Download Week Four Review Questions and Problems

WEEK FOUR
REVIEW QUESTIONS AND PROBLEMS
Returns, Risks, Portfolio Selection and Market Theory
Do the following textbook questions and problems to review your readings. Then check
your answers below.
Chapter 6, page 176: Questions 6-3, 6-5, 6-9, 6-11 and 6-14.
Chapter 6, pages 180 to 181: Problems 6-1, 6-3, 6-5, 6-13, 6-17 (a), (b) and (c).
Chapter 7, pages 214 to 215: Questions 7-2, 7-4, 7-7, 7-10, 7-11, and 7-23.
Chapter 7, page 216: Problem 7-1.
Chapter 8, page 241: Questions 8-2, 8-4, 8-5 and 8-9.
Chapter 9, pages 274 to 275: Questions 9-1, 9-2, 9-3, 9-17 and 9-27.
Chapter 9, page 277: Problem 9-11.
Chapter 10, page 316: Questions 10-1, 10-4, 10-8, 10-14 and 10-15.
ANSWERS TO REVIEW QUESTIONS
CHAPTER 6
6-3.
The arithmetic mean should be used when describing the average rate of return
without considering compounding. It is the best estimate of the rate of return for
a single period. Thus, in estimating the rate of return for common stocks for next
year, we use the arithmetic mean and not the geometric mean. The reason is
that because of variability in the returns, we will have to average the arithmetic
rate in order to achieve a rate of growth given by the smaller geometric mean.
6-5.
TR, which is another name for holding period yield, is a percentage return, such
as +10% or –15%. The term “holding period return” is sometimes used instead
of TR.
Return relative adds 1.0 to the TR so that all returns can be stated on the basis
of 1.0 (which represents no gain or loss), thereby avoiding negative numbers so
that the geometric mean can be calculated.
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6-9.
The return on Japanese investment is now worth less in dollars. Therefore, the
investor’s return will be less after the currency adjustment.
EXAMPLE: Assume a Canadian investor in the Japanese market has a 30%
gain in one year, but the Yen declines in value relative to the dollar by 10%. The
percentage of the original investment after the currency risk is accounted for is
(0.9)(130%) = 117%. Therefore, the investor’s return is 17%, not 30%. In effect,
the investor loses 10% on the original wealth plus another 10% on the 30% gain,
or a total of 13 percentage points of the before-currency-adjustment wealth of
130% of investment.
6-11. Dividing the geometric mean return for common stocks by the geometric mean
rate of inflation for a given period produces the inflation-adjusted rate of return.
6-14. The geometric mean is a better measure of the change in wealth over more than
a single period. Over multiple periods the geometric mean indicates the
compound rate of return or the rate at which an invested dollar grows, taking into
account the variability in the returns.
The geometric mean is always less than the arithmetic mean because it allows
for the compounding effect ― the earning of interest on interest.
CHAPTER 7
7-2.
The expected return for one security is determined from a probability distribution
consisting of the likely outcomes, and their associated probabilities, for the
security.
The expected return for a portfolio is calculated as a weighted average of the
individual securities’ expected returns. The weights used are the percentages of
total investable funds invested in each security.
7-4.
Each security in a portfolio, in terms of dollar amounts invested, is a percentage
of the total dollar amount invested in the portfolio. This percentage is a weight,
and the general assumption is that these weights sum to 1.0, accounting for all of
the portfolio funds.
7-7.
The key assumption of the single-index model is that securities are related only
in their common response to the return on the market; that is, the residual errors
for security I are uncorrelated with those of security j.
7-10. A stock with a large risk (standard deviation) could be desirable if it has high
negative correlation with other stocks. This will lead to large negative
covariances, which help to reduce the portfolio risk.
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7-11. Markowitz was the first to formally develop the concept of portfolio diversification.
He showed quantitatively why and how portfolio diversification works to reduce
the risk of a portfolio to an investor. In effect, he showed that diversification
involves more than the number of securities ― it involves the relationships
among securities.
7-23 . Based on past history, investors should expect stock and bond returns to be
positively related. Returns on bonds and T-bills have also been positively
related. Stocks and gold have been negatively related, while stocks and real
estate have been positively related.
