MGEC72-Assignment-2

Question 3 Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for 7,500 and to use these proceeds to buy another stocks for your portfolio. Assume the new stock's beta to 1.75. Calculate your portfolio's new beta.

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…

8. Risk and return Suppose Valerie is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Fraction of Portfolio in Diversified Average Annual Standard Deviation of Portfolio Return Stocks Return (Risk) Combination (Percent) (Percent) (Percent) 1.00 B 25 2.00 5. 50 3.00 10 75 4.00 15 100 5.00 20 If Valerie reduces her portfolio's exposure to risk by opting for a smaller share of stocks, she must also accept a average annual return. Suppose Valerie currently allocates 25% of her portfollo to a diversined group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 2% to 4%. In order to do so, she must do which of the following? Check all that apply. O Sell some of her stocks and place the proceeds…

P5-3 Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Currently, the firm eams 12% on its investments, which have a risk index of 6%. The expected return and expected risk of the investments are as follows: Expected return Expected risk index Investment 14% 7% Y 12 z 10 a. If Sharon were risk-indifferent, which investments would she select? Explain why. b. If she were risk-averse, which investments would she select? Why? c. If she were risk-seeking, which investments would she select? Why? d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why?

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?

8. Risk and return Suppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Combination A BUDW C E Fraction of Portfolio in Diversified Stocks (Percent) 0 25 50 75 100 Average Annual Return (Percent) 3.50 7.50 11.50 15.50 19.50 Standard Deviation of Portfolio Return (Risk) (Percent) 0 5 10 Sell some of her stocks and place the proceeds in a savings account O Sell some of her bonds and use the proceeds to purchase stocks Accept more risk Sell some of her stocks and use the proceeds to purchase bonds 15 20 As the risk of Caroline's portfolio increases, the average annual return on her portfolio Suppose Caroline currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the…

3.) An investor is thinking of purchasing blue-chip stocks as part of his portfolio. At present, he is considering three blue chip stocks: Alpha, Bravo and Charlie. Based on the forecast of economists, there are three possible states of nature in the economy: growth, stagnation, recession, depression. Economists predicted that their respective probabilities are 0.25, 0.35, 0.30 and 0.10. Historical returns for the three blue chip stocks are summarized below: Stock Growth Stagnation Recession Depression Alpha 11% 3% -2% -20% Bravo 20% -1% -5% -3% Charlie 7% 2% 0% -5% (a) Determine the expected return for each stock. (b) Which stock is the riskiest using the standard deviation as a criterion? (c) Which stock is the least risky using the coefficient variation?

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%.

The value of Jon’s stock portfolio is given by the function v(t) = 50 + 77t + 3t2,  where v is the value of the portfolio in hundreds of dollars and t is the time in months.  How much money did Jon start with? (y-intercept) What is the minimum value of Jon’s portfolio? (vertex)

D&R A3 6-1 Question 6. VAR Calculation A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 15% and annual volatility of 20%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 25% and an annual volatility of 30% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these two stocks is 0.3.   What is the 5% daily VAR for the portfolio? Assume 365 days per year.

D&R A3 6-1 Question 6. VAR Calculation A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 15% and annual volatility of 20%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 25% and an annual volatility of 30% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these two stocks is 0.3. Compute the 5% annual VAR for the portfolio. Interpret the resulting VAR.

D&R A3 6-3 Question 6. VAR Calculation A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 15% and annual volatility of 20%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 25% and an annual volatility of 30% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these two stocks is 0.3. If the firm sells $10 million of stock A and buys $10 million of stock B, by how much does the 5% annual VAR change?

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.

What is the expected return from an investment if there is a 20 percent chance of a 4 percent return, a 40 percent chance of a 8 percent return, and a 40 percent chance of a 12 percent return

19 - Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the first factor portfolio is 4%, and the risk premium on the second factor portfolio is 3%. If portfolio A has a beta of 1.2 on the first factor and 0.4 on the second factor, what is its expected return? a) 8.0% b) 13.2% 12.0% d) 7.0% o1383176 9.2%

An investor allocates $30,000 and $50,000 to two assets (A1 and A2). These assets generate 5% and -4.5% rate of returns, respectively. She allocates the remaining 50% of her portfolio to an asset (A3), which provides 4.5% rate of return. Calculate the portfolio's rate of return.

Given the following information, what is the standard deviation of the returns on a portfolio that is invested 35 percent in both Stocks A and C, and 30 percent in Stock B? (see attached chart)

(a) Calculate the risk-premium on this portfolio and provide a brief interpretation of it (b) Calculate the minimum sale price of the capital assets for the average investor.

