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2 S1. (5 points) Which of the following is NOT true about gamma? (There may be more than one correct answer, indicate all that are true) a.
A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral b.
The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price c.
A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a bigger loss or smaller gain d.
A long position in either a call or a put has a positive gamma e.
None of the above S2. (5 points) Suppose that a central bank’s policy is to allow an exchange rate to fluctuate between 0.97 and 1.03 against the USD. Which of the following would you expect to see? (There may be more than one correct answer, indicate all that are true.) a. The right and left tails of the distribution of exchange rates will be fatter than for a log-normal distribution b. The right and left tails of the distribution of exchange rates will be thinner than for a log-normal distribution c. Both out-of-the-money and in-the-money calls and puts can be expected to have lower implied volatilities than at-the-money calls and puts d. Both out-of-the-money and in-the-money calls and puts can be expected to have higher implied volatilities than at-the-money calls and puts e. None of the above S3. (5 points) Which of the following could be possible explanations for backwardization in the forward curve for a commodity? (There may be more than one correct answer, indicate all that are true.) a. The storage cost rate for the commodity exceeds the risk-free rate b. The convenience yield for the commodity exceeds the risk-free rate c. It is a perishable agricultural commodity and the amount harvested is expected to be increasing over the next several months d. It is a perishable agricultural commodity and the amount harvested is expected to be decreasing over the next several months e. Storage costs are currently elevated but are expected to gradually fall
3 L1. A firm has 60,000 shares outstanding and a current market price per share of $78. The risk-free rate is 2.75% per annum on a continuously compounded basis (flat yield curve). The stock does not pay dividends. a. (5 points) Assume that the stock price follows a log-normal process. If on a binomial tree representing the evolution of the stock price the up multiplier “u” is 1.1451 and the down multiplier “d” is .87328, and where each time step represents 3 months, what is the annual volatility of the stock price? Create a binomial tree for the 9-month evolution of the stock price (with each time-step representing one quarter)? Use the u and d multipliers to assign a label to each node of the tree below. S21 S11 S0 S22 S12 S23 b. (3 points) What is the risk-neutral probability of an up move on the tree? S31 S32
S33 S34
4 c. (3 points) If the beta of the stock is .4, is the risk-neutral probability of an up move on the tree greater than the physical (i.e., real-world) probability of an up move on the tree? Why or why not? Explain briefly. d. (6 points) You work for an investment bank that offers an exotic American-style call option on the stock with a strike price that increases over time. Specifically, the strike price per share is $85 in 3 months, $90 in 6 months, and $100 in 9 months. Your boss asks you to estimate the value of that option written on 80 shares of the stock. What do you tell her? Show your calculations.
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Related Questions
Which ones of the following statements about portfolio beta are correct?
O 1. If portfolio beta is between 0 and 1, then the portfolio expected return is between risk-free rate and the market expected return.
O 2. If the return of an asset has zero correlation with the market portfolio returns, the beta of this asset must be zero.
O 3. A portfolio that has the same portfolio weights as the market portfolio should have a beta of 1.
O 4. Diversification is not a way to reduce portfolio beta.
O 5. If two portfolios have the same portfolio weights, but different dollar values, their betas are the same.
arrow_forward
Suppose you have an investment portfolio with fraction x invested in a market portfolio and (1-x) in a risk-
free asset. Increasing fraction x invested in the market portfolio and consequently decreasing (1-x) invested
in the risk-free asset shall
(select any correct answer, if there are multiple correct answers)
Select one or more:
O decrease the Sharpe ratio of the resulting portfolio
O decrease the expected return of the resulting portfolio
increase the Sharpe ratio of the resulting portfolio
increase the expected return of the resulting portfolio
Dincrease the risk of the resulting portfolio
arrow_forward
1. The diversifiable risk of a portfolio:
a. Is correlated with systematic risk.
b. Can be made sufficiently small.
c. Is zero in the real world.
d. Is the risk that investors lose because of transaction costs.
Which one of the following conditions determines the investor’s overall optimal portfolio?
a. The marginal ratio of substitution of the investor’s utility function must be equal to the Sharpe ratio of the optimal risky portfolio.
b. The standard-deviation of the overall portfolio in minimised.
c. The expected return of the overall portfolio is maximised.
d. The slope of the Sharpe-ratio is equal to zero.
4. Markets can never be strong-form efficient because:
a. There are too many traders in them.
b. Investors are rational.
c. Information is costly to acquire.
d. All information is public.
5. Which one of the following is not a property of a pure arbitrage portfolio? a. Zero investment.
b. Zero systematic risk.
c. Positive net return.
d. All of the above.
arrow_forward
4. Suppose that there are 2 assets with ri
012 = 0.005.
=
0.20, 01
=
=
0.40, 2
=
0.10, 02 = 0.25 and
(a) If ro = 0.02, what are the market portfolio return and variance? What are the corre-
sponding weights (i.e. how much to invest in asset 1, asset 2, and the risk-free asset to
get the market portfolio)? Answer.
