1.You work for Innovation Partners and are considering creating a new security. This security would pay out $1000 in one year if the last digit in the closing value of the Dow Jones Industrial index in one year is an even number and zero if it is odd. The one-year risk-free interest rate is 5%. Assume that all investors are averse to risk.
a. What can you say about the price of this security if it were traded today?
b. Say the security paid out $1000 if the last digit of the Dow is odd and zero otherwise. Would your answer to part (a) change?
c. Assume both securities (the one that paid out on even digits and the one that paid out on odd digits) trade in the market today. Would that affect your answers?
2.Suppose a risky security pays an expected cash flow of $80 in one year. The risk-free rate is 4%,and the expected return on the market index is 10%.
a. If the returns of this security are high when the economy is strong and low when the economy is weak, but the returns vary by only half as much as the market index, what risk premium is appropriate for this security?
b. What is the security’s market price?
3.Suppose Hewlett-Packard (HPQ) stock is currently trading on the NYSE with a bid price of $28.00 and an ask price of $28.10. At the same time, a NASDAQ dealer posts a bid price for HPQ of $27.85 and an ask price of $27.95.
a. Is there an arbitrage opportunity in this case? If so, how would you exploit it?
b. Suppose the NASDAQ dealer revises his quotes to a bid price of $27.95 and an ask price of $28.05. Is there an arbitrage opportunity now? If so, how would you exploit it?
c. What must be true of the highest bid price and the lowest ask price for no arbitrage opportunity to exist?