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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.

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

QUESTION 26 A deck of 52 playing cards consists of 4 suites: clubs, spades, hearts, and diamonds. Each suite consists of 13 cards. Draw one from a deck of cards. Let A=a card "2" is drawn, B=a "diamond" card is drawn. Which is the value of P(A and B), i.e., {probability that the card drawn is "diamond" and "2"} ? 1/52 4/52 13/52 16/52

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?

You are at a casino and there are three slot machines you can use to bet on. You must have a return of .5% of higher on what you are betting. Below is the expected returns for each slot machine under various scenarios. What combination of machines do you play to maximize your average return? Decision Variables Data Slot 1 100.0% Monday Tuesday Wednesda Average Slot 2 0.0% Slot #1 8% 4% 5% 5.667% Slot 3 0.0% Slot #2 2% -3% 3% 0.667% Slot #3 6% -2% 4% 2.667% Objective 5.7% Constraints 0.08 >= 0.5% 0.04 >= 0.5% 0.05 >= 0.5% 100.0% .: 100%

Online sale Suppose a student is considering selling their used smartphone online. They can sell it now for $p or wait and sell it next month for a different price. If they wait, they will receive a random offer with an equal probability of being either $300 or $100. The student can only receive one offer and cannot sell the phone after the second month. 1. Calculate the expected price in the next month. 2. Suppose that the current price p is equal to 200. (a) Give a reason why selling today could be a good idea. (b) Give a reason why selling next month could be a good idea.

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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)

Q3/ The probability that a consumer will rate a new antipollution device for cars What are the probabilities that it will rate the device (a) very poor, poor, fair, or good; (b) good, very good, or excellent? Rate Poor Fair Very good Excellent Very poor Good Probability 0.07 0.12 0.17 0.32 0.21 0.11

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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.

You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald's or a Penn Station East Coast Subs franchise. McDonald's indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be -$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and -$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.

4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?

2. A consumer has utility function for wealth U(W) = w}, wealth W = $1,000, and faces a 50% chance of facing a loss of $875. The consumer's expected utility is (a) 7.5 (b) 8.0 (c) 8.5 (d) 9.0

a) (3) Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is u(x) = x? u(x) = x u(x) = 1-e 10 () (i) (ii)

15. A city mayor decides to construct a new bridge over the major river in the town. The estimated life of such a structure will be 20 years. There is a 70% probability that the total initial costs (consulting fees and construction) will be $800,000 and a 30% probability that such costs would be $1 million. There is 100% probability that the maintenance costs would be $30,000 every 5 years. How much money should the city borrow now in order to carry out the entire project including maintenance? The interest rate is 5%.

Choice under uncertainty Alice would be willing to pay up to £15 for a gamble giving a 35% chance of £50 and a 65% chance of £10. 5. (a) What is the expected value of this gamble? Represent Alice's preference over risk in a large, suitably labelled graph. The graph should include Alice's expected utility from the gamble described above. (b) Represent on the same graph the maximum amount that Alice would pay to remove the risk from this gamble.

Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%

Optimal Portfolio: Mean-Variance OptimizationIf you are a portfolio manager who predicted that the tension in Ukraine might spiral into a global economic problem back in December 2021. She decided to construct a portfolio that, she think, would outperform in a war scenario, or in a heightened war risk scenario. Please use the following ETFs:IAU: iShares Gold Trust ETFVDE: Vanguard Energy ETFXLB: Materials Sector SPDR ETFDBC: Invesco DB Commodity Index Tracking FundCQQQ: China Technology Index ETFConstraints:i. Use all ETF products. (Weight of each ETF>= 2% )ii. No ETF is to have more than 40% weight in portfolioObjective: Maximize Expected Return, Minimize volatility, ie. MaximizeSharpe RatioStep 1: Collect historical price/return data for the ETFs over Jan-2018 to Dec-21 period.Step 2: Assume the Average Historical Return is the Expected Return for each asset (strong assumption) and Historical Volatility is the Expected Volatility (strong assumption).Step 3: Present the var-cov…

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"A financial investor has $31,000 to invest. The choices have been narrowed down to the following two options.-OPTION 1:Invest in a foreign bond that will mature in one year. This will entail an immediate brokerage fee of $100. For simplicity, assume that the bond will provide interest of $2,470, $2,130, or $1,527 over the one-year period and that the probabilities of these occurrences are assessed to be 0.29, 0.43, and 0.28, respectively.-OPTION 2:Invest in a $31,000 certificate with a savings-and-loan association. Assume that this certificate has an effective annual rate of 5.6%.Which form of the investment should the investor choose in order to maximize her expected financial gains? Enter the expected net gain (total return - initial investment - fee) of the preferred option."

