Assume 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 $400,000 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 one-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 table; you will fill in the blanks later.)
The bank’s economic forecasting staff developed the probability estimates for the state of the economy, and the trust department used a sophisticated computer program 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 the following questions.
1. Why is the risk-free return independent of the state of the economy? In the real world, do T-bills promise a completely risk-free return?
2. Why are High Tech’s returns expected to move with the economy, whereas Collections are expected to move counter to the economy?
3. Calculate the expected rate of return on each alternative and fill in the row for in the table.
You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because the beneficiaries of the trust, like virtually everyone, are risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns.
4. Calculate this value for each alternative and fill in the row for σ in the table.
5. What type of risk does the standard deviation measure?
Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of total risk than only the standard deviation when the alternatives being considered have widely differing expected returns and standard deviations.
6. Calculate the CVs for the different securities and fill in the row for CV in the table. Does the CV measurement produce the same risk rankings as the standard deviation?