(b) If ro
0.05, what are the market portfolio return and variance? What are the corre-
sponding weights? Answer.
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b. Suppose that you have the following information of three risky assets.
Security
Return (%)
Standard
Covariance with
Deviation (%)
A
B
A
11
10
4
14
6.
30
17
Risk free rate = 6%, (assume that A = 6).
Requirement: Find the optimal portfolio weight of risky assets. How do you allocate the capital between
optimal portfolio of risky asset and risk-free assets.
arrow_forward
2. Based on the chart above, which portfolio is “better” based on Markowitz approach to portfolio construction? A. A, because it has zero risk B. B, because it is safe than C C. C, because it has higher return D. B & C are equally good because both have same “return relative to the risk taken” and the choice between the two is a matter of investors preference
arrow_forward
Suppose you observe the following situation:Security Beta Expected ReturnDiamond Co 1.3 0.2Spade Co 0.8 0.14 (a) According to the above information, could we figure out the market return and risk-free rate? Explain your answer. (b) Discuss the possibility of including zero beta or negative beta assets in your portfolio. Explain the pros and cons of including these types of assets.
arrow_forward
As diversification increases, the firm-specific risk of a portfolio approaches
A. 1.
B. infinity.
C. 0.
D. (n – 1) × n.
arrow_forward
choose which one ?
3.Assume CAPM holds. What is the correlation between an efficient portfolio and the market portfolio?a.1b.-1c.0d.Not enough information
arrow_forward
The CAPM states that the expected (required) return on an asset is :
E(Ri)=Rf+βi[E(RM)−Rf]
where the term in square brackets is the risk-premium earned by the market portfolio. Therefore, the beta of the market portfolio (βM) must be equal to __________ .
A) zero
B) 0.5
C) 1.0
D) an unknown estimate
arrow_forward
Question 2 a) Plot the Security Market Line (SML).b) Superimpose the CAPM’s required return on the SML.c) Indicate which investments will plot on, above and below the SML?d) If an investment’s expected return (mean return) does not plot on the SML, what doesit show? Identify undervalued/overvalued investments from the graph
arrow_forward
A portfolio that is positively correlated with the market portfolio but not particularly sensitive to market risk factors would have a beta that is
A.
Equal to zero.
B.
Equal to one.
C.
Less than zero.
D.
Between 0 and 1.
E.
Greater than 1.
arrow_forward
Return on a portfolio of two risky assets which are perfectly negatively correlated is equivalent to
a. Risk-free rate
b. Return on market portfolio
c. Zero return
d. -1%
arrow_forward
Which of the following statements is correct?
A delta-neutral portfolio is protected against large changes in the underlying asset price.
The delta hedging error increases as gamma decreases.
To change the vega of a portfolio, we need to trade the portfolio’s underlying asset.
A delta-neutral portfolio needs to be rebalanced more frequently as the gamma increases to maintain delta-neutrality.
Please explain and justify your choice using your own words.
arrow_forward
When a portfolio consists of only a risky asset and a risk-free asset, increasing the fraction of the overall portfolio invested in the risky asset will
a.
Increase the expected return and standard deviation of the portfolio
b.
Increase the standard deviation of the portfolio
c.
Decrease the standard deviation of the portfolio
d.
Increase the expected return of the portfolio
arrow_forward
A beta of 1.0 represents an asset that
O is less responsive than the market portfolio
has the same response as the market portfolio
O is unaffected by market movement
O is more responsive than the market portfolio
arrow_forward
9.1
q1-
How would you describe the relationship between risk and return for large portfolios of investments?
Select one:
a.
There is no clear relationship.
b.
The relationship is precisely a positive linear relationship.
c.
The relationship approximates a positive linear relationship.
d.
The relationship approximates a negative linear relationship.
arrow_forward
d. Would this asset be considered more or less risky than the market?
The asset is a. Equally as risky the market portfolio, which has a beta of a. 1
b. less risky than b. 0
c. more risky than c. -1
arrow_forward
Supposing the return from an investment has the following probability distribution
Return Probability
R (%)
8 0.2
10 0.2
12 0.5
14 0.1
Required:
What is the expected return of the investment?
What is the risk as measured by the standard deviation of expected returns?
arrow_forward
Suppose that there are two assets: A and B. Asset A has expected return of 20%. B has expected return of 12% and standard deviation of σ*
σ* = standard Deviation (σ)
(a) “As B is strictly dominated by A in terms of total risk (standard deviation), there is no value in having B in portfolio formation.” (Without doing any calculation)
(b) “If the correlation coefficient ρ between A and B = 1, it is always optimal to invest in A only.” (Show your proof)
(c) “If the correlation coefficient ρ between A and B = -1, it is always optimal to invest in 50% in A and 50% in B when forming a minimum variance portfolio of the two.” (Show your proof) [
(d) “Given that σA= σB=σ*, it is always optimal to combine half of A and half of B when forming a minimum variance portfolio of the two when ρ ε (-1,1).” (Show your proof)
arrow_forward
Question 1-
Which one of the following conditions determines the investor’s overall optimal portfolio?
a. The marginal ratio of substitution of the investor’s utility function must be equal to the Sharpe ratio of the optimal risky portfolio.
b. The standard-deviation of the overall portfolio in minimised.
c. The expected return of the overall portfolio is ma is maximised.
d. The slope of the Sharpe-ratio is equal to zero.
