The CAL is also called the efficient frontier of risky assets in the absence of a risk-free asset
Given the capital allocation line, an investor’s optimal portfolio is the portfolio that
maximises her expected utility
An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a. T-bill that pays 6%. His portfolio’s expected return and standard deviation are … and … respectively
0.087; 0.06
E(r.p) = 0.3(15%) + 0.7(6`5)
S.p = 0.3(0.04)^0.5
An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.13 and a variance of 0.03 and 70% in a T-bill that pays 6%. His portfolio’s expected return and standard deviation are … and … respectively
0.081; 0.052
E(r.p) = 0.3(13%) + 0.7(6%)
s.p = 0.3(0.03)^0.5
An investor invests 40% of his wealth in a risky asset with an expected rate of return of 0.17 and a variance of 0.08 and 60% in a T-bill that pays 4.5%. His portfolio’s expected return and standard deviation are … and … respectively
0.095; 0.113
E(r.p) = 0.4(17%) + 0.6(4.5%)
s.p = 0.4(0.08)^0.5
An investor invests 70% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 30% in a T-bill that pays 5%. His portfolio’s expected return and standard deviation are … and … respectively.
0.120; 0.14
E(r.p) = 0.7(15%) + 0.3(5%)
s.p = 0.7(0.04)^0.5
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.
What percentage of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.09?
57% and 43%
9% = w(12%) + (1-w)(5%)
w = 0.57
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.
What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.06?
60% and 40%
0.06 = x(0.15); x=40%
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.
A portfolio that has an expected outcome of $115 is formed by
borrowing $43 at the risk-free rate and investing the total amount ($143) in the risky asset
(115-100)/100 = 15%
0.15 = w(0.12) + (1-w)(0.05)
0.10 = 0.07w
w = 1.43($100)
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.
The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to
0.4667
(0.12-0.05)/0.15
Consider a T-bill with a rate of return of 5% and the following risky securities:
Security A: E(r) = 0.15; Var = 0.04
Security B: E(r) = 0.10; Var = 0.0225
Security C: E(r) = 0.12; Var = 0.01
Security D: E(r) = 0.13; Var = 0.0625
From which set of portfolios, formed with the T-bill and any one of the four risky securities, would a risk-averse investor always choose his portfolio?
The set of portfolios formed with the T-bill and security C
Security C has the highest reward-to-volatility ratio
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40 respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill and P, respectively?
0.19; 0.81
E(r.p) = 0.6(14%) + 0.4(10%) = 12.4%
11% = 5x + 12.4(1-x)
x = 0.189; (1-x) = 0.811
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest in the T-bill, X, and Y, respectively, if you keep X and Y in the same proportions to each other as in portfolio P?
0.32; 0.41; 0.27
10 = 5w + 12.4(1-w); w=0.32 (weight of T-bills)
As composition of X and Y are 0.6 and 0.4 of P, then for 0.68 weight in P, the respective weights must be 0.41 and 0.27;
0.6(0.68) = 41%; 0.4(0.68) = 27%
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills?
$240; $160
$400(0.6) = $240 in X; $400(0.4) = $160 in Y
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120?
568, 378, 54
(1120-1000)/1000 = 12%
(0.6)14% + (0.4)10% = 12.4%
12 = w5 + 12.4(1-w)
w = 0.054
w = 0.054(1000) = 54 (T-bills)
0.946(1000) = 946 (portfolio)
946 x 0.6 = 568 (X)
946 x 0.4 = 378 (Y)
A reward-to-volatility ratio is useful in
understanding how returns increase relative to risk increases
The change from a straight to a kinked capital allocation line is a result of
borrowing rate exceeding lending rate
The first major step in asset allocation is
assessing risk tolerance
Based on their relative degrees of risk tolerance
investors will hold varying amounts of the risky asset and varying amounts of the risk-free asset in their portfolios
Asset allocation may involve
the decision as to the allocation between a risk-free asset and a risky asset and the decision as to the allocation among different risky assets
In the mean-standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called
the capital allocation line
Treasury bills are commonly viewed as risk-free assets because
their short-term nature makes their values insensitive to interest rate fluctuations and the inflation uncertainty over their time to maturity is negligible
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets
E(R.p) = 12%
SD of P = 7.2%
T-Bill rate = 3.6%
Proportion of Complete Portfolio in P = 80%
Proportion of Complete Portfolio in T-Bills = 20%
Composition of P:
Stock A = 40%
Stock B = 25%
Stock C = 35%
What is the expected return on Bo’s complete portfolio?
