A hedger is short spot and long futures. Today, spot is 4.40 and the June future is 5.00. A bit later, spot goes to 5.00 and the June future goes to 5.10. What has happened to basis in this period? A) Remained the same B) Cannot tell C) Weakened D) Strengthened
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- Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.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.If the current risk free rate is 2.3% and a particular security (priced today at $45) pays no dividends what is the best estimate of the one year futures price of this asset?(use at least 3 decimals)
- 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.Assume investors are indifferent among security maturities. Today, the annualized 2-year interest rate is 2.20 percent, and the 1-year interest rate is 2 percent. What is the forward rate according to the pure expectations theory? Group of answer choices 2.25% 2.20% 2.00% 2.40%A one-year gold futures contract is selling for $1,247. Spot gold prices are $1,200 and the one-year risk-free rate is 2%. a) According to spot-futures parity, what should be the futures price? b) What risk-free strategy can investors use to take advantage of the futures mispricing, and what would be the profits from that strategy?
- This example is part of "Hedged Portfolios" to minimize risk. Assume you have $9000 to invest; A stock is trading at $90.00. A call option that expires in one year with a strike price of $90.00 is trading at $10.00. What is your portfolio's 1-year return if you invest in "Only Stocks" and the the stock price after one year is $48.00? Enter your answer in the following format: + or - 0.1234 Hint: Answer is between -0.4212 and -0.5042 ___________? ANSWER IN TYPINGThe market portfolio (M) has the expected rate of return E(rM) = 0.12. Security A is traded in the market. We know that E(rA) = 0.17 and βA = 1.5. (1) What is the rate of return of the risk-free asset (rf)? (2) Security B is also traded in the market. βB = 0.8. Then what is “fair” expected rate of return of security B according to the CAPM? (3) Security C is a third security traded in the market. βC = 0.6, and from the market price, investors calculate E(rC) = 0.1. Is C overpriced or underpriced? What is αC?What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the dividend yield 3 percent, and the futures expires in three months? A. $73.70 B. $77.48 C. $72.60 D. $76.32 E. none of the above Please explain step by step
- The table here shows the no-arbitrage prices of securities A and B that we calculated.Cash Flow in One YearSecurity Market Price Today Weak Economy Strong EconomySecurity A 231 0 600Security B 346 600 0a. What are the payoffs of a portfolio of one share of security A and one share of security B?b. What is the market price of this portfolio? What expected return will you earn from holdingthis portfolio Suppose security C has a payoff of $600 when the economy is weak and $1800 when the economy isstrong. The risk-free interest rate is 4%.a. Security C has the same payoffs as which portfolio of the securities A and B in problem A-1?b. What is the no-arbitrage price of security C?c. What is the expected return of security C if both states are equally likely? What is its riskpremium?d. What is the difference between the return of security C when the economy is strong and when itis weak?e. If security C had a risk premium of 10%, what arbitrage opportunity would be available?Suppose you observe the following situation: Security Beta Expected Return Pete Corp. 1.70 0.180 Repete Co. 1.39 0.153 What is the risk - free rate? (Do not round intermediate calculations. Round the final answer to 3 decimal places.) Risk - free rate % Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? (Do not round intermediate calculations. Round the final answers to 2 decimal places.) Expected Return on Market Pete Corp. % Repete Co. %Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?