# Investor Return Calculation

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"Investor Return Calculation"

```					                              Chapter 6
THE RISKS AND RETURNS FROM INVESTING

Multiple Choice Questions
Return

1.       Total return is equal to:

a.       capital gain + price change.
b.       yield + income.
c.       capital gain - loss.
d.       yield + price change.

(d, easy)

2.       The return component that gives periodic cash flows to the investor is
known as the:

a.       capital gain
b.       interest rate
c.       yield
d.       unrealized gain

(c, easy)

Risk

3.       Investors should be willing to invest in riskier investments only:

a.       if the term is short.
b.       if there are no safe alternatives except for holding cash.
c.       if the expected return is adequate for the risk level
d.       if they are true speculators.

(c, easy)

4.       If interest rates are expected to rise, you would expect:

a.       bond prices to fall more than stock prices
b.       bond prices to rise more than stock prices
c.       stock prices to fall more than bond prices
d.       stock prices to rise and bond prices to fall

(a, moderate)

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The Risks and Returns from Investing
5.       An impending recession is an example of:

a.       interest rate risk
b.       inflation risk
c.       market risk
d.       financial risk

(c, moderate)

6.       Financial risk is most associated with:

a.       the use of equity financing by corporations
b.       the use of debt financing by corporations
c.       equity investments held by corporations
d.       debt investments held by corporations

(b, moderate)

7.       Political stability is the major factor concerning:

a.       exchange risk
b.       systematic risk
c.       nonsystematic risk
d.       country risk

(d, moderate)

8.       Liquidity risk:

a.       is the risk that investment bankers normally face.
b.       is lower for small OTC stocks than for large NYSE stocks.
c.       is the risk associated with secondary market transactions.
d.       increases whenever interest rates increase.

(c, moderate)

9.       Which of the following is not related to overall market variability?

a.       Financial risk.
b.       Interest rate risk.
d.       Market risk.

(a, moderate)

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The Risks and Returns from Investing
10.      If a U.S. investor buys foreign stock, his dollar-denominated return will
increase if the dollar:

a.       appreciates in value.
b.       depreciates in value.
c.       remains unchanged.
d.       moves to a net gain position.

(b, difficult)

11.      New financial disclosure regulations affecting the brokerage industry are
a type of:

a.       market risk.
b.       financial risk.
d.       liquidity risk.

(c, moderate)

12.      If interest rates rose, you would expect ------------ to also rise.

b.       financial risk.
c.       liquidity risk.
d.       inflation risk.

(d, moderate)

Measuring Returns

13.      The best return measure to use if you are trying to measure the total effect
of returns over time given some stated beginning amount is the:

a.       total return
b.        return relative
c.       cumulative wealth index
d.       total yield

(a, moderate)

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The Risks and Returns from Investing
14.      Total return as defined in the text is:

a.       the difference between the sale price and the purchase price of an
investment.
b.       measured by dividing the sum of all cash flows received by the amount
invested.
c.       the reciprocal of a return relative.
d.       measured by dividing all cash flows received by its selling price.

(b, moderate)

15.      Which of the following is true regarding the cumulative wealth index? It:

a.       is measured by adding up the total returns over the holding period and
dividing by the investment.
b.       uses index values to have a specified beginning value.
c.       is the present value of the future cash flows expected from the investment.
d.       uses the arithmetic mean as the rate of growth of one’s wealth.

(b, difficult)

16.      The ----------- is stated on the basis of 1.0.

a.       total return
b.       return relative
c.       cumulative wealth index
d.       geometric mean

(b, difficult)

17.          The return relative solves the problem of:

a.      inflation.
b       negative returns.
c.      interest rates.
d.      tax differences.

(b, moderate)

18.      If the Dow Jones Industrials had a price appreciation of 6 percent one year
and yet total return for the year was 11 percent, the difference would be
due to:

a.       the tax treatment of capital gains.
b.       the cumulative wealth effect.
c.       dividends.
d.       profits.

(c, moderate)

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The Risks and Returns from Investing
Summary Statistics for Returns

19.      In order to determine the compound growth rate of an investment over
some period, an investor would calculate the:

a.       arithmetic mean
b.       geometric mean
c.       calculus mean
d.       arithmetic median

(b, moderate)

20.      A major difference between real and nominal returns is that:

a.       real returns adjust for inflation and nominal returns do not.
b.       real returns use actual cashflows and nominal returns use expected
cashflows
c.       real returns adjust for commissions and nominal returns do not.
d.       real returns show the highest possible return and nominal returns show the
lowest possible return.

