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Consider an economy with three states which occur with probability (0.2, 0.4, 0.4)

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Exercise Set 3;Due Thursday, 10/9;This problem set consists of four questions. You can obtain a maximum of 40 points.;Question 1 [8 points];Suppose a risk neutral agent has $100,000 today that he wants to save for one year. Compare;the following three savings plans.;Bank A offers a standard savings account with 4% p.a. (per annum).;Bank B offers the following alternative;There is a basis interest rate of 1% p.a. and 50% participation on the performance of the;S&P500. The maximum interest rate is capped at 8% p.a. (E.g. If the S&P increases by 6%;there is a bonus of 3% so that the total return is 4% p.a. If the return of the S&P is 20%, the;plan has a return of 8%. Note, if the S&P has a negative return, the interest rate remains at;1%.);Bank C offers the following alternative;There is a basis interest rate of 1% p.a. and 40% participation on the performance of the;S&P500. The maximum interest rate is capped at 10% p.a.;Suppose the S&P has 1000 points at t=0. At t=1 it can have {900, 990, 1000, 1020, 1040;1100, 1120, 1230, 1300, 1400} points with equal probability.;(a);Draw the payoff of alternative B as a function of the S&P (with the S&P performance;on the X-axis, and the (total) return of the plan on the Y-axis.) [2p];(b);The agent maximizes the expected amount at t=1. Which plan is best? How much can;the agent spend in expectation at t=1 if he chooses the best one? [6p];1;Question 2 [14 points];Suppose Real Option Inc. has a product that generates the following cash flow.;At t=1, the demand can be high or low. There is a probability of 0.6 that demand is high. If;demand is high (low) the cash flow is CFH=400 (CFL=200).;At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at;t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises;with probability 0.2. If demand is high (low) at t=2 then CFH=400 (CFL=200). The (risk;adjusted) interest rate for this project is 10%.;(a);Draw the event and decision tree. [3p];(b);What is the market price (expected value) of Real Option Inc. at t=0? [3p];Now suppose Real Option Inc. can rent a platform to run a marketing campaign. For this;purpose Real Option Inc. must sign a two year contract with the platform provider. The costs;for using the platform are 200 per period. Marketing itself does not cost anything and has the;following effect. In the high demand state, marketing doubles the demand. In the low demand;state it has no effect.;(c);Should Real Option Inc. rent the platform at t=0 and run the marketing campaign? [4p];Contracts can only be signed at t=0. But suppose Real Option Inc. can terminate the contract;after the first year by paying a fine of 20.;(d);What is the optimal strategy of Real Option Inc. and the maximum market value of the;firm? [4p];Question 3 [10 points];Consider the expected return and standard deviation of the following two assets;Asset 1;E[r1]=0.1;und 1=0.2;Asset 2;E[r2]=0.3;und 2=0.4;(a);Draw (e.g. with Excel) the set of achievable portfolios for the cases: (i) 12=1, (ii);12=0. [4p];(b);Suppose 12=0. Which portfolio has the minimal variance? What is the variance and;expected return of that portfolio? [6p];2;Question 4 [8 points];Consider an economy with three states which occur with probability (0.2, 0.4, 0.4). Suppose a;firm has a project which generates the state dependent cash flows (100, 200, 200) at t=1. The;investment costs are 160 at t=0. The firm owns this money. The market portfolio generates;the payoff (200, 250, 300) and has an expected return of 10%. The risk free rate is 2%.;Suppose the CAPM holds.;(a);What is the beta of this project? [4p];(b);Explain whether the firm should conduct the project. [4p];3;View Full Attachment;Additional Requirements;Min Pages: 1;Max Pages: 3;Level of Detail: Show all work

 

Paper#30152 | Written in 18-Jul-2015

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