A portfolio's value increases by 20% during a financial boom and by 7% during normal times. It decreases by 14% during a recession. What is the expected return on this portfolio if each scenario is equally likely?

4. Suppose that a set of portfolio managers has a chance p = 50% of beating the market by 10% in a given year and chance 1 - p of underperforming by 10%. Performance from one year to the next is independent and uncorrelated. Returns are simple returns and compounding is ignored. (a) What is the probability that a manager will achieve a five-year track record which beats the market for at least 4 out of 5 years? (b) Suppose that unsuccessful managers get forced out of business as soon they are down overall -30%; that is, as soon as as their record contains 3 more losing years than winning years. What is the probability of failure over a five-year horizon? (c) Among those who survive, what is the expected total return?

49. Suppose that a particular light bulb is advertised as having an average lifetime of 2,000 hours and is known to satisfy an exponential failure law. Suppose for simplicity that the bulb is used continuously. Find the probability that the bulb lasts a. More than 3,000 hours. b. Less than 1,500 hours. c. Between 2,000 and 2,500 hours.

The following table lists several corporate bonds issued during the second quarter of 2015. Company AT&T Bank of America General Electric Goldman Sachs Verizon Wells Fargo Time toMaturity(years) 10 10 2 3 8 7 AnnualRate (%) 3.40 4.00 5.25 6.15 5.15 3.50 If you spent $30,000 on Bank of America bonds, how much interest would you earn every 6 months? HINT [See Example 3.]   How much interest would you earn over the life of the bonds?