10.32%
E(r) = 0.8 x 12 + 0.2 x 3.6
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets
E(R.p) = 12%
SD of P = 7.2%
T-Bill rate = 3.6%
Proportion of Complete Portfolio in P = 80%
Proportion of Complete Portfolio in T-Bills = 20%
Composition of P:
Stock A = 40%
Stock B = 25%
Stock C = 35%
What is the standard deviation of Bo’s complete portfolio?
5.76%
= 0.8 x 7.20
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets
E(R.p) = 12%
SD of P = 7.2%
T-Bill rate = 3.6%
Proportion of Complete Portfolio in P = 80%
Proportion of Complete Portfolio in T-Bills = 20%
Composition of P:
Stock A = 40%
Stock B = 25%
Stock C = 35%
What is the equation of Bo’s capital allocation line?
E(r.c) = 3.6 + 1.167 x Standard Deviation of C
The intercept is the risk-free rate (3.6%) and the slope is (12 - 3.6)/7.2 = 1.167
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets
E(R.p) = 12%
SD of P = 7.2%
T-Bill rate = 3.6%
Proportion of Complete Portfolio in P = 80%
Proportion of Complete Portfolio in T-Bills = 20%
Composition of P:
Stock A = 40%
Stock B = 25%
Stock C = 35%
What are the proportions of stocks A, B and C, respectively in Bo’s complete portfolio?
32%, 20%, 28%
0.8 x 40%; 0.8 x 25%; 0.8 x 35%
To build an indifference curve we can first find the utility of a portfolio with 100% in the risk-free asset, then
change the standard deviation of the portfolio and find the expected return the investor would require to maintain the same utility level
The capital market line
I) is a special case of the capital allocation line
II) represents the opportunity set of a passive investment strategy
III) has the one-month T-bill rate as its intercept
Iv) uses a broad index of common stocks as its risky portfolio
I, II, III and IV
An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%. His portfolio’s expected return and standard deviation are … and …, respectively.
0.089; 0.111
E(r.p) = 0.35(18%) + 0.65(4%) = 8.9%
s.p = 0.35(0.10)^0.5
An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.11 and a variance of 0.12 and 70% in a T-bill that pays 3%. His portfolio’s expected return and standard deviation are … and … respectively.
0.054; 0.104
E(r.p) = 0.3(11%) + 0.7(3%)
s.p = 0.3(0.12)^0.5
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.
What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08?
62.5% and 37.5%
8% = w(11%) + (1-w)(3%)
w = 0.625
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.
What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08?
60% and 40%
0.08=x(0.20); x = 40% in risky asset
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.
The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to
0.40
(0.11-0.03)/0.20 = 0.40
You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04.
What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11?
53.8% and 46.2%
11 = w(17%) + (1-w)(4%)
w = 0.538
You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04.
What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.20?
50% and 50%
0.20 = x(0.40)
You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04.
The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to
0.325
(0.17-0.04)/0.40
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.13?
130.77% and -30.77%
13 = w(11) + (1-w)(4.5)
w = 1.3077
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08?
61.9% and 38.1%
0.08 = x(0.21)
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
A portfolio that has an expected outcome of $114 is formed by
borrowing $43 at the risk-free rate and investing the total amount ($146) in the risky asset