Question 2---
Which one of the following is not a property of a pure arbitrage portfolio? a. Zero investment.
b. Zero systematic risk.
c. Positive net return.
d. All of the above.
Question 3---
Select the incorrect statement about the optimal portfolio weights in the SIM from the following:
a. When short sales are not allowed, the investor will hold more assets in her portfolio than when short sales are allowed.
b. When the single index is tradeable, securities with negative will be shorted.
c. When the single index is tradeable, securities with higher (given…
arrow_forward
Consider the following performance data for a portfolio manager:
Benchmark
Portfolio
Index
Portfolio
Weight
Weight
Return
Return
Stocks
0.65
0.7
0.11
0.12
Bonds
0.3
0.25
0.07
0.08
Cash
0.05
0.05
0.03
0.025
a.Calculate the percentage return that can be attributed to the asset allocation decision.
b.Calculate the percentage return that can be attributed to the security selection decision.
arrow_forward
Which two portfolios lie on the same indifference curve? Ignore feasibility.
Expected
Return, E(r)
OH and G
OH and F
O F and E
0
2
4
3
H
O G and E
O No two portfolios lie on the same indifference curve
G 4
3
N
E
Capital
Allocation
Line (CAL)
Risk, o
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1. calculate the beta of the portfolio below consisting of assets x, y and z. discuss the meaning of the number calculated and include in your answer what type of investor is likely to invest in this portfolio.
Asset
Weight (Wi)
Beta (βi)
X
0.30
0.09
Y
0.50
0.90
Z
0.20
0.16
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if asset A has lower volatility than asset B, then it contributes less to the overall volatility when added to a portfolio.
True or false?
arrow_forward
Consider the following financial market with two
risky assets x and y as well as a risk-free asset f:
E[r].
x (10%, 8%)
•z (6.6%, 6.3%)
y (8%, 5%)
(0%, 3%) f
Is it possible to construct portfolio z with existing
assets? Explain.
arrow_forward
An efficient capital market is best defined as a market in which security prices reflect which one of the following?
Multiple Choice
A Current inflation
B A risk premium
C All available information
D The historical arithmetic rate of return
E The historical geometric rate of return
arrow_forward
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- Which ones of the following statements about portfolio beta are correct? O 1. If portfolio beta is between 0 and 1, then the portfolio expected return is between risk-free rate and the market expected return. O 2. If the return of an asset has zero correlation with the market portfolio returns, the beta of this asset must be zero. O 3. A portfolio that has the same portfolio weights as the market portfolio should have a beta of 1. O 4. Diversification is not a way to reduce portfolio beta. O 5. If two portfolios have the same portfolio weights, but different dollar values, their betas are the same.arrow_forwardSuppose you have an investment portfolio with fraction x invested in a market portfolio and (1-x) in a risk- free asset. Increasing fraction x invested in the market portfolio and consequently decreasing (1-x) invested in the risk-free asset shall (select any correct answer, if there are multiple correct answers) Select one or more: O decrease the Sharpe ratio of the resulting portfolio O decrease the expected return of the resulting portfolio increase the Sharpe ratio of the resulting portfolio increase the expected return of the resulting portfolio Dincrease the risk of the resulting portfolioarrow_forward1. The diversifiable risk of a portfolio: a. Is correlated with systematic risk. b. Can be made sufficiently small. c. Is zero in the real world. d. Is the risk that investors lose because of transaction costs. Which one of the following conditions determines the investor’s overall optimal portfolio? a. The marginal ratio of substitution of the investor’s utility function must be equal to the Sharpe ratio of the optimal risky portfolio. b. The standard-deviation of the overall portfolio in minimised. c. The expected return of the overall portfolio is maximised. d. The slope of the Sharpe-ratio is equal to zero. 4. Markets can never be strong-form efficient because: a. There are too many traders in them. b. Investors are rational. c. Information is costly to acquire. d. All information is public. 5. Which one of the following is not a property of a pure arbitrage portfolio? a. Zero investment. b. Zero systematic risk. c. Positive net return. d. All of the above.arrow_forward
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- Suppose you observe the following situation:Security Beta Expected ReturnDiamond Co 1.3 0.2Spade Co 0.8 0.14 (a) According to the above information, could we figure out the market return and risk-free rate? Explain your answer. (b) Discuss the possibility of including zero beta or negative beta assets in your portfolio. Explain the pros and cons of including these types of assets.arrow_forwardAs diversification increases, the firm-specific risk of a portfolio approaches A. 1. B. infinity. C. 0. D. (n – 1) × n.arrow_forwardchoose which one ? 3.Assume CAPM holds. What is the correlation between an efficient portfolio and the market portfolio?a.1b.-1c.0d.Not enough informationarrow_forward
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