15. If a financial institution has a portfolio that half (50%) consists of bonds with a tenor of five years and the other half is in the form of bonds with a duration of seven years, what is the duration/tenor of the financial institution's portfolio? A) 12 years B) 7 years C) 6 years D) 5 years 16. If the corporation/company begins to experience large losses, the default risk on the company's bonds will be A) increases and the uncertainty of bond returns increases, meaning that the expected return on the company's bonds will decrease. B) increases and the uncertainty of bond returns decreases, which means the expected return on the company's bonds will decrease. C) decreases and the uncertainty of bond returns decreases, which means the expected return of the company's bonds will decrease. D) decreases and the uncertainty of bond returns decreases, which means the expected return of the company's bonds will increase.

53. Car rental patterns A car rental agency in a major city has a total of 2200 cars that it rents from three loca- tions: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return pat- terns are shown in the table (note that Airport means Metropolis Airport). Rented from Returned to АР DT CA Airport (AP) Downtown (DT) 90% 10% 10% 5% 80% 5% At the beginning of a week, how many cars should be at each location so that same number of cars will be there at the end of the week (and hence at the start of the next week)? 54. Nutrition A psychologist studying the effects of nutrition on the behavior of laboratory rats is feeding one group a combination of three foods: I, II, and III. Each of these foods contains three additives, A, B, and C, that are being used in the study. Each additive is a certain percentage of each of the foods as follows: Foods II II Additive A 10% 30% 60% Additive B Additive C 0% 4% 5% 2% 2% 12% If the diet requires 53 g per day of A, 4.5…

Question 3 (6.5 points): Hedge October 15th: A producer plans to sell wheat in early July; currently, July wheat futures are trading at 680'6. The expected basis is $0.60 under. July 1 • Does the producer have a long or short cash position? Does the producer have a long or short futures position? To hedge: The producer will per bushel. What is the expected cash price? (buy/sell) July wheat futures at 680'6 ⚫ The producer must (buy/sell) wheat locally in the cash market at 562'2 per bushel. To offset their future position, they must. 599'4 per bushel. • What is the actual basis? • (buy/sell) July futures at 。 Was the basis stronger, weaker, or the same as expected? What is the realized price for the producer? Method 1: 。 Method 2: 。 The hedge resulted in a realized price of

True or False: Increasing the number of stocks in a portfolio reduces firm-specific risk. TrueFalseConsider two stock portfolios. Portfolio A consists of 20 different stocks from firms in different industries. Portfolio B consists of four different stocks, also from firms in different industries. The return on Portfolio A is likely to be volatile than that of Portfolio B.Suppose a stock analyst recommends buying stock in the following companies:Company  IndustryToyonda AutomotiveSaalvo AutomotiveGMW AutomotiveHonsubishi AutomotiveShexxon Oil and gasMobron Oil and gasAiring AircraftBoebus AircraftGoohoo TechnologyPherk PharmaceuticalEach of the following portfolios contains four of the stock picks. Which portfolio is the least diversified? Pherk, Airing, Goohoo, ShexxonToyonda, Honsubishi, Boebus, AiringToyonda, Saalvo, GMW, HonsubishiBoebus, Airing, Shexxon, Mobron

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?

D & R A1 11 - 3 Question 11. Hedging with Stock Index Futures You manage a portfolio that is currently all invested in equities in companies in five major Canadian industries. The market value involved and beta for each industry are shown in the table below. Industry Market Value Beta Oil and Gas $1,100,000 1.2 Technology 900,000 1.5 Utilities 1,500,000 0.8 Financial 1,000,000 1.3 Pharmaceutical 800,000 1.1   You believe that the Canadian equity market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and re-establishing your equity position. Instead, you decide to hedge your portfolio with three-month S&P/TSX 60 index futures contracts for one month. Currently, the level of the S&P/TSX 60 index is 851.38, the three-month futures price of the S&P/TSX 60 is 856.40, and one contract is for $200 times…

Suppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds.CombinationFraction of Portfolio in Diversified StocksAverage Annual ReturnStandard Deviation of Portfolio Return (Risk)(Percent)(Percent)(Percent)A 0 1.50 0B 25 3.00 5C 50 4.50 10D 75 6.00 15E 100 7.50 20There is a relationship between the risk of Caroline's portfolio and its average annual return.Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase…

5. Investor attitudes toward risk Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 1 100% chance of receiving $1,100 2 50% chance of receiving $1,000; 50% chance of receiving $1,200 3 50% chance of receiving $200; 50% chance of receiving $2,000 If Erik is risk averse, which investment will he prefer? The investor will choose option 1. The investor will choose option 2. The investor will choose option 3. The investor will be indifferent toward these options. Suppose the market risk premium is currently 6%. If investors were to become more risk-averse, the market risk premium might increase to 8%. What effect would you expect this to have on the prices of most financial assets? Prices would be unaffected. Prices would decrease. Prices would increase.