If two securities are perfectly negatively correlated then the global-minimum variance portfolio has a standard deviation that is always A) greater than zero. B) equal to zero. C) equal to the sum of the securities' standard deviations. D) equal to −1. Choose the correct answer and justify it

Question 1 Are the following statements true or false? Provide a short justification for your answer. (You are evaluated on your justification.) Remember that a statement is false if any part of the statement is false. A single correct counterexample is sufficient to show that a statement is false. a) assets A, B, C, with expected returns and standard deviations: Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky E [řa] = 10%, SD [FA] = 5% E [řB] = 15%, SD [řB] = 7% E [řc] = 12%, SD [řc] = 9% You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets (A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer the set of assets (A, B) to the set assets (A, C). b) the same market B's. The covariance matrix between A, B, C is: Suppose the CAPM holds. Consider…

ich of the following will not reduce risk in a portfolio?   Select one: a.   Selecting two securities that are perfectly positively correlated.   b.   Selecting two securities that are positively correlated.   c.   Selecting two securities that are perfectly negatively correlated.   d.   Selecting two securities that are negatively correlated.

According to modern portfolio theory, pair-wise covariance is more important to total portfolio risk than individual security variance. True or False

Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO

Portfolios that offer the highest expected return for a given variance (or standard deviation) are known as efficient portfolios. O true false

Which of the following statements are correct? I.The standard deviation is a measure of risk.II.The variance of yearly returns is roughly the variance of monthly returns multiplied with 12.III.To decide whether asset A is more risky than asset B we can either use their standard deviations or their variances.     Group of answer choices II and III only I, II and III I and II only I and III only

Given the following probability distribution, what is the standard deviation of returns for Security J? (Expresss your answer in percentage, but do not include the percent sign, %, i.e., 4.65) State Pi rJ 1 0.2 8 % 2 0.6 12    3 0.2 17

Consider a risky portfolio, A, with an expected rate of return of 0.16 and a standard deviation of 0.25, that lies on a given indifference curve. Which one of the following portfolios is not likely to lie on the same indifference curve for a risk-averse investor with a mean- variance utility function? a. Expected return = 0.20; Standard deviation = 0.15 b. Expected return = 0.10; Standard deviation = 0.20 Expected return= 0.15; Standard deviation = 0.20 Expected return = 0.12; Standard deviation = 0.10 Expected return = 0.10; Standard deviation = 0.10 C. d. e.

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.