Chapter 1—The investment decision
TRUE/FALSE

	1.	Investment returns are received from two sources; interest and dividends.

ANS:	F
The answer is false. Investments returns arise from three sources. Time value of money, pure rate of interest and rate of inflation.

PTS:	1	DIF:	Easy	REF:	1.1 Introduction

	2.	Generally speaking, equity is the least risky of the asset classes.

ANS:	F
The answer is false. Equity is the most risky asset class because of the uncertainty of equity cash flows. First, companies need not pay dividends; also, equity holders only have a residual claim to the cash flows of the company after all other security holders have been paid.

PTS:	1	DIF:	Easy	REF:	1.3.2 Classifying investments

	3.	The use of discrete returns ignores compounding.

ANS:	T
The nominal return is the return for a certain, or single, period. It therefore assumes there is only a single period, and hence ignores the impact of compounding.

PTS:	1	DIF:	Easy	REF:	1.4.1.1 Measuring returns on an investment

	4.	A continuously compounded return is always less than the equivalent discrete return.

ANS:	T
To illustrate, consider an investment with a total return of 10% over two periods. Using discrete returns, the periodic return must be 5% per period, to result in a 10% return over two periods. However, if we allow for compounding, the required periodic return will be less than 5%. Therefore, a compounded return (e.g. continuous) will always be less than the equivalent discrete return.

PTS:	2	DIF:	Moderate	REF:	1.4.1.1 Measuring returns on an investment

	5.	An advantage of using discrete returns is to reduce the distorting effect a low share price may have on returns.

ANS:	F
The answer is false. As returns are calculated as the relative change in price, shares with low prices may appear to have relatively large returns. However, since continuously compounded returns are always less than discrete returns, the distorting effect of low prices is reduced by using compounding. For example, an investment that changes in value from $0.02 to $0.03 will have a discrete return of 50% [i.e. (0.03 – 0.02)/2], whereas the continuously compounded return will be approximately 41% [i.e. ln(0.03/0.02)]. So, in fact it is the use of continuous compounding returns rather than discrete returns that will reduce the low price effect. Therefore, the answer is false.

PTS:	3	DIF:	Difficult	REF:	1.4.1.1 Measuring returns on an investment

	6.	A geometric return is always less than the corresponding arithmetic return.

ANS:	F
In general the statement is correct, as the geometric return tends to be lower than the corresponding arithmetic return. Indeed, the greater the difference between the returns, the higher the level of volatility in the returns. Therefore, under a situation where there are constant returns, the geometric and arithmetic returns will be equal, and hence the statement is not always correct.

PTS:	3	DIF:	Difficult	REF:	1.4.3.2 Calculating return over time

	7.	Zero volatility in returns results in identical arithmetic and geometric returns.

ANS:	T
The statement is true. The greater the difference between the returns, the higher the level of volatility in the returns. In contrast, under a situation where returns are constant, the geometric and arithmetic returns will be equal.

PTS:	2	DIF:	Moderate	REF:	1.4.3.2 Calculating return over time

	8.	An advantage of covariance over correlation is that it is bound to be between positive and negative 1.

ANS:	F
The statement is false. It is actually the correlation that is bound between positive and negative 1, and not the covariance. This feature is an advantage of the correlation over the covariance.

PTS:	2	DIF:	Moderate	REF:	1.4.4.2 Covariance and correlation

	9.	If two normal distributions are multiplied, the outcome distribution is normal.

ANS:	F
The outcome distribution is not normal. A normal distribution has several properties. Firstly, if returns from one normal distribution are mixed with returns from another normal distribution, the resultant distribution is normal. Secondly, when two normal distributions are added together this has the property of additive stability. If two normal distributions are multiplied the outcome distribution is not normal.

PTS:	2	DIF:	Moderate	REF:	1.4.2 Distribution

	10.	The lognormal distribution is symmetrical.

ANS:	F
The lognormal distribution has positive skewness. Skewness represents the degree to which returns are symmetrical around the mean. Therefore, the statement is incorrect.

PTS:	2	DIF:	Moderate	REF: 1.4.2 Distribution

MULTIPLE CHOICE

	1.	Steps involved in the asset allocation decision are considered to be:
A.	collective, rather than in isolation.	
B.	indirectly related to investors holding period and risk tolerance.	
C.	effective in reducing future uncertainty	
D.	all of the above	

ANS:	A
Investment decisions cannot be made independently, therefore the asset allocation process is collective.

