FIN 320 SPRING 2024 Problem Set 6

Suppose one uses the single-index model to estimate characteristics of securities.Which of the following statements is correct? (a)The covariances between securities are the same as in the data. (b)The variance of a portfolio is the same as in the data. (c)The expected return and the variance of a security are the same as in the data. (d)The expected return,variance and covariances of a security are the same as in the da

Required information [The following information applies to the questions displayed below.] A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Stock fund (5) Bond fund (B) The correlation between the fund returns is 0.15. Expected Return 158 98 Required: Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places.) Answer is complete but not entirely correct. 15.55% 84.45 X % 9.93 X % 25.52 % Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation Standard Deviation 32% 23% 4

3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions.  (a)  Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset? (b)  Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?

QUESTION 2 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​  Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases. The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases. The standard deviation of the portfolio returns increases as the coefficient of correlation increases. The standard deviation of the portfolio returns decreases as the coefficient of correlation increases. The standard deviation of the portfolio returns increases as the coefficient of correlation decreases.

Which of the following statements regarding risk objectives for an investor is incorrect. a) Institututional investors risk objectives must include downside risk measure(s) b) Risk measures could be absolute or relative risk measure. c)Institutional investors risk objectives must consider the willingness and the ability to take risk. d) Risk objectives can include more than a single constraints. e) Retail investors risk objectives must consider the willingness and the ability to take risk.

10. Which one of the following measures may be used to measure the risk of an investment on its own? a) Expected return of the investment. b) Expected utility of the investment for an investor. c) Standard deviation of the possible outcomes of the investment. d) The Bernoullian utility function's value of a good investment outcome.

Exercise 9.2 (start-up and venture capitalist exit strategy).  There are three periods, t = 0, 1, 2. The rate of interest in the economy is equal to 0, and ev- eryone is risk neutral. A start-up entrepreneur with initial cash A and protected by limited liability wants to invest in a fixed-size project. The cost of invest- ment, incurred at date 0, is I > A. The project yields, at date 2, R > 0 with probability p and 0 with prob- ability 1 − p. The probability of success is p  = pH if the entrepreneur works and p = pL  = pH − ∆p (∆p > 0) if the entrepreneur shirks. The entrepre- neur’s effort decision is made at date 0. Left unmon- itored, the entrepreneur obtains private benefit B if she shirks and 0 otherwise. If monitored (at date 0), the private benefit from shirking is reduced to b B. There is a competitive industry of venture capi- talists (monitors). A venture capitalist (general part- ner) has no fund to…

5. You have been hired as a portfolio manager for a fancy hedge fund. Your first job is to invest $100,000 in a portfolio of two assets. The first asset is a safe asset with a certain return of 5%. The second asset is shares of a dying video-game store that has become popular with retail investors, it has a 20% expected rate of return, but the standard deviation of this return is 10%. Your manager wants a portfolio with as high a rate of return as possible while keeping the standard deviation at or below 4%. How much of the fund's money do you invest in the safe asset?

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows: Expected Return Standard Deviation Stock fund (S) 20% 30% Bond fund (B) 12 15 The correlation between the fund returns is 0.10. a-1. What are the investment proportions in the minimum - variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond a-2. What are the expected value and standard deviation of the minimum variance portfolio rate of return? (Do not round intermediate calculations. Enter your answers as percentage rounded to 2 decimals.) Expected return % Standard deviation %

19. An individual has initial wealth Wo = 3 and has the opportunity to invest some quantity of money x in an extremely risky corporate bond. With probability p= 1/4, the bond will be worth 10x at maturity. With probability 1 – p, it will be worth zero. The individual's utility function over final wealth is u(W) = W0.5. What is the level of investment x that maximizes expected utility? (а) 0 (b) 1 (c) 4/3 (d) V3 (e) 2

QUESTION 1 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​ Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are uncorrelated. 17.4%. 27.4%. 7.4%. 11.4%. QUESTION 2 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​  Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases. The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases. The standard deviation of the portfolio returns increases as the coefficient…

Discuss: i) diversifiable risk; ii) market risk; iii) systematic risk iv) unsystematic risk;

16. The market consists of only two assets, A and B, with normally distributed re- turns. Asset A's returns have a mean of 18% and a standard deviation of 14% and Asset B's returns have a mean of 15% and a standard deviation of 18%. In such a scenario a risk-averse investor would always want to invest all of her money in Asset A.   17. A call option offers the purchaser limited downside loss as given by the option premium paid, combined with limited upside potential.   18. The return earned on a risk free portfolio must be equal to the risk free interest rate.   19. CAPM assumes that all investors' optimal portfolio has a fraction invested in the risk-free asset and the remaining in the minimum variance portfolio.   20. For any frontier portfolio p, except the minimum variance portfolio, there exists a unique frontier portfolio with which p has zero covariance.   21. The market portfolio of all available assets is the supply of risky assets.   22. An arbitrage opportunity is an…

BNQ12.2 Case: Suppose an Investor is concerned about a Business Choice in which there are 3 prospects the Probabilities and Returns are given below: Probability 0.4 0.3 0.3 Return $100 30 -30 Question: What is the Expected Value of the Uncertain Investment?

Suppose you identify 50 possible investments whose payoffs are completely independent of one another. All the investments have the same expected value and standard deviation. You have $5,000 to invest. In terms of risk, would the benefit of spreading your $5,000 across all 50 investments be the same, greater, or smaller compared with dividing your funds between just two investments? OYes. The gains from spreading your investments would be larger if you spread the $5000 across 50 investments. No. Because in this case diversification does not help to spread risk, it doesn't matter how many investments you spread your $5,000 across. No. Because the payoffs from these investments are independent, it doesn't matter how many investments you spread your $5,000 across, as there is no benefit in terms of reduced risk. O Yes. Because the payoffs from these investments are negatively correlated with one another, spreading your $5,000 across a targer number of investments reduces your risk.