CHAPTER 8
8-2. Rational, risk-averse investors seek efficient portfolios because these portfolios
promise maximum expected return for a specified level of risk, or minimum risk for
a specified expected return.
8-4. Lending portfolios refer to the case where part of the portfolio funds are placed in
the risk-free asset, which is typically proxied by Treasury bills. When an investor
purchases T-bills, he or she is, in effect, lending money to the government.
8-5. Systematic risk is the variability in a security’s total returns that is directly
associated with overall movements in the general market or economy. Nonsystematic risk is firm-specific, meaning that it only affects one firm or a small
number of firms.
Proper diversification cannot reduce systematic risk because this type of risk
affects virtually all companies on the stock market. For example, an unexpected
increase in interest rates will have a negative effect on almost all companies, since
their borrowing costs will increase.
8-9. If an investor were very conservative and risk-averse, he or she would probably be
a risk-free lender. In other words, they would invest all their money in the risk-free
asset, T-bills. (See curve U1.)
If an investor became very risk-tolerant, he or she would probably borrow and
invest that borrowed money in the risky assets. (See curve U2.)
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CHAPTER 9
9-1.
The basic difference between graphs of the SML and the CML is the label on the
horizontal axis. For the CML, it is standard deviation while for the SML, it is beta.
Also, the CML is applicable to portfolios only while the SML applies to individual
securities and portfolios.
9-2.
In theory, the market portfolio (portfolio M) is the portfolio of all risky assets, both
financial and real, in their proper proportions. Such a portfolio would be
completely diversified; however, it is a risky portfolio. In equilibrium, all risky
assets must be in portfolio M because all investors are assumed to hold the
same risky portfolio.
9-3.
The major problem in testing capital market theory is that the theory is formulated
ex-ante, concerning what is expected to happen. The only data we typically have
are ex-post.
9-17. Using some methodology (such as the dividend valuation model), to estimate the
expected returns for securities, investors can compare these expected returns to
the required returns obtained from the SML. Securities whose expected returns
plot above the SML are undervalued because they offer more expected return
than investors require. If they plot below the SML, they are overvalued because
they do not offer enough expected return for their level of risk.
9-27. We can evaluate how each security affects the standard deviation of the market
portfolio by evaluating the way it would change if the proportion invested in a
particular security changes. In effect, we take the partial derivative of the
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standard deviation of the market portfolio with respect to the proportion of
portfolio funds invested in that particular security.
The result is that a security's contribution to the risk of the market portfolio is
given by:
Si,M /SM
where Si,M = the covariance between stock i and the market portfolio.
CHAPTER 10
10-1.
An efficient market is defined as one in which the prices of securities fully
reflect all known information quickly and accurately.
10-4.
If the EMH is true, there are several implications for investors:



10-8.
Technical analysis has no validity or, at the very least, is seriously in doubt.
Conventional fundamental analysis ― the type done by the majority of
analysts ― is of little value, producing, at best, average results. What is
necessary is to perform clearly superior fundamental analysis.
As for money management activities, passive strategies would receive
much more emphasis. Nevertheless, several tasks must still be performed,
such as diversifying, establishing, and maintaining the risk level, and being
concerned with the tax status of the investor and his or her transaction
costs.
The three (cumulative) forms of market efficiency are
1. the weak form, which states that market data (price and volume
information), are reflected in current prices and should be of no value in
predicting future price changes;
2. the semi-strong form, which states that all publicly known and publicly
available data are incorporated into stock prices; and
3. the strong form, which states that prices fully reflect all information, public
and nonpublic (i.e., information that can be restricted to certain groups).
10-14. Market anomalies are research findings that do not support market efficiency;
that is, they are evidence that inefficiencies do exist. These results are in
contrast to what would be expected in a totally efficient market.
Well known anomalies include:

the SUE effect, or the proposition that the adjustment of stock prices to
quarterly earnings announcements occurs with a lag;
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



the P/E effect, or the proposition that low P/E stocks will, on average,
outperform high P/E stocks;
the size effect, or the proposition that small capitalization stocks have
earned higher risk-adjusted returns than large capitalization stocks;
the seasonal effect, or the proposition that stocks have exhibited higher
returns than expected in January (this could also include the monthly effect,
the weekend effect, and so forth); and
the Value Line results, which seem to indicate that this investment advisory
service has classified stocks into five groups that have performed in a
monotonic fashion, with very impressive results for the top (expected best
performers), two groups.
