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Answers to Concepts in Review
1. The return on investment is the expected profit that motivates people to invest. It includes
both current income and/or capital gains (or losses). Without a positive expected return,
there is no benefit to investing and individuals have no reason to save and invest. Since net
demanders are willing to pay net savers a positive return for their funds, the opportunity to
earn a positive return exists.
Return on investment can come from either current income or capital gains, or both. Current
income, most commonly, is periodic payments, such as interest received on bonds, dividends
on stock, or rent received from real estate. To be considered income, these payments must be
received in cash or be readily convertible to cash. Capital gain refers to the change in the
market value of the investment. The amount by which the proceeds from the sale of an
investment exceed the original purchase is called a capital gain. If it is sold for less than the
original purchase price, a capital loss is realized.
The use of percentage returns is generally preferred to dollar returns to allow investors to
directly compare different sizes and types of investments.
2. Although future returns are not guaranteed by past performance, historical data often gives
the investor a meaningful basis on which to form future expectations. Past return data, such
as average returns or trends seen in certain time periods, can be used along with the
investor’s insights about future prospects of the investment. Together the historical data and
future prospects help the investor to formulate an expected return on the investment.
The level of expected returns depends on many internal characteristics of the investment and
the external forces on the investment. Internal characteristics include the type of investment,
the quality of management, the method by which the investment is financed, and the
customer base of the issuer. External forces include war, shortages, price controls, Federal
Reserve actions, and political events, among others. External forces, unlike internal
characteristics, cannot be controlled by the issuer of the investment. Investment vehicles are
affected differently by these forces—the expected return of one investment may increase
while the expected return of another may decrease in response to external forces.
History tells us that stock market returns have averaged well above the interest rates payable
on savings accounts at banks. In recent years especially during the latter part of the 1990s
the returns were well above the stock market averages for the earlier part of the century.
Unfortunately, investors often assume that history will repeat itself. Hence, they buy shares
of firms that have experienced increased share prices. If the investor is looking for shortterm gains over a year or two, the probabilities are mixed depending on what time periods
are cited. The best advice, given these statistics, is for an investor to hold for the long term in
order to ride out the market’s twists and turns.
3. Ignoring risk, a satisfactory investment is one for which the present value of benefits
(discounted) equals or exceeds the present value of costs. If the present value of benefits
exceeds the cost, the investor would earn more than the discount rate, i.e. the return on the
investment is greater than the discount rate.
4. (a) The real rate of return is the return earned in a certain, risk-free world. It would equal
the nominal rate of return on a risk-free security less inflation. Historically, it has been
relatively stable in the range of 0.5 to 2%.
(b) The expected inflation premium represents the expected average future rate of inflation.
It is the compensation that investors demand for future expected inflation; that is, the
decline in the purchasing power of the dollar.
(c) The risk premium varies for different security issues and represents the additional return
required to compensate an investor for the risk characteristics of the issue and the issuer.
It is the return on a risk security (e.g. stocks, bonds) minus the risk-free rate of return,
which is the rate on a 90-day T-Bill.
The risk-free rate of return equals the real rate of return plus the expected inflation
premium:
RF = r * + IP. It is the return on a riskless security as measured by the 90-day T-Bill.
The required rate of return equals the real rate of return plus the expected inflation
premium (together, the risk-free rate) and the risk premium: ri = RF + IP. Alternatively,
it equals the risk-free rate of return plus the risk premium.
5. The holding period is simply the period of time over which the investor wishes to measure
the return on an investment. In comparing alternative investment vehicles, it is essential to
use equal-length holding periods so that the two vehicles being compared are judged under
identical conditions. This adds objectivity to the comparison. Most interest rates are quoted
on an annual basis, so it is generally convenient to use a one-year holding period.
The holding period return (HPR) is the total return earned from holding an investment for a
specified period of time. To calculate HPR, all that is needed is the beginning- and end-ofperiod investment values along with the value of current income received by the investor.
Because HPR doesn’t account for the time value of money, the holding period is usually one
year or less.
6. The yield, or IRR, is the annual rate of return earned by a long-term investment. It is also
defined as the discount rate that produces a present value of benefits received equal to the
present value of costs/investments. Unlike the HPR, it takes into account the time value of
money and can be used to calculate the return on investments held for over one year. The
HPR is inappropriate for investments held for more than one year.
7. The critical assumption underlying the use of yield as a return measure is an ability to earn a
return equal to the calculated yield on all income received from the investment during the
holding period. If you earn 10 percent on all income received from an investment during the
holding period, your yield on the investment will be 10 percent. On the other hand, if you
earn 0 percent on the income received, your rate of return on the investment would actually
be less than 10 percent. If the interest-on-interest earned from the investment is less than its
calculated yield, the investment’s return will fall below the yield. Clearly when using yield
as a measure of investment return, the validity of this assumption must be recognized and
evaluated. If the interest-on-interest assumption does not hold, use of the calculated yield
could lead to poor investment decisions. (Note: The instructor may want to use the
discussion of interest-on-interest and Figure 4.1 to demonstrate this somewhat complex, but
extremely important, yield concept.)
