You find a stock is selling at $20, and its futures is selling at the same price. The risk-free rate for the maturity of the futures is 5%. The stock does not pay any dividend. Is there any arbitrage opportunity?
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- Question 1. Let St be the current price of a stock that pays no dividends. a)Let rbid be the interest rate at which one can invest/lend money, and roff be theinterest rate at which one can borrow money, rbid≤roff. Both rates are continuously compounded. Using arbitrage arguments, find upper and lower bounds for the forwardprice of the stock for a forward contract with maturity T > t. b)How does your answer change if the stock itself has bid price St,bid and offer price St,off?The market price of a security is $52. Its expected rate of return is 12.1%. The risk-free rate is 4%, and the market risk premium is 7.3%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Market priceA particular stock does not pay dividends and is currently priced at $12. Suppose that the quoted futures price for delivery in 1 year is $12.45. The continuously compounded interest rate is 2%. The underlying does not pay dividends and there are no costs of trading. How could you make a riskless arbitrage profit? a. There is no way to make a risk-less profit in this scenario. b. Today you buy futures, short sell the stock and invest the receipts from the short sale c. Today you buy futures, borrow money and purchase the stock. d. Today you sell futures, borrow money and purchase the stock.
- At time t = 0, a trader takes a long position in a futures contract on stock i that willexpire at time T. the present value of this contract to the long is given by: See Image.Assume no-arbitrage pricing. Show analytically that if the return from stock i is positively correlated with the overall return on the stock market, then the futures market must be in backwardation at time t = 0.At time t = 0, a trader takes a long position in a futures contract on stock i that willexpire at time T. the present value of this contract to the long is given by: See Image. Assume no-arbitrage price, briefly descthat if the return from stock i is positively correlated with the overall return on the stock market, then the futures market must be in backwardation at time t = 0.A stock has an expected return of 14% based on its performance. Under the APT, given its risk exposure, the fair expected return is 18%. What would an arbitrageur trade in this situation? a. Buy the stock as price is too low. Buying increases price, reducing return. b. Buy the stock as price is too low. Buying increases price, increasing return. c. Do nothing - without risk free rate cannot tell. d. Short the stock as the price is too high. Selling reduces price, increasing return
- Suppose a stock paying no income has spot price S0 = 80 and the continuouszero rate is 1.5%. You observe that the price of an American 75-strike call with maturity 6months is $4.00. Does this violate the assumption of no-arbitrate? Explain why or why not.Suppose the quoted futures price for delivery in 1 year is $7.10. The current underlying price is $7 and the continuously compounded interest rate is 5%. The underlying does not pay dividends. How could you make a riskless arbitrage profit? Question 2Answer a. buy futures contracts, short sell the stock and invest in a bank account b. borrow from the bank to buy futures contracts and short sell the stock c. sell futures contracts, borrow and buy the stock d. sell future contacts, short sell the stock and invest in a bank account1. Assume that the risk-free rate of interest is 5% and the expected rate of return on the market is 17%. A stock has an expected rate of return of 6%. What is its beta? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) 2. Suppose that borrowing is restricted so that the zero-beta version of the CAPM holds. The expected return on the market portfolio is 14%, and on the zero-beta portfolio it is 6%. What is the expected return on a portfolio with a beta of 0.8? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- Suppose the risk-free rate goes up to 7%.What effect would higher interest rates have onthe SML and on the returns required on highrisk and low-risk securities? (2) Suppose insteadthat investors’ risk aversion increased enoughto cause the market risk premium to increase to8%. (Assume the risk-free rate remains constant.)What effect would this have on the SML and onreturns of high- and low-risk securities?Consider a two period economy. You can buy stocks in period 0, and then sell them in period 1. You can also enter into futures contracts in period 0, which expire in period 1. Suppose a stock has a β of 0.5. The stock pays no dividends, and is trading at $100. The market has an expected return of 10%. The interest rate is 2%. Suppose the CAPM holds. What is the stock’s expected return? What is the expected price of the stock in period 1? Consider a futures contract on the stock, expiring at t = 1. What is the fair price of the futures contract, in t = 1 dollars? Suppose you take a long position in the futures contract in period 0 (so, you promise to pay money, in exchange for getting the stock in period 1). When the futures contract expires in period 1, you receive the stock and immediately sell it. What is the expected amount you will pay in money for the stock? What is the expected amount you get from selling the stock? Since buying single-stock futures appears to be a fairly…The market price of a security is $90. Its expected rate of return is 12%. The risk-free rate is 6% and the market risk premium is 9.6%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. (Do not round intermediate calculations. Round your answer to 2 decimal places.)