# Risk & Return

Investment returns is the expectation of earning money in the future on the amount of money invested. The return is the financial performance of the investment. The return is the difference between the amount invested and the amount you are returned after said investment.

There are two ways to show return on investment.

1. By dollar return.

Amount to be received – Amount invested

= $1,100 - $1,000 = $100 in return

The problems with expressing returns in dollars, you don’t know the size of the investment for that dollar return and you don’t know the timing of the return.

2. Rate of Return or percentage returns

Amount received – Amount invested / Amount invested

= $100 / $1000 = .10 = 10%

The rate of return “standardizes” the dollar return by considering the timing

b. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bill’s promise a completely risk-free return? (2)Why are Alta Industries’s returns expected to move with the economy whereas Repo Men’s are expected to move counter to the economy?

(1) The 8% T-bill does not depend on the state of the economy because the treasury estimated returns is constant whether in recession, average, or booming state of the economy. Treasury securities are backed by the full faith and credit of the U.S. Treasury; they represent the rate at which investment is considered risk-free. The T-bill has a fixed rate of return and will not fluctuate with the change in the market. (2) Alta Industries’s returns expected to move with the economy because it’s considered a cyclical stock and Repo Men’s are counter to the economy because it’s considered a counter-cyclical stock. Repo Men’s company is more active and more common in a time of recession than when the economy is booming.

c. Calculate the expected rate of return on each alternative and fill in the blanks in the row for ^r in the table.

Alta Industries

^r = 0.1(-22%) + 0.2(-2.0%) + 0.4(20%) + 0.2(35%) + 0.1(50%) = = -0.022 + -0.0040 + 0.08 + 0.07 + 0.05 = -0.0240 = 17.4%

2-Stock Portfolio – you can’t determine the expected rate of return because the probability of distribution for 2-Stock Portfolio does not sum to 1.0. ^r = 0.1(3%) + 0.4(10%) + 0.1(15%) = N/A

d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, 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 in the row for standard deviation 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 Alta Industries, American Foam, and T-bills.

(1) = Alta Industries

((-22 – 17.4)^2 0.10 + (-2 -17.4)^2 0.20 + (20 – 17.4)^2 0.40 + (35 – 17.4)^2 0.20 + (50 – 17.4)^2 0.10)^1/2= 20%

2-Stock Portfolio – you can’t determine the standard deviation, because you can’t determine the expected rate of return because the probability of distribution for 2-Stock Portfolio does not sum to 1.0.

(2) Standard deviation is a weighted average of the deviations from the expected value, and it provides an idea of how far above or below the expected value the actual value is likely to be. Any form of risk with different probabilities and returns should be measured using standard deviation. Alta Industries standard deviation is 20% compared to Repo Men which is 13.4%. Alta has the larger standard deviation, which shows a greater variation of returns, thus a greater chance that the actual return will be lower than the expected return of 17.4%. Repo Men has a lower standard...

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