8. If the present value of returns from an investment is greater than the initial cost of the
investment, it is a satisfactory investment and should be acceptable. If the yield from an
investment is greater than the required return for that investment, the present value and
yield provide the same conclusion regarding acceptability.
In the example given, Investment A is clearly acceptable since its yield (8 percent) is greater
than the required rate of return (7 percent). Investment B, on the other hand, is not
acceptable since its present value of returns ($150) is $10 less than its cost ($160).
Investment C is not acceptable since its yield (8 percent) is lower than the required rate of
return (9 percent).
9. Risk is the chance that the actual return from an investment may differ from what is
expected. The standard deviation is the statistic used to measure risk. The risk-return
tradeoff is the relationship between the expected returns from an investment and the risk
associated with them. The required returns from an investment increase as risk increases to
provide an incentive for him or her to take higher risks i.e. in order to accept higher risks,
the investors have to be compensated with higher returns.
10. (a) Business risk is concerned with the degree of uncertainty associated with an
investment’s earnings and the investment’s ability to pay investors interest, dividends,
and other returns owed them. Business risk is usually related to the firm’s line of
business.
(b) Financial risk is the risk associated with the mix of debt and equity (capital structure)
used to finance the firm. The greater the firm’s debts and interest obligations, the greater
its financial risk.
(c) Purchasing power risk arises because of uncertain inflation rates and price-level
changes in the future. When prices rise, each dollar invested has less value—it can buy
less, and vice versa.
(d) Interest rate risk is risk associated with changes in the prices of fixed-income securities
resulting from changing market interest rates. As the market interest rates change, the
prices of these securities change in the opposite direction, thereby changing the level of
return that an investor can expect to obtain from them. Another important aspect of
interest rate risk involves the ability to reinvest income received at the initial rate of
return in order to earn the fully compounded rate of return.
(e) Liquidity risk is the risk of not being able to liquidate an investment conveniently and at
a reasonable price. In general, investment vehicles traded in markets with small demand
and supply characteristics tend to be less liquid than those traded in broad markets.
(f) Tax risk is the risk that tax laws enacted by Congress will adversely affect certain types
of investments and decrease their after-tax returns.
(g) Market risk is the risk of changes in investment returns caused by factors independent of
the given investment vehicle. It results from factors such as political, economic, and
social events, or changes in investor tastes and preferences.
(h) Event risk is the risk that comes from a largely or totally unexpected event that has a
significant and usually immediate effect on the underlying value of an investment. The
effect of this risk seems to be isolated in most cases, affecting only certain companies
and properties.
11. Standard deviation is the most common measure of an asset’s risk. It measures the
dispersion of returns around an asset’s average or expected return. Standard deviation is an
absolute measure of risk and thus can be used to compare the riskiness of competing
investments with the same expected return. The coefficient of variation (CV) measures the
relative dispersion of an asset’s average or expected returns. Like standard deviation, the
higher the CV, the higher the risk. CV differs from standard deviation because it is a relative
measure of risk and can be used to compare the riskiness of competing investments with
different expected returns.
12. Investors’ attitudes toward risk or their risk-return tradeoffs may be classified as one of the
following:
Risk-indifferent investors do not require a greater return in exchange for each unit of
additional risk.
Risk-averse investors require greater return in exchange for each unit of additional risk. The
tradeoff here is positive; return must increase as risk increases.
Risk-taking investors accept a lower return in exchange for greater risk. This tradeoff is
negative; such investors enjoy risk and are therefore willing to accept lower returns for
increasing levels
of risk.
In general, most investors are risk averse. They require increased returns from an investment
as its risk increases. The risk preference of an investor is an important determinant of his/her
investment decisions. Risk-averse investors may not make speculative investments, while
risk-taking investors may. Thus, an investment that is considered unsatisfactory by a riskaverse investor may be deemed satisfactory by a risk-taking investor.
13. The investment process can be summarized in four steps:
(1) Estimate the expected return over a given holding period using historical data or
projected return data, or both. The time value of these returns must be considered for
long-term investments.
(2) Assess the risk of the investment returns through the subjective (judgmental) evaluation
of historical returns and by using beta (for securities).
(3) Evaluate the risk-return behavior of each alternative investment. The expected return
must be “reasonable” given the level of risk possessed by the investment. Only
investments offering the highest expected return for a given level of risk are considered
reasonable.
(4) Select the vehicles with the highest return for the level of risk the investor is willing to
take. These fit the definition of a good investment.