Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship:
EðRAÞ = ð1:1Þλ1 + ð0:8Þλ2 EðRBÞ = ð0:7Þλ1 + ð0:6Þλ2 EðRCÞ = ð0:3Þλ1 + ð0:4Þλ2
a. If λ1 = 4% and λ2 = 2%, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year.
b. Suppose that you know that next year the prices for Stocks A, B, and C will actually be $31.50, $35.00, and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these mispriced securities. What is the profit from your investment? You may assume that you can use the proceeds from any necessary short sale.