10-15. Earnings surprises are directly related to fundamental analysis. First, earnings
are a primary component of fundamental analysis. Second, stock prices should
be expected to adjust to any unexpected information contained in the earnings.
The question is how long this adjustment takes.
ANSWERS TO PROBLEMS
CHAPTER 6
6-1. Using WSC data from Demonstration Problem 6-2:
Year
20X3
20X4
20X5
20X6
20X7
Capital Gain / Loss ($)
-10.30
3.40
-11.00
39.55
25.75
Total Return ($)
-6.86
6.84
-7.56
42.99
29.46
TR for 20X5 = {$3.44 + ($56.70 - $67.70)}/$67.70 = -0.1117 or -11.2%
TR for 20X6 = {$3.44 + ($96.25 - $56.70)}/$56.70 = 0.7582 or 75.8%
6-3. Calculate future value of $100 using tables at end of text: @12%. Or use the
financial calculator. Assume annual compounding.
$100 (1.762) =
$100 (3.106) =
$100 (9.646) =
$100 (29.96) =
$176.20 after 5 years, or $176.23 by financial calculator
$310.60 after 10 years, or $310.58 by financial calculator
$964.60 after 20 years, or $964.63 by financial calculator
$2996.00 after 30 years, or $2995.99 by financial calculator
Calculate present value of $100 using tables at end of text: @12%. Or use the
financial calculator. Assume annual compounding.
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$100 (.567)
$100 (.322)
$100 (.104)
$100 (.033)
6-5.
Year
20X3
20X4
20X5
20X6
20X7
=
=
=
=
$56.70 after 5 years, or $56.74 by financial calculator
$32.20 after 10 years, or $32.20 by financial calculator
$10.40 after 20 years, or $10.37 by financial calculator
$3.30 after 30 years, or $3.34 by financial calculator
(1 + r)
1.0122*
1.1522**
1.3868**
1.0284**
1.1152***
GM = [(1.0121)(1.1522)(1.3868)(1.0284)(1.1152)]1/5 - 1.0
= (1.8547268)1/5 = 1.1315 = (1 + r)
r = 1.1315 - 1 = .1315, r = 13.15%
* this is based on a 20X2 price of $25.50
** as shown in the table for Demonstration Problem 1
*** as calculated in Demonstration Problem 1
(11)1/79 – 1.0 = 0.0308 or 3.08%
6-13.
NOTE: For this problem, there are 79 years.
6-17. (a)
TR (2000) = (1.50 + 72 – 65)/65 = 13.08%
TR (2001) = (1.50 + 67 – 72)/72 = -4.86%
TR (2002) = (1.60 + 70 – 67)/67 = 6.87%
TR (2003) = (1.60 + 72.5 – 70)/70 = 5.86%
RR (2000) = 1 + 0.1308 = 1.1308
RR (2001) = 1 + (-0.0486) = 0.9514
RR (2002) = 1 + 0.0687 = 1.0687
RR (2003) = 1 + 0.0586= 1.0586
(b)
AA = (13.08 – 4.86 + 6.87 + 5.86) / 4 = 5.24%
(c)
GA = [(1.1308) (0.9514) (1.0687) (1.0586)] 1/4 – 1 = 0.0504 = 5.04%
CHAPTER 7
7-1. (a)
(.25)(15) + (.25)(12) + (.25)(30) + (.25)(22) = 19.75%
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(b)
(.10)(15) + (.30)(12) + (.30)(30) + (.30)(22) = 20.70%
(c)
(.10)(15) + (.10)(12) + (.40)(30) + (.40)(22) = 23.50%
CHAPTER 9
9-1. a)
b)
βp = 0.25 (0.32) + 0.25 (1.4) + 0.25 (0.69) + 0.25 (1.11) = 0.88
βp = 0.5 (0.32) + 0.25 (1.4) + 0.15 (0.69) + 0.10 (1.11) = 0.7245
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