(a, moderate)

21.      When most people refer to the mean, they are referring to the:

a.       median.
b.       arithmetic mean.
c.       geometric mean.
d.       cumulative mean.

(b, easy)

22.      Which of the following statements regarding the arithmetic mean and the
geometric mean is true?

a.       The arithmetic mean is always a better measure of average performance.
b.       The geometric mean is always a better measure of average performance.
c.       The arithmetic mean is a better measure of performance over single
periods.
d.       The geometric mean is the best estimate of the expected return for the next
period.

(c, difficult)

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The Risks and Returns from Investing
Measuring Risk

23.      The equity risk premium is:

a.       the difference between stocks and bonds
c.       the difference between stocks and the risk-free rate.
d.       the difference between a stock market index and the inflation rate.

(c, moderate)

24.      Which of the following statements concerning the equity risk premium is
true?

a.       Some scholars think it is too low.
b.       There is no direct way to measure it..
c.       It predicts high future returns on stocks.
d.       All of the above are true statements.

(b, difficult)

25.      The standard deviation measures:

a.       systematic risk of a security.
b.       unsystematic risk of a security.
c.       total risk of a security.

(c, moderate)

Compounding and Discounting

26.      Present value is based on the concept of:

a.       compounding.
b.       systematic risk.
c.       duration.
d.       discounting.

(d, easy)

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The Risks and Returns from Investing
Realized Returns and Risks from Investing

27.      Which of the following statements regarding returns from 1920-2004 is
true?

a.       Bonds averaged returns during this period below the inflation rate.
b.       Common stocks had annual average returns almost double that of bonds.
c.       After considering purchasing power, bonds outperformed stocks during
this period.
d.       Common stocks returns averaged almost 15 percent for this period.

(b, difficult)

28.      The cumulative wealth index is composed of the:

a.       dividend component and the price change component.
b.       price change component and the inflation rate.
c.       dividend component and the risk-free rate.
d.       total return and return relative.

(a, difficult)

Taking A Global Perspective

29.      If you invest in Japanese bonds and the Japanese yen becomes stronger

a.       you will be able to buy back few dollars.
b.       your dollar-denominated return will increase.
c.       your-dollar denominated return will decrease.
d.       a and c

(b, difficult, p. 6-15)

30.      As the dollar falls,

a.       foreign investors owning U.S. stocks suffer.
b.       U.S. investors owning U.S. stocks suffer.
c.       U.S. investors owning foreign stocks suffer.
d.       foreign investors owning foreign stocks suffer.

(a, moderate)

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The Risks and Returns from Investing
True-False Questions
Return

1.       Another name for a capital gain is the yield.

(F, easy)

Risk

2.       Return and risk are inversely related.

(F, easy)

3.       The less variability of return, the greater the risk.

(F, easy)

4.       It would be expected that most security prices would fall if interest rates
rose.

(T, moderate)

5.       It is generally easier to predict interest rate risk than market risk.

(T, difficult)

6.       New regulations concerning auto emissions would be a type of market risk
for the auto industry.

(F, moderate)

7.       International mutual funds offer investors global diversification without
exchange rate risk.

(F, difficult)

Taking A Global Perspective

8.       A Chinese stock denominated in Chinese yuans will have an increase in its
dollar-denominated return if the yuan strengthens.

(T, difficult)

Chapter Six                                     77
The Risks and Returns from Investing
Summary Statistics for Returns

9.       The best estimate of the average return for stock in any one year would be
the geometric mean.

(F, moderate)

10.      The most common measure of inflation is the Producer Price Index.

(F, easy4)

Measuring Risk

11.      The standard deviation, calculated as the square root of the variance, is a
measure of total risk of an asset or portfolio.

(T, moderate)

Compounding and Discounting

12.      Future value is based on the concept of compound interest.

(T, easy)

1.       Assume you are a U. S. citizen who purchases \$20,000 worth of bonds of
the Deep Shaft Mining Company in Kenya. What sources of risk can you
identify with this investment?

(moderate)

2.       What common variable is used in the calculation of both the cumulative
wealth index and the geometric mean return? How is the common
variable calculated? How is it used in each?

Answer:          The total return (TR) is used in both calculations.
TR         =      [CFt + (PE - PB)]/PB.
CWIn       =      WI0 (1 + TR1)(1 + TR2) . . . (1 + TRn)
G          =      [(1 + TR1)(1 + TR2) . . . (1 + TRn)] 1/n - 1

(difficult)

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The Risks and Returns from Investing
3.       When should an investor use the arithmetic mean return? The geometric
mean return?