2 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) SAFE RISKY INVESTMENT AMOUNTⓇ 40+ 40+ GOOD SCENARIO OUTCOME 45+ 80+ AVERAGE+ SCENARIO PROB OUTCOME 0.40* 0.40€ 42+ 45+ BAD+ SCENARIO PROB OUTCOME PROB 0.20 35+ 0.20 10+ 0.40€ 0.40+ b) a) Suppose I have utility function U(*) = (x)2. What is the expected utility from each investment? Which investment will I choose, if any? Show and explain your work and provide the intuition. c) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. d) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< +

You are currently a worker earning $60,000 per year but are considering becoming an entrepreneur. You will not switch unless you earn an accounting profit that is on average at least as great as your current Salary. You look into opening a small grocery store. Suppose that the store has annual cost of $150,000 for labor, $60,000 for rent and $30,000 for equipment. There is one-half probability that revenues will be $20,000 and a half probability that revenue will be $420,000   a. WHat is your accounting and economic profit? b. Will you quit your job and try your hand at being an entrepreneur? c. Suppose the government imposes a 25 percent tax on accounting profits: this tax is only levied if a firm is earning positive accounting profits. What will your after tax accounting profit be in the low revenue case?

You are currently a worker earning $60,000 per year but are considering becoming an entrepreneur. You will not switch unless you earn an accounting profit that is on average at least as great as your current Salary. You look into opening a small grocery store. Suppose that the store has annual cost of $150,000 for labor, $60,000 for rent and $30,000 for equipment. There is one-half probability that revenues will be $20,000 and a half probability that revenue will be $420,000   a. In the high revenue case?  what will your average after tax Accounting profit be? hat about your average after tax economic profit? will you Want to quit your job and try your hand at being an entrepreneur?  other things equal, does the imposition of the 25 percent profit tax increase or decrease the supply of entrepreneurship in the economy?

You are currently a worker earning $60,000 per year but are considering becoming an entrepreneur. You will not switch unless you earn an accounting profit that is on average at least as great as your current Salary. You look into opening a small grocery store. Suppose that the store has annual cost of $150,000 for labor, $60,000 for rent and $30,000 for equipment. There is one-half probability that revenues will be $20,000 and a half probability that revenue will be $420,000   a. In the low revenue Situation, what will your accounting profit or loss be? b. In the high revenue situation, what will your accounting profit or loss be? c. On average, how much do you expect your revenue to be?

You are evaluating the possibility that your company bids $150,000 for a particular construction job. (a) If a bid of $150,000 corresponds to a relative bid of 1.20, what is the dollar profit that your company would make from winning the job with this bid? Show your work. (b) Calculate an estimate of the expected profit of the bid of $150,000 for this job. Assume that, historically, 55 percent of the bids of an average bidder for this type of job would exceed the bid ratio of 1.20. Assume also that you are bidding against three other construction companies. Show your work.

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- Suppose you have some money to invest-for simplicity, $1-and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 w, into a bond mutual fund. Suppose that $1 invested in a stock fund yields Re after 1 year and that $1 invested in a bond fund yields R₂, suppose that R, is random with mean 0.08 (8%) and standard deviation 0.07, and suppose that R, is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between R, and R, is 0.25 If you place a fraction w of your money in the stock fund and the rest, 1 - w, in the bond fund, then the return on your investment is R = wRs + (1-w)Rp Suppose that w=0.5. Compute the mean and standard deviation of R (Round your response to three decimal places.) The mean is The standard deviation is (Round your response to three decimal places:)

QUESTION 24 A deck of 52 playing cards consists of 4 suites: clubs, spades, hearts, and diamonds. Each suite consists of 13 cards. Draw one from a deck of cards. Let A=a card "2" is drawn, B=a "diamond" card is drawn. Which is the value of P(A|B), i.e., {probability that the card drawn is "2" given that we have known it is "diamond"} ? 1/52 1/4 1/13 16/52

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