Problem
Assume that you recently graduated with a major in finance, and you just landed a job in the trust department of a large regional bank. Your first assignment is to invest $100,000 from an estate for which the bank is trustee. Because the estate is expected to be distributed to the heirs in approximately one year, you have been instructed to plan for a 1-year holding period. Furthermore, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.) Estimated Returns on Alternative Investments State of the Proba- High Collec- U.S. Market Two-Stock Economy bility T-Bills Tech tions Rubber Portfolio Portfolio Recession 0.1 8.0% -22.0% 28.0% 10.0% -13.0% Below Average 0.2 8.0 -2.0 14.7 -10.0 1.0 Average 0.4 8.0 20.0 0.0 7.0 15.0 Above Average 0.2 8.0 35.0 -10.0 45.0 29.0 Boom 0.1 8.0 50.0 -20.0 30.0 43.0 r ˆ σ CV The bank's economic forecasting staff has developed probability estimates for the state of the economy, and the trust department has a sophisticated computer program that was used to estimate the rate of return on each alternative under each state of the economy. High Tech, Inc., is an electronics firm; Collections, Inc., collects past due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. The bank also maintains an "index fund" that includes a market-weighted fraction of all publicly traded stocks; by investing in that fund, you can obtain average stock market results. Given the situation as described, answer these questions:
i. Why is the risk-free return independent of the state of the economy? Do T-bills promise a completely risk-free return?
ii. Why are High Tech's returns expected to move with the economy whereas Collections' are expected to move counter to the economy?