4. Measuring Risk: Suppose you have a risk free asset with return ry = 5%. Additionally, t whole market return is rm = 7%. Find the risk adjusted expected return for the following assets. (a) Asset 1 has a risk relative to the rest of the market of 31 = 1. (b) Asset 2 has a risk relative to the rest of the market of 3₂ = 5. (c) Asset 3 has a risk relative to the rest of the market of 33 = -2.
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- SHOW IN EXCEL SHOW EACH PROCESS IN EXCEL Gasoline EV Purchase Cost $50,000 $80,000 Annual - Maintenance $5,000 $2,500 Annual Fuel $7,500 $3,000 Service Life Probability Service Life Probability 55% 52% 6 10% 65% 7 25% 7 10% 8 35 % 8 25% 9 20% 9 50 % 10 5 % 10 8% a) (5 Points) What is the expected value of the present worth and expected value of the standard deviation of each option? b) (5 Points) Which option should be chosen, and why? c) (5 Points) If the company' s MARR is 20%, which option would they choose and why? d) (5 Points) What value of the MARR makes the company indifferent between choosing gasoline or electric vehicles?(Measuring risk and rate return) Given the following holding-period returns, calculate the standard deviation for the market. answer is 6.02 Month Champ Inc. Market 1 2.8% 1.8% 2 3.2% 1.2% 3 9.0% 11.0% 4 -2.6% -1.0% 5 -2.9% -4.7% 6 12.0% 8.0%1. In a one-period model, the share price starts at $12 and in one year's time is either $24 or $6. Simple interest on USD is 20% per year. (a) Construct a replicating portfolio for a one year call option with strike K = $15. (b) Explain how The Law of One Price allows you to calculate the pre- mium of the call option. (c) Construct risk-neutral probabilities for the model for the share price and verify the risk-neutral value for the call option is the same as the value given by the replicating portfolio. |3D
- 5. Exercise 2.6 Two investments have the following expected returns (net present values) and standard deviation of returns: Project Expected Returns ($) Standard Deviation ($) A B Which project is riskier? Project B Project A 50,000 250,000 30,000 125,0001 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) P 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 a) What are the expected payoffs (E(x)) and standard deviations for each investment? b) Suppose I have utility function U(*) = √(x). What is the expected utility from each investment? c) Which investment will I choose, if any? Show and explain your work and provide the intuition.< d) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. e) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< 43 A ✔ →2. Airtight Manufacturing produces plastic cases that utility companies buy to protect electronic components on utility poles from weather damage. (a) The protective case currently used by utility companies has a 0.045 probability of cracking or breaking in any given year. When a protective case cracks or breaks, the utility company incurs a $800 expense to replace the case. What is the expected value of the utility company’s repair costs per protective case? Show your work. (b) Airtight has recently developed a stronger material for its protective case. The use of this stronger material reduces the case’s probability of cracking or breaking and serves as a differentiating factor for estimating this product’s VTC. Use the product-needs matrix described in the course to classify this differentiating factor. What type of product characteristic is it? What type of customer need does it satisfy? Justify your answers. (c) If this stronger material enables Airtight’s new protective…
- (ii) Jack, initially, has a wealth (W) equal to 2000 and will lose 1200 if his investment in a risky bond is unsuccessful and will gain 1200 if it is successful. The probability that the investment is successful is 0.75 and his utility function is given by U(W) = W^0.5. (a) Is this bond a fair bond? (b) What is Jack;s expected utility? (c) Suppose, there is a secured non-risky. gold bond. How much return should this gold bond offer, so that Jack chooses the gold bond instead of the risky bond.Question 8 The January 2023 S&P 500 cash index is 3950 points while the S&P 500 futures March 2023 index is 4000 and the contract value of each index point is $150. You are convinced the futures market will fall 20% by expiry. You are only prepared to buy or sell one futures contract.EXTRA RISK PROBLEMS Sanck A Sk Expected Retun Standand Deviatim 12 75 16 Comelation cnefficieit wth the Market Comelation coeficient with Stock B Risk fre e 2% Expected etu on the Market 12 Standund deviation of the Market E 1. What is the expected retum on a portfolio comprised of S60o00 of Suck A and S4000 of Sock B7 2. Whe is the Stnderd deviation of this portidio? 3. Does it make sense to combine these two in this way? Pease explain why. 4 What is the ocoefficient of variation for Stock A? What is the coefficient of variation for Stock B?
- A 40-year-old man in the U.S. has a 0.244% risk of dying during the next year. An insurance company charges $300 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar. Expected Value: S-55 Question Help: Video Submit Question Question 5 x for the year Message instructor Based on historical data, an insurance company estimates that a particular customer has a 2.6% likelihood of having an accident in the next year, with the average insurance payout being $2700. If the company charges this customer an annual premium of $180, what is the company's expected value of this insurance policy? S Question Help: Message instructorThe owners of a small manufacturing concern have hired a vice president to run the company with the expectation that he will buy the company after five years. Compensation of the new vice president is a flat salary plus 75% of the first $150,000 profit, and then 10% of profit over $150,000. Purchase price for the company is set at 4.5 times earnings (profit), computed as average annual profitability over the next five years. a. Plot the annual compensation of the vice president as a function of annual profit. b. Assume the company will be worth $10 million in five years. Plot the profit of buying the company as a function of annual profit. c. Does this contract align the incentives of the new vice president with the profitability goals of the owners? d. Redesign the contract to better align the incentives of the new vice president with the profitability goals of the owners.Determine whether or not to stock a large supply of steel. There is uncertainty in the price of steel. Based on past history the following data are available Price (future) Prob (Price) PW if stocked PW if not stocked High 0.3 100000 0 Medium 0.5 -10000 0 Low 0.2 -50000 0 What is the probability that stocking steel will result in a negative present worth (PW)?