Assume the one period binomial model with initial share price £400, up and down factors u = 1.25, d = 0.9 and interest compounded at nominal rate (per time period) of 7%. Consider an option with payoff (S(0) + S(1))/2. The replicating portfolio for this option at time 0 will have shares and pounds in a bank. State your answers to three significant figures.

Assume the one period binomial model with initial share price £400, up and down factors u = 1.25, d = 0.9 and interest compounded at nominal rate (per time period) of 7%. Consider an option with payoff (S(0) + S(1))/2. The replicating portfolio for this option at time 0 will have shares and pounds in a bank. State your answers to three significant figures.

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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A share price is modelled via a two-period binomial model with initial stock price S=40, up/down multiplication factors u = per time period r = 4%. and d = and interest rate Explain Does this model satisfy the no-arbitrage assumption? Write 0 if your answer is 'no' and 1 if your answer is 'yes'. Answer: your argument in your hand-written answer (b) Calculate the risk-neutral probabilities of up and down movements in the share price. State your answer to three valid digits. Answer: P = Pd= (c) to three valid digits. Answer: Determine the no-arbitrage price of a European call option on the share with strike price K = 70 and expiry time T = 2. State your answer Explain your calculation steps in your hand-written answer.
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 O in order to copy the contents of the data table below into a spreadsheet.) ne Risk-free Market rate, R return, rm Beta, b nts 4% 0.7 1% The required return for the asset is %. (Round to two decimal places.) eТext edia Librai ial Calculat er Resource Enter your answer in the answer box and then click Check Answer. Check Answer mic Study ules Clear All All parts showing 10: DExercise(14); ools > This course (Introduction to Finance (FIN-101-D02) Distance Spring 2021) is hased on Zutter/Smart Princinles of Managerial Finance Rrief Re 4/13 O Type here to search insert
Suppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.
Let S = $100, K = $95, \sigma = 30%, r = 8%, T = 1, and \delta = 0. For simplicity, let u = 1.3, d = 0.8 and n = 2 (that is, 2 periods). When constructing the binomial tree for the European call option, what is A (Stock Share Purchased in the replicating portfolio) at the first node (Time 0)? Question 11 options: 0.1789 0.3886 1.0000 0.2550 0.6912
You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.
1. Consider a one period binomial model. Suppose So = 1 att = To; and Su = 2 and Sd = ½ at time T₁. If we assume the risk free rate R is 1.2, compute the current value of a European put with strike K = 1. Please round your answer to 2 decimals. Enter answer here 2. Compute the number of units of stock we need to short in order to replicate the option in the previous question. Please round your answer to 2 decimals. Enter answer here 3. Use Black-Scholes Formula to calculate the call price of a European call option with: So = 20, K = 20, r = 5%, c = 0,0 = 40%, T = 5; (round to two decimal digits).
Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .
8. Assume the risk-free rate is 6.7% and the expected return on the market portfolio is 7.8%. Use the capital asset pricing model (CAPM) to find the required return for each of the securities in the table here, 7. Review On Click the icon to see the Worked Solution. The required return for investment A is %. (Round to one decimal place.) The required return for investment B is %. (Round to one decimal place.) The required return for investment C is %. (Round to one decimal place.) The required return for investment D is %. (Round to one decimal place.) The required return for investment E is %. (Round to one decimal place.) 7: Data Table (Click on the icon here in order to copy its contents of the data table below into a spreadsheet.) Security Beta A 1.34 в 0.93 0.13 0.96 E 0.67
Suppose that you have estimated the CAPM betas for the equity shares of the following two firms: Levi Strauss & Co. ( NYSE: LEVI): \beta ^ LEVI = 1.10 Tesla Inc. (Nasdaq: TSLA) : \beta ^ TSLA = 1.90 Assume that the risk - free rate is estimated at 4%, stable over the entire CAPM estimation period, and will remain in the foreseeable future. Answer questions a) and b) below. (Lecture notes p.12, pp.15-17) Suppose the expected return on S&P 500 index, a proxy for the market portfolio, is estimated at 17%. Find the CAPM required returns on equity shares of Levi's and Tesla, respectively. Answer (show the steps/calculation toward your results): Suppose the market risk premium is estimated at 9%. Find the CAPM required returns on equity shares of Levi's and Tesla, respectively. Answer (show the steps/calculation toward your results):
You're considering purchasing Proctor and Gamble Stock. Suppose the risk-free interest rate is 5.0% and the stock market's expected return is 13.50%. Also, suppose that if the stock market's value rises by 1%, stock in Proctor and Gamble typically rises by 1%. a. What is the percentage of Proctor and Gamble's risk premium? c. What is the correct discount rate to use according to the Capital Asset Pricing Model (CAPM) when analyzing the present value of future cash flows from this stock?
Consider a one-period model with N = {1,2,3} and two risky assets S1, S2 whose with current prices are 71 = 42 and 12 = 23 respectively. At time one, the price of S1 is believed to be either 44, 43, or 40 while the price of S2 is believed to be either 27, 22, or 20. Suppose that the risk-free interest rate is 3%. What is the unique risk-neutral probability measure Q in this situation? Select one: О а. Q(1) — 0.35, Q(2) — 0.27, Q(3) — 0.38 O b. Q(1) = 0.63, Q(2) = 0.34, Q(3) = 0.03 Ос. Q(1) — 0.25, Q(2) — 0.62, Q(3) — 0.13 O d. Q(1) = 0.35, Q(2) = 0.62, Q(3) = 0.03
Consider the discrete-time binomial tree model with three periods of length 1, i.e. T = 3 and t = 0, 1, 2, 3. In each period the price can move up or down, St+1 is either uSt or dSt. Assume that the factor for moving up is u = 4/3, the factor for moving down is d = 3/4, and that the interest rate is r = 0.0. The initial stock price is So = 1. (a) Compute the price process (i.e. prices at all times and states) for a European Put option on the stock with strike price K = 1 and maturity T = 3. (x - ž) (b) Compute the price at time t = 0 of the Australian option K with ST K = 1. Note: As this option is path dependent, you will not be able to use the recursive method, nor will you be able to use the CRR formula.

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