Suppose that in a two-period Arrow-Debreu economy with three states, the state probabilities are 7₁ = 0.1, 7₂ = 0.55, 73=0.35 and the state prices are 9₁ = 0.2, 9₂=0.5, 93 = 0.8 for states 1, 2, and 3 respectively. Assume that an asset has the state-contingent dividend given in the following table, and the observed price of the asset is 4.1. State-contingent dividend State 2 State 3 Asset's dividend 3 2 According to information above, which one of the following statements regarding arbitrage opportunities is correct? State 1 5 OA. In this case, arbitrage opportunities do not exist. OB. In this case, arbitrage opportunities exist because the asset is over-priced.

Suppose that in a two-period Arrow-Debreu economy with three states, the state probabilities are 7₁ = 0.1, 7₂ = 0.55, 73=0.35 and the state prices are 9₁ = 0.2, 9₂=0.5, 93 = 0.8 for states 1, 2, and 3 respectively. Assume that an asset has the state-contingent dividend given in the following table, and the observed price of the asset is 4.1. State-contingent dividend State 2 State 3 Asset's dividend 3 2 According to information above, which one of the following statements regarding arbitrage opportunities is correct? State 1 5 OA. In this case, arbitrage opportunities do not exist. OB. In this case, arbitrage opportunities exist because the asset is over-priced.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose two asset returns are described by a two factor model, n = 0% + 11 + 1.82 + e1 2 = -1% + 2/1 + 0.52 + e2 where the volatility of first factor is 30%, the volatility of the second factor is 10%, and the correlation between the two factors is 0.5. Suppose also that the volatilities of the error terms ej and ez are both 10%. What is the covariance of n and r2 ? (Nearest 0.0001).
2. Suppose that you have a riskfree asset and N risky assets for investment. The rate of return on the riskfree asset is r,, while the (Nx1) vector of the rate of return on the N risky assets is r, which is multivariate normal, i.e., r N(u, E). Your utility function for a portfolio that consists of the riskfree asset and the N risky asset is u(r,)=r,-=o, 2 Suppose that the sum of investment proportions on the riskfree and risky assets is one. Answer the following question. A. What is your optimal investment proportion in the risky assets? How is your investment on the riskfree asset affected by different values of 2? B. Suppose that there is only one risky asset i. Show the effects of the Sharpe ratio (4,/0, ) on the investment proportion in the risky asset.
There is one period. Assume a representative agent with utility function U(ct) = αc_t − βc^2_tassume the following: α = 100, β = 1, and δ = 0.97. Consumption at t = 0 is C0 = 24. At t = 1 one of two states θ1 and θ2 eventuate with probability π1 = 0.5, and π2 = 0.5,respectively. There are two complex securities s^1 and s^2.s^1 has a payoff of 23 in θ1 and 27 in θ2.s^2 has a payoff of 20 in θ1 and 32 in θ2.What is the stochastic discount factor mt+1? hint: Recall mt+1 =δU′(ct+1)/U′(ct)
Consider 1-factor model and assume that the price of a certain fixed income security P(y) for y=9%, 9.05% and 8.95% is given by P(0.09)=$5,000; P(0.0905)=$4,980; P(0.0895)=$5,030. Find the estimate for DV01, Duration, and Convexity of this security. Keep at least 4 decimal digits while performing your calculations.
The variance ratio (VR) can be used to determine whether returns satisfy the efficient market hypothesis (EMH). Let n = 5 and r5,t be the five period log return at time t, where t = 1, 2,..., T. 1. Express (r5,t — Ã5) in terms of deviations of the relevant one period log returns from their respective means. Denote 75 to be the mean of the five period log return.
Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? O FV = PV / (1+1)N O FV = PV + (PV XIX N) O FV = PV x (1 + I)N Simple interest? OFV = PV + (PV XIX N) O FV = PV XIX N O FV = PV/(PV XIX N)
Consider the calculation of an external rate of return (ERR). The positive cash flows in the cash flow profile are moved forward to t = n using what value of i in the (F|P,i,n–t) factors? a. 0 b. The unknown value of ERR (i′) c. MARR d. IRR.
Annuity Present Value Inputs Payment Discount Rate/Period Number of Periods Present Value using a Time Line Period Cash Flows Present Value of Each Cash Flow Present Value Annuity Present Value using the Formula Present Value Annuity Present Value using the PV Function Present Value
Suppose that we can describe the world using two states and that two assets are available, asset X an asset Y. We assume the asset’s future prices have the following distribution State Future Price Asset X Future Price Asset Y 1 $25 $50 2 $20 $40 The values of the unit claims implied by these assets are such that: A. C1 and C2 cannot be determined B. C1=1 and C2=1 C. C1=1, but we cannot determine C2 D. C1=5/4 and C2=5/4
Capital asset pricing model (CAPM) For the asset shown in the following table, use the capital asset pricing model to find the required return. (Click on the icon here in order to copy the contents of the data table below into a spreadsheet.) Risk-free rate, RF 1% The required return for the asset is %. (Round to two decimal places.) C Market return, m 5% Beta, b 0.5
Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO
What is the risk neutral probability of state 1?

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