Question 11 The beta of an active portfolio is 1.45. The standard deviation of the returns on the market index is 22%. The nonsystematic variance of the active portfolio is 3%. The standard deviation of the returns on the active portfolio is a) 36.30%. b) 5.84%. c) 19.60%. d) 24.17%. e) 26.0%.

5. Shift-in-charge Nazar Al Rushdy: Nazar is pessimistic about the market price. What is your guidance for Nazar? The decision to employ decision trees in crucial situations has been taken by Salem Al Harthi, the plant manager. The table below presents data on demand for a duration of 6 hours along with their respective probabilities. The first row of the table provides the probability of demand for the initial three hours when a leak occurs, denoted in parentheses. Subsequently, the following three rows indicate the probabilities of high, medium, and low demand for the succeeding three hours. To illustrate, if the initial 3-hour market price was low, the probabilities of high demand, medium demand, and low demand in the next three hours are 0.2, 0.3, and 0.5, respectively. Market price High Market price Medium Initial 3-hrs (0.2) Initial 3-hrs (0.5) Market price Low Initial 3-hrs (0.3) High demand (next (0.5) (0.4) (0.2) 3 hrs) Medium demand (0.3) (0.2) (0.3) (next 3 hours) Low demand…

5. Find the expected value assuming the risk factor is 30 % and the interest rate is 12% , if you will receive $20,000 one year from today.

Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #

1. George maximizes expected utility and he has a von-Neumann-Morgenstern utility function u (c) = √e. He has an initial wealth of $1,000. He finds an investment opportunity. The project has a startup cost of $1000, and a 9% chance of success. If the project succeeds, the payoff is $100,000; if it fails, its payoff is $0. (a) Would George invest in this project? (b) Suppose George has an initial wealth of $100, 000 instead of $1,000. Would he invest in this project? (c) Comparing your answers in parts (a) and (b), how does George's risk appetite change? Why?

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows: Standard Deviation Expected Return 23% Stock fund (S) 29% Bond fund (B) 14 17 The correlation between the fund returns is 0.12. a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond a-2. What are the expected value and standard deviation of the minimum-variance portfolio rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Rate of Return Expected return Standard deviation

Banks often close Repo-Deals with other banks. Today the lower Rhine-Bank (LRB) owns a 6% CHF-fixed coupon bond which was issued by the Swiss Novartis Group and is subject of a Repo-Deal. Three months ago the bank closed the Repo-Deal which originally had a maturity of six months. 1. Please name the risk which is hedged by Repo Deal.  2. Please name two risks which are related to the above mentioned bond.  3. Select one risk of the above mentioned bond and name one means/financial instrument in order to hedge the selected risk. 4. Briefly describe the events or actions which  a. Took place three months ago, b. will take place in three months.

John Davidson is an investment adviser at Leeds Asset Management plc. He is asked by a client to evaluate various investment opportunities currently available and he has calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets: Portfolio Expected return Standard deviation Q 7.8% 10.5% R 10.0% 14.0% S 4.6% 5.0% T 11.7% 18.5% U 6.2% 7.5%   (a) For each portfolio, calculate the risk premium per unit of risk (Sharpe ratio) that you expect to receive. Assume that the risk-free rate is 3.0%.  (b) If you are only willing to make an investment with a standard deviation of 7.0%, is it possible for you to earn a return of 7.0%?  (c) What is the minimum level of risk that would be necessary for an investment to earn 7.0%? What is the composition of the portfolio along the Capital Market Line (CML) that will generate that expected return?

1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this decision in the second. Question 6 options: 2. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the conservative approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to derive this solution in the second. Question 7 options: 8 3. Suppose a company must consider two…

Sam, after taking a $200 loan from the bank to finance an investment that pays $1000 50% of the time and $0 50% of the time at a 100% interest, discovers another riskier investment that pays out $5,000 but only 10% of the time, while the other 90% of the time it pays zero. Would the he want to switch to the riskier investment?   Question 4 options:   ​Yes because his return has increased   ​No because his liability to the bank has increased   ​No because his return has decreased   ​None of the above

1. Which of the following is INCORRECT? a All of a stock's risk could be unsystematic. b. A negative beta stock has an expected return less than the risk-free rate. c. Anticipated returns on any given stock are always greater than 0. d. Two assets with a correlation of -1 could be combined to create a portfolio with a standard deviation of zero (no risk). 2. Which of the following measures the total risk of a portfolio? a. Beta b. Standard Deviation c. Correlation Coefficient d. Alpha 3. Which of the following stocks have the highest systematic risk? a A stock with high correlation to the market and high returm volatility. b. A stock with low correlation to the market and a high return volatility. c A stock with high correlation to the market and a low return volatility. d. A stock with low correlation to the market and a low return volatility. 4. Which of the following companics have the lowest systematic risk? a A company that sells soups (Campbells), beta=0.60 b. A coffee company…

A new company is offering its shares for sale in an initial public offering (IPO) through an auction. There is a 50% probability that the company will be very successful, in which case each share is worth $28. Otherwise, each share is worth $0. You are competing with professional investors such as hedge funds that know if the company will be successful or not. Part 1If you bid $14 per share, what is your expected return?

4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.