a. (1)Why is T-bill’s return independent of the state of the economy? Do T-bill’s promise a completely risk-free return? Explain (2)Why are High Tech’s returns expected to move with the economy, whereas, Collections’ are expected to move counter to the economy?
1. The 5.5% T-bill return does not depend on the state of the economy because the Treasury must redeem the bills at par regardless of the state of the economy; therefore, T-bills are risk-free in the default risk sense because the 5.5% return will be realized in all possible economic states. Consequently, this return is composed of the real risk-free rate, (i.e. 3%, plus an inflation premium, say 2.5%). As the economy is full of uncertainty about inflation, it is unlikely that the realized real rate of return would equal the expected 3%. For example, if inflation averaged 3.5% over the year, then the realized real return would only be 5.5% – 3.5% = 2%, not the expected 3%. To simplify matters, in terms of purchasing power, T-bills are not riskless. Investors are fully aware of the changes within a portfolio of T-bills, and as rates declined, the nominal income will fall; and T-bills are exposed to reinvestment rate risk. In summary, it is concluded that there are no truly risk-free securities within the United States. If the Treasury sold inflation-indexed, tax-exempt bonds, they would be truly riskless, but all actual securities are exposed to some type of risk.
2. High Tech’s returns move with, hence are positively correlated with, the economy, because the firm’s sales, and hence profits, will generally experience the same type of difficulties as the economy. If the economy is booming, so will High Tech. On the other hand, Collections is considered by many investors to be a hedge against bad times and high inflation, so if the stock market crashes, investors in this stock should do relatively well. Stocks such as Collections are thus negatively correlated with the economy.
b. Calculate the expected rate of return on each alternative and dill in the blanks on the row for in the previous table.
The expected rate of return is expressed as follows:
Here Pi is the probability of occurrence of the state, ri is the estimated rate of return for that state, and N is the number of states. Here is the calculation for High Tech:
High Tech= 0.1(-27.0%) + 0.2(-7.0%) + 0.4(15.0%) + 0.2(30.0%) + 0.1(45.0%) = 12.4%.
We use the same formula to calculate r’s for the other alternatives:
U.S. Rubber= 9.8%.
c. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like most people, is 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. (1) Calculate this value for each alternative and fill in the blank on the row for in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills.
1. The standard deviation is calculated as follows:
High Tech= [(-27.0 – 12.4)2(0.1) + (-7.0 – 12.4)2(0.2) + (15.0 – 12.4)2(0.4) + (30.0 – 12.4)2(0.2) + (45.0 – 12.4)2(0.1)] ½ = = 20.0%.
Here are the standard deviations for the other alternatives:
U.S. Rubber= 18.8%.
2. The standard deviation is a measure of a security’s stand-alone risk. The larger the standard deviation, the higher the probability that actual realized returns will fall far below the expected return, and that losses rather than profits will be incurred.
3. The data provided the most risky investment is High Tech and the least risky are T-bills.
d. Suppose you...