Consider a XYZ stock index spot price is 69 and 7-months forward price is 70. The continuously compounded dividend yield and risk-free interest rate are 3% and 5% respectively. Market maker could take arbitrage opportunity by (long/short) forward contract and (long/short) synthetic forward contract which includes (buying/selling) stock and (borrowing / lending) money.

Consider a XYZ stock index spot price is 69 and 7-months forward price is 70. The continuously compounded dividend yield and risk-free interest rate are 3% and 5% respectively. Market maker could take arbitrage opportunity by (long/short) forward contract and (long/short) synthetic forward contract which includes (buying/selling) stock and (borrowing / lending) money.

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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Forward prices of the form Fo = S,e"" are sometimes referred to as “risk-adjusted expected future spot prices". If a stock's expected annualized log return is a (i.e. E[Sr] Soear, or – In ("5") = a), show that the expected annualized log return over the period So t = 0 → T (i.e. the rate of appreciation in F) on a forward contract with maturity T years written on that stock must be equal to the risk premium a – r, where r is the annualized risk-free rate. Explain the surprising result that an asset that requires zero initial
b) You are given the following information about Stock X and the market: The annual effective risk-frec rate is 5%. The expected return and volatility for Stock X and the market are shown in the table below: Expected Return Volatility Stock X 5% 40% Market 8% 25% The correlation between the returns of stock X and the market is -0.25. Assume the Capital Asset Pricing Model holds. Calculate the required return for Stock X and determine if the investor should invest in Stock X.
A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.
Assume that the risk-free and rate is 5.50% and the market risk premium is 7.75%. What is the expected return for the overall stock market (rm)?
3) Suppose that the price of a non-dividend-paying stock is $27, its vo itility is 20%, and the risk- free rate for all maturities is 6% per annum. Provide a table showing the relationship between profit and final stock price for a butterfly spread using European put option with strike prices of $20, $25, and $30 and a maturity of one year. Ignore the impact of time a e of money.
Assume that the risk-free rate of return is 4% and the market risk premium (ie., Rm- Rf) is 89%. If use the Capital Asset Pricing Model (CAPM) to estimate the expected rate of return on a stock with a beta of 128, then this stock's expected retum should be ---- A) 10.53% B) 14.24% 23.15% D) 6.59%
(d) Suppose the risk-free rate is 4%, the market risk premium is 15% and the betas for stocks X and Y are 1.2 and 0.2 respectively. Using the CAPM model, estimate the required rates of return of Stock X and Stock Y. (e) Given the results above, are Stocks X and Y overpriced or underpriced? Explain.
Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, r. The characteristics of two of the stocks are as follows: Stock A B Correlation-1 Rate of return. Expected. Return 79 10% Standard Deviation 30% 70% Required: a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be formed to create a "synthetic" risk-free asset?) (Round your answer to 2 decimal places.) b. Could the equilibrium ry be greater than rate of return? Yes No
You live in a world where assets are priced by the CAPM. The following information is given to you regarding stock X. The expected payoff from the stock X=£105.00 Expected return of stock X = 18% Risk-free rate =5% Market Risk Premium = 9% Assume there are no other changes, except that the correlation between the returns of Stock X and the market becomes twice what it is currently. How would this change affect the current price of Stock X? Explain why the change of the correlation causes the observed change in the stock price. [hint: Provide a risk-based explanation]
Assume the Black-Scholes framework. Let S be a stock such that S(0) = 21, the dividend rate is δ = 0.02, the risk free rate is r = 0.05, and the volatility is σ = 0.2. (a) Calculate the expected payoff of a 6 month call with strike price 17. (b) Calculate the cost of such a call. (c) Calculate the cost of a 6 month put with strike price 17. (d) Calculate the price of a derivative that pays |S(0.5) − 17| in six months
Assume that the risk-free rate of return is 4% and the market risk premium (ie., Rm - Re) is 89%. If use the Capital Asset Pricing Model (CAPM) to estimate the expected rate of return on a stock with a beta of 128, then this stock's exoected return should be A) 10.53% B) 14.24% 23.15% D) 6.59%
(d) Suppose the risk-free rate is 4%, the market risk premium is 15% and the betas for stocks X and Y are 1.2 and 0.2 respectively. Using the CAPM model, estimate the required rates ofreturn of Stock X and Stock Y. (e) Given the results above, are Stocks X and Y overpriced or underpriced? Explain.

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