Consider an economy with three assets and two dates (t-0,1) and three states at t=1. Let12 3(1.4X =| 214p=|1.8131P3be the matrix of asset payoffs at t=1 and p the vector of asset prices at t=0.Suppose p3=2.(a)Is there an arbitrage?(b)If yes, find anage portfolio.Suppose p3=1.2.(c)Does an arbitrage portfolio exist?you create a portfolio with payoff of (120, 190, 220) at t=1 and what is the t=0price of such a portfolio?(d)Can(e)Determine the (implicit) risk free rate in this economy

Arbitrage is the concurrent buy and offer of similar resources in various business sectors to…

Answered: Consider an economy with three assets…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider an economy with two dates (t=0,1) and at t=1 there are three states. The following three stocks are traded: x1=(10,0,30) x2=(0,20,40) x3=(20,20,0) The t=0 prices of these stocks are given as follows (p1, p2, p3)=(12, 14, 8) (a) Is there an arbitrage? Suppose an investment firm sells options (b) What is the t=0 price (premium) of a call option on stock 2 with exercise price E=8? (c) What is the t=0 price (premium) of a put option on stock 1 with exercise price E=12? Suppose a start-up company wants to go public. The firm has total costs of $100,000 at date t=1 and sales of $140,000 in state 1, $130,000 in state 2, and $220,000 in state 3. The firm wants to issue 1,000 IPO shares. (A share is endowed with a cash flow right of 0.1% of the total profits of the firm.) (d) The underwriter suggests an IPO price of $60 per share. Will this IPO be successful, i.e. will there be a positive demand for the shares?
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_______________%
Excercise: Consider the Diamond-Dybvig model of bank runs utility function is given by U(c) = √c and that the parameter values are R = 4, discount factor ß = 1/3, and π = 2/5 A) How much do type-1 agents and type-2 agents consume in periods 1 and 2 under autarky, i.e., if there are no banks, insurance companies, or markets? What is the ex-ante expected utility that they derive in this scenario? B) How much do type-1 agents and type-2 agents consume in periods 1 and 2 in the "good" banking equilibrium? What is the ex-ante expected utility that they derive in this scenario? C) How many agents are able to execute their claims in period 1 (i.e., withdraw the maximum amount they have been promised) in the bank run equilibrium?
Under the Pure Expectations Theory, if these investors believe that interest rates will rise in the near future, a. Two statements are correct. b. they will make up for the lower short-term yield when the short-term securities mature, and they reinvest at a higher rate (if interest rates rise) at maturity. c. All statements are correct. d. the large supply of funds in the short-term market will force annualized yields down, while the reduced supply of long-term funds forces long-term yields up. e. they will invest their funds mostly in the short-term risk-free securities so that they can soon reinvest their funds in securities that offer higher yields after interest rates increase. f. their actions cause funds to flow into the short-term market and away from the long-term market. g. Three statements are correct.
Consider the Diamond-Dybvig model of bank runs utility function is given by U(c) = √c and that the parameter values are R = 4, discount factor ß = 1/3, and π = 2/5 A) How much do type-1 agents and type-2 agents consume in periods 1 and 2 under autarky, i.e., if there are no banks, insurance companies, or markets? What is the ex-ante expected utility that they derive in this scenario? How much do type-1 agents and type-2 agents consume in periods 1 and 2 in the "good" banking equilibrium? What is the ex-ante expected utility that they derive in this scenario? How many agents are able to execute their claims in period 1 (i.e., withdraw the maximum amount they have been promised) in the bank run equilibrium?
Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 14%. According to the capital asset pricing model: a. What is the expected return on the market portfolio?b. What would be the expected return on a zero-beta stock?c. Suppose you consider buying a share of stock at a price of $30. The stock is expected to pay a dividend of $4 next year and to sell then for $31. The stock risk has been evaluated at β = -0.5. Is the stock overpriced or underpriced?
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n)/n . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. What are risk preferences of this investor, are they risk-averse, risk- neutral or risk-loving? Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases?.
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = x^n/n . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. 1. What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? 2. Find A as a function of w. 3. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? 4. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? 5. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = X^n/n . There is a safe asset (such as a US government bond) that has a net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth?
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!
13 Using the spot curve, an analyst computes the following implied forward rates: Implied Forward Rates 0y1 0.25% 1y1 1.05% 2y1 1.30% 3y1 1.60% 4y1 1.70% Construct an interest rate tree using a binomial model using all the implied forward rates assenting a 35% standard deviation. PLEASE SHOW WORK IN EXCEL.
Explain the micro factors and macro factors which affect the cost of money? What are the conclusions of Beta stability tests and Tests based on the slope of the SML? (hint: refer to Ch 25 in the textbook) Suppose Asset A has an expected return of 10 percent and a standard deviation of 20 percent. Asset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between A and B is 0.35, what are the expected return and standard deviation for a portfolio comprised of 40 percent Asset A and 60 percent Asset B? 1) Calculate what is called Beta, , from the table below (hint : use excel for calculation for beta) and then 2) make the equation with beta and intercept to calculate the expected return of i asset. (hint; use SML equation in Chapter 25 and rRF=5%, M =9% ) Year M i 1 16% 19% 2 -6% -11% 3 12% 17% 4 14% 19% Calculate the expected return of portfolio and standard deviation of portfolio…

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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.