Suppose that we can describe the world using two states and that two assets are available, asset Kand asset L. We assume the assets' future prices have the following distributions: State Future Prices Asset K Future Prices Asset L Kat state 1 = $25 Lat state 1 = $21 Kat state 2 = $20 Lat state 2 = $27 Let K(1) = $20 denote the time O price of asset K and L(1) = $19 the time 0 price of asset L. (a) Assuming no arbitrage opportunities, what are the values of the unit claims, at time 0? (b) What is the risk-free rate of return that must exist in this market?
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- Suppose that we can describe the world using two states and that two assets are available, asset K an asset L. We assume the asset’s future prices have the following distribution State Future Price Asset K Future Price Asset L 1 $55 $60 2 $45 $30 The current price of asset K is $50, and the current price of asset L is $50. You plan to buy a home for $100,000 in the future. To guarantee that you will have the money, what would you buy/sell today to accomplish this, and what would it cost today?3. Consider a world in which production of a good or service consists of a number of definitive tasks, which must all be performed correctly for the product to have positive value. Each task is filled by a single worker i whose skill level qirepresents the probability the worker performs her task correctly. Mathematically, if there are n tasks in the production of a good, and average production per worker with one unit of capital is 1 when all tasks are performed correctly, the production technology can be represented as: A) Give an example of an industry for which this might be a good model of production. What does this production function imply about the tradeoff between quality and quantity of labor in a given task? In this, how does it differ from a Cobb Douglas production function? B) Find the marginal product of increasing the skill of the ith worker. Suppose now there were two firms in the same industry that will bid for workers, and can pay them differentially according to…INV 1 5aiv Suppose that you have the following utility function: U=E(r) – ½ Aσ2 and A=3 Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum. You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows: ETFUS : E(r)= 0.070584 standard deviation = 0.173687 ETFCDA : E(r)= 0.073763 standard deviation = 0.16816 Covariance between ETFUS and ETFCDA = 0.02397 What is the standard deviation for ETFCDA?
- 3.Suppose that you observed the following set of data: Average Business School tuition: $30,000 Average Salary for non-MBA’s: $50,000 per year Average MBA salary: $90,000 per year. The length of an MBA program is 2 years and is assumed that and MBA will have a working career of 20 years after graduation. Further, suppose that, instead of going to get an MBA,2you could keep your current non-MBA job and invest what you could have used to pay for tuition, risk free, at 4% per year.SHOW ALL YOUR WORKING.a) Is this set of data consistent with market equilibrium? Explain.b) If your answer to (a) is no, how will markets adjust?In equilibrium U′(Yt)qet = δEt[U′(Yt+1)(qet+1 + ˜ Yt+1)] holds. Assume the following: . Infinite periods . δ = .97 . The agent follows ln utility . There are 2 futures states where (Y 1, Y 2) = (2, .50) which evolve based on transition matrix T. . The transition matrix T is: T = [.60 .40 .40 .60] (hint: Answering this question involves solving the system of equations: U′(Yt)qet = δEt[U′( ˜ Yt+1)(˜qt+1 + ˜ Yt+1)] U′(Yt)qet = δEt[U′( ˜ Yt+1)( ˜ Yt+1)] + δEt[U′( ˜ Yt+1)(˜qt+1)] What are the 2 equilibrium conditions? What is the price of q(2) and q(.50)?Seung’s utility function is given by U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work. (a) What is Seung’s expected utility without insurance? (b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it? (c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?
- 1.a. What is the purpose of understanding: .contingent claims? .contingent strategies?b. How is the concept of "states of the world" useful in making decisions underrisk? Under uncertainty?c. What is meant by a unit contingent claim and why is this concept useful infinancial economics?d.Suppose that we can describe the world using two states and that two assets areavailable, asset K and asset L. We assume the assets' future prices have thefollowing distributions:INV 1 5ai Suppose that you have the following utility function: U=E(r) – ½ Aσ2 and A=3 Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum. You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows: ETFUS : E(r)= 0.070584 standard deviation = 0.173687 ETFCDA : E(r)= 0.073763 standard deviation = 0.16816 Covariance between ETFUS and ETFCDA = 0.02397 What is the portfolio expected return for ETFUS?suppose that Charlie faces the same choice, but he always integrates the gains or losses of both days regardless of how he chooses to check his investment. Also, assume now that if he decides to check at the end of each day, he has an additional option of pulling all his money out of the stock market at the end of the first day if he wishes. Would Charlie pull his money out at the end of the first day, if he finds that his investment has gone up by $3000? Explain. Would Charlie pull his money out at the end of the first day, if he finds that his investment has gone down by $1000? Explain. Given the investment decisions in Questions (2) and (3), which will he prefer, to check at the end of each day or to check only at the end of the second day?
- The interest rate is 6 percent a year and you expect to receive $1,000 next year and the following year. What is the present value of $1,000 to be received next year? What is the present value of $1,000 tobe received in two years? The present value of $1,000 to be received next year is $ ____. >>>>Answer to 2 decimal places.The demand ? (in billions of £) for a bond with coupon rate 5% and face value ?? = 1000, and two years to maturity as a function of its price ? is ? = 4000 − 2?. The supply in (billions of £)asafunctionofthepriceofthebondis ? = 2?+ 400. There is a business cycle expansion, so both supply and demand shifts. After the shift, the new demand curve is given by: ?=4000+?−2? ,whereas the new supply curve is ?=2? + 200. For which values of ? will the interest increase/decrease? Which values of ? are in line with empirical data?A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?