Answer:          The arithmetic mean is better for single period returns, whereas,
the geometric mean is better for multiple periods.

(moderate)

4..      What is the best measure of risk for returns of a sole proprietorship?

Answer:          The best measure of risk for a sole proprietorship (a single asset) is
standard deviation of returns to capture total risk, since there is no
diversification.

(moderate)

5.       What was the effect on foreign investors owning U.S. stocks when the
dollar fell in 2002?

Answer:          Foreign investors owning U.S. stocks suffered from the
unfavorable currency movement as well as decline in the U.S.
stock markets.

(moderate)

Critical Thinking/Essay Questions

1.       The returns and risk measures on this chapter are calculated from
historical data. Are such measures good predictors of the future? What
are some circumstances that could change to change future return and
risk? How can an investor use these return and risk measures to help
construct a portfolio?

Answer:          Historical risk and returns are a starting point for the analyst to
assess future prospects. The return and risk parameters for
individual companies can change due to changes in management,
product decisions, competition, regulation, changes in financial
structure, etc. An analyst can use historical data and temper it with
judgment about the future for constructing a portfolio.

(moderate)

2.       What is the major drawback of the total return measure? Why is it the
most common return calculation used by investors?

Answer:          The total return measure does not account for the time value of
money. The cashflows received are not discounted using present

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The Risks and Returns from Investing
value techniques. This is a serious flaw in the measure. However,
since many investors do not consider inflation in their calculations
and the total return measure is a quick way to measure return, it is
widely used by investors.

(moderate)

Problems
1.       A stock is purchased for \$50 on January 1 and sold on December 31 for
\$72. A \$5.00 per share dividend is paid during the year.

(a)      Calculate the TR.
(b)      Calculate the RR.

Solution:    (a)          TR       =      (Dividend + Change in Price)/ Beginning
Price

=      (\$5 + \$22)/\$50        =       0.54 or 54
percent

(b)    RR       =      TR + 1.0        =     0.54    + 1.0 = 1.54

OR

RR       =         (\$5 + 72)/\$50          = 77/50 = 1.54

(moderate)

2.       The S&P 500 showed the following TRs for a 6 year period: 11.1 percent,
-5.2 percent, 20.3 percent, 26.7 percent, -12.4 percent, and 2.2 percent.

(a)      Calculate the arithmetic mean return for the 6 year period.
(b)      Calculate the geometric mean return for the 6 year period.

Solution:      (a)    Arithmetic mean = X/n             = [11.1 + (-5.2) + 20.3 +
26.7 + (-12.4) + 2.2]/6
= 42.7/6 = .0712 or 7.12 percent

(b)      To calculate the geometric mean, convert to RRs and obtain the product of
the six RRs.

G        = [1.111 x .948 x 1.203 x 1.267 x .876 x 1.022]1/6 -
1
= [1.4372] 1/6 - 1 = 1.0623 - 1 = .0623 or 6.23 percent

(difficult)

Chapter Six                                      80
The Risks and Returns from Investing
3.       Calculate the future value of \$100,000 at the end of 64 years given an
interest rate of 10.38 percent.

Solution:     Future Value =            Present Value (1 + r)n
=      \$100,000 (1.1038) 64
=      \$100,000 (555.8849840)           or on a financial calculator:
=      \$55,588,498.40                   100000 PV, 64N, 10.38 Int,
Solve for FV = \$55,588,498,40
(easy)

4.       John Crossborder buys 1 share of Telmex at 140 pesos when the value of
the peso is stated in dollars at \$0.35. One year later, Telmex is selling for
155 pesos and paid a dividend of 5 pesos during the year. If after 1 year
the value of the pesos is \$0.29, what will John's rate of return be in U. S.
dollars?

Solution:     Return Relative in pesos = [(155 - 140 + 5)/140] + 1.0 =
1.1429

Domestic TR =         1.1429[0.29/0.35] - 1 = -0.0531 or -5.31 percent

(difficult)

5.       If you deposit \$1,000 today at 12 percent, how much will you have in 10
years?

Solution:        Using a financial calculator: 1000 PV, 12 interest rate, 10 N,
solve for FV = \$3,105.85

(easy)

6.       What is the present value of \$20,000 to be received in 40 years if the
interest rate is 9 percent?

Solution:        Using a financial calculator: 20000 FV, 9 interest rate, 40 N,
solve for PV = \$636.75

(easy)

Chapter Six                                    81
The Risks and Returns from Investing

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