Consider an economy with three assets and two dates (t-0,1) and three states at t=1. Let [1 2 3 (1.4 X =| 2 4 p =|1.8 |1 3 1 P3 be the matrix of asset payoffs at t=1 and p the vector of asset prices at t=0. Suppose p;=2. (a) Is there an arbitrage? (b) If yes, find an arbitrage portfolio.
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- Consider a simple two-period economy with two possible states of the world in the second period. Two financial assets are traded and the matrix of returns is given by (columns refer to assets, rows to states of nature): [: ] 1 6. 1 4 (a) If the prices of assets 1 and 2 are given by 1 and 5, respectively, what are the risk-neutral probabilities in this economy? (b) Could prices 3 and 18 be the equilibrium prices for asset 1 and 2, respec- tively? (c) If the price of asset 1 is 3 and the risk-neutral probabilities are 2/3 and 1/3 for state 1 and 2, respectively, what is the no-arbitrage equilibrium price of the second asset?Assume you can invest in 2 projects whose payoff depend on the state of the economy. The profits from each project for each state of the economy are presented below. What are the expected payoffs of each project if there is a 30% chance of a recession and a 70% of no recession? Profit under recession Profit under normal conditions Project 1 |100,000 150,000 Project 2 50,000 240,000 Project 1: $130,000 and Project 2: $180,000 O Project 1: $135,000 and Project 2: $183,000 O Project 1: $135,000 and Project 2: $180,000 O Project 1: $130,000 and Project 2: $183,0001. Consider the Arrow's portfolio model with one risky asset and one risk-free asset. The von Newmann-Morgenstern utility functions of an investor is: u(w) = In w, where w represents wealth, and In natural log. Denote as a the amount invested in the risky asset. Let the initial wealth be $10,000, the interest rate of the risk-free asset 5%, and the probability distribution of the return of the risky asset X = (1%, 5%; 0.55, 0.45). 1.1 Write the equation of the expected utility of final wealth 1.2 Take the first derivative of the expected utility with respect to a. 1.3 Now evaluate the first derivative, that you found in 1.2 above, at a = 0. What can you conclude about the optimal value of a? Why is that so? %3D %3D
- D7 You run an oil company that wants to extract an oil reserve. The total stock of oil in the reserve is 600 barrels. You must sell all of the oil in two time periods, so the quantity extracted will be q1 +q2 = 600. The price per barrel you can sell the oil for is pt = 710 − 1 2 qt in each period. The cost of extracting a single barrel is not constant, but increases as more oil is extracted in a period, c(qt) = 1 2 qt. If the interest rate is 5%, how much oil will you extract in periods 1 and 2 if you wanted to maximize profits.Suppose you observe that short-term interest rates are higher than long-term interest rates. a. What expectations must people have regarding future interest rates? b. Why might the above relationship signal a recession? Why might it not? c. What will the yield curve for this problem look like? Q4 Why is the fact that stock prices follow a random walk a signal of stock market efficiency? What would have to be true if stock prices did not follow a random walk?Using Treasury securities, design a trading strategy that makes a profit if the yield curve flattens, i.e., if y10 – Y2 decreases. You may use the following approximation: Y2,t = Levelt – 0.1Slopet Y10,t = Levelt + 0.4Slope: where Levelț is the level factor of the yield curve and Slope is the slope factor (so, Level and Slope are the first two principal components). Design the trading strategy such that it is immune to changes in the level of the yield curve. Further, size the trades such that for every basis point decrease in the slope factor, the strategy makes $10,000. For the quantitative calculations, you may ignore transaction and financing costs. Furthermore, you may use the following information: 2-year T-note 10-year T-bond Yield 1.6% 1.8% Modified duration 1.96 9.11
- Consider an investor based in the FC that invests in the DC. To hedge the FX risk the FC investor could (select all that are true): A. Engage in a swap for DC at the investment's open date to FC at the invesment's close date B. Engage in a forward DC to FC with an unnknown counter party and no escrow (margin) C. Write a call option FC to DC at today's spot FX rate D. Write a put option FC to DC at today's spot FX E. Exercise a futures contract DC to FC at the date of the investment return trip F. Purchase a futrues contract FC to DC for the return trip Detailed Explanation Please, Thank you!A firm goes to the markets to raise capital. The investor can either invest V₁ on the firm or buy government bonds. If she invests, the expected value of the dividend she receives the following period is Et[Dt+1]. Where Et[] denotes the mathematical expectation, taken at time, t. If she buys a government bond, and receive a gross return (1 + r) for sure. 1. Let Et [Vt+1] denote the expected value of the stock the following period, explain why this is not the only return that the investor can expect from owning the stock. 2. Write down an expression for the gross return on the stock. [Hint: This is a ratio.] 3. Suppose investor's objective is to maximize their expected return. If the return from bonds is higher than the expected return from stocks, will they buy stocks or bonds? How about the other way around? 4. Since investors hold both stocks and bonds, what must be true about the expected return of stocks and bonds in equilibrium? Show that this implies the following no arbitrage…Hi there, I need help solving a problem and am unsure how to go about solving the question. It is a practive question from a textbook and am trying to understand it further. I need a bit more help solving 1 a) and b). I have already obtained the values of the expected return at t = 0 and the expected utilities at t = 0 for both scenarios (direct investing) and (depositing with the bank). Thanks Here is the question: Consider the basic setup of the Diamond-Dybvig (1983) model. Specifically, thereare three periods, denoted t = 0, 1, 2, a single consumption good, and an illiquidinvestment opportunity that pays gross return 1.1 if liquidated at t = 1, or grossreturn 2.2 if liquidated at t = 2. There are 30 people in the economy, each endowed with 1 unit of the consumptiongood at t = 0. At t = 1, exactly 11 will randomly realize that they need to consumeat t = 1 (the early consumers), the remaining 19 people will need to consume at t = 2(the late consumers). The utility derived from…
- (Ch7) Historically, the default rate on a commercial loan is 20 percent. If a bank makes 100 commercial loans, what is the approximate probability that more than 25 loans will result in default? (hint: use the normal approximation to the binomial. And, by continuity correction, you should use 25.5 as the new cutoff.) Question 2Select one: a. 0.0668 b. 0.0838 c. 0.2000 d. 0.0336Assume that the economy can experience high growth, normal growth, or recession. Under these conditions, you expect the following stock market returns for the coming year: Probability State of the Economy High Growth Return 0.2 +30% Normal Growth 0.7 +12% Recession 0.1 -15% a. Compute the expected value of a $1,000 investment over the coming year. If you invest $1,000 today, how much money do you expect to have next year? What is the percentage expected rate of return? Instructions: Enter dollar values rounded to the nearest whole dollar and percentages rounded to one decimal place. The expected value is $ 1129 and the expected rate of return is 12.9 %. b. Compute the standard deviation of the percentage return over the coming year. Standard deviation 11.7 % c. If the risk-free return is 7 percent, what is the risk premium for a stock market investment? Risk premium 17.5 %Suppose that, holding yield constant, investors are indifferent as to whether they hold bonds issued by the federal govemment or bonds issued by state and local governments (that is, they consider the bonds the same with respect to default risk, information costs, and liquidity) Suppose that state governments have issued perpetuities (or consoles) with $78 coupons and that the federal govemment has also issued perpetuities with $78 coupons. If the state and federal perpetuites both have after-tax yields of 8%, what are their pre-tax yields? (Assume that the relevant federal income tax rate is 31.13%) * The pre-tax yield on the state perpetuity will be______________% * The pre-tax yield on the federal perpetuity will be_______________%