If at the end of the year you had sold the stock for only $900, your dollar return would
have been $100.
Although expressing returns in dollars is easy, two problems arise: (1) To make a
meaningful judgment about the return, you need to know the scale (size) of the in-
vestment; a $100 return on a $100 investment is a good return (assuming the invest-
ment is held for one year), but a $100 return on a $10,000 investment would be a poor
return. (2) You also need to know the timing of the return; a $100 return on a $100 in-
vestment is a very good return if it occurs after one year, but the same dollar return af-
ter 20 years would not be very good.
The solution to the scale and timing problems is to express investment results as
rates of return,or percentage returns.For example, the rate of return on the 1-year stock
investment, when $1,100 is received after one year, is 10 percent:
The rate of return calculation “standardizes” the return by considering the return per
unit of investment. In this example, the return of 0.10, or 10 percent, indicates that
each dollar invested will earn 0.10($1.00) $0.10. If the rate of return had been neg-
ative, this would indicate that the original investment was not even recovered. For ex-
ample, selling the stock for only $900 results in a minus 10 percent rate of return,
which means that each invested dollar lost 10 cents.
Note also that a $10 return on a $100 investment produces a 10 percent rate of re-
turn, while a $10 return on a $1,000 investment results in a rate of return of only 1
percent. Thus, the percentage return takes account of the size of the investment.
Expressing rates of return on an annual basis, which is typically done in practice,
solves the timing problem. A $10 return after one year on a $100 investment results in
a 10 percent annual rate of return, while a $10 return after five years yields only a 1.9
percent annual rate of return.
Although we illustrated return concepts with one outflow and one inflow, rate of
return concepts can easily be applied in situations where multiple cash flows occur
over time. For example, when Intel makes an investment in new chip-making technol-
ogy, the investment is made over several years and the resulting inflows occur over
even more years. For now, it is sufficient to recognize that the rate of return solves the
two major problems associated with dollar returns—size and timing. Therefore, the
rate of return is the most common measure of investment performance.
Differentiate between dollar return and rate of return.
Why is the rate of return superior to the dollar return in terms of accounting for
the size of investment and the timing of cash flows?
Stand-Alone Risk
Riskis defined in Webster’sas “a hazard; a peril; exposure to loss or injury.” Thus, risk
refers to the chance that some unfavorable event will occur. If you engage in sky-
diving, you are taking a chance with your life—skydiving is risky. If you bet on the
0.1010%.
Dollar return
Amount invested
$100
$1,000
Rate of return
Amount receivedAmount invested
Amount invested
Stand-Alone Risk 103
Risk and Return 101