PTS:	1	DIF:	Easy	REF:	1.3 Allocation decision

	2.	Investment assets differ in risk because of:
A.	cash flow uncertainty	
B.	time value of money uncertainty	
C.	uncertainty regarding the rate of inflation	
D.	all of the above	

ANS:	A
The risk of an investment is dependent on the uncertainty; specifically, the uncertainty associated with the investment cash flows. Uncertainty regarding the time value of money and the rate of inflation, while contributing to the risk of an investment, is the same across all investments.

PTS:	2	DIF:	Moderate	REF:	1.1 Introduction

	3.	A risk-averse investor will, all other things being equal, prefer investing in which of the following asset classes?
A.	equity	
B.	property	
C.	fixed interest	
D.	shares	

ANS:	C
A risk-averse investor will prefer investments that have the lowest risk. Of the asset classes listed, equity and property are both relatively high risk. Note that shares are not an asset class, but are instead an investment in the equity asset class. The lowest risk asset class is fixed interest.

PTS:	2	DIF:	Moderate	REF:	1.3.3 Investor preferences

	4.	Which of the following holding periods is an active investor more likely to invest in?
A.	short term	
B.	medium to long term	
C.	long term only	
D.	none of the above	

ANS:	A
Active investment typically involves taking positions to profit from imbalances in the market. These imbalances tend to be short term in nature.

PTS:	2	DIF:	Moderate	REF:	1.3.3 Investor preferences

5.		Which of the following is not a documented feature of equity returns in Australia?
A.	platykurtosis	
B.	lognormality	
C.	skewness	
D.	none of the above	

ANS:	A
Research into Australian returns, for example by Beedles (1986), documented evidence of non-normality and positive skewness. Hence, the only incorrect answer is platykurtosis, as this is not a documented feature of Australian equity returns.

PTS:	3	DIF:	Difficult	REF:	1.4.5.3 Lognormal distribution

	6.	The excess kurtosis of a normal distribution is:
A.	0	
B.	1	
C.	3	
D.	6	

ANS:	A
A normal distribution is defined as having a skewness of 0 and a kurtosis of 3. However, the excess kurtosis measure for a normal distribution is 0.

PTS:	2	DIF:	Moderate	REF:	1.4.5.2 Normal distribution

	7.	Under a normal distribution, what proportion of observations fall within two standard deviations of the mean?
A.	50%	
B.	68%	
C.	75%	
D.	95%	

ANS:	D
Standard tables exist that list the probabilities of observations falling above or below certain values. For a normal distribution, approximately 95% of values fall within two standard deviations of the mean.

PTS:	2	DIF:	Moderate	REF:	1.4.5 Distribution

	8.	Which of the following is true regarding the investor’s life cycle of Seigal (1991)?
A.	As investors age, less wealth is allocated to risky investments	
B.	As investors age, their wealth increases	
C.	Younger investors tend to make better investments	
D.	Investment composition changes little with age	

ANS:	A
The investor life cycle of Seigal (1991) states that the composition of an investor’s portfolio will tend towards lower-risk investments as an investor’s age increases.

PTS:	2	DIF:	Moderate	REF:	1.5 Review stage

9.	Which of the following best describes the changes in asset class composition that occur with increased age, according to the investor life cycle theory of Seigal (1991)?
A.	more wealth allocated to equity	
B.	more wealth allocated to fixed interest	
C.	less wealth allocated to property	
D.	less wealth allocated to cash	

ANS:	B
The investor life cycle of Seigal (1991) states that the composition of an investor’s portfolio will tend towards lower-risk investments as an investor’s age increases. Therefore investors will tend to increase holdings of the cash, fixed interest and property asset classes and decrease holdings of equity.

PTS:	3	DIF:	Difficult	REF:	1.5 Review stage

	10.	Which of the following statements is true when comparing the log normal distribution to the normal distribution?
A.	the log normal distribution has a higher mean and standard deviation	
B.	the log normal distribution has negative skewness	
C.	the log normal distribution has negative skewness and high standard deviation	
D.	the log normal distribution has positive skewness	

ANS:	D
The normal and lognormal distributions can be differentiated according to their higher moments (i.e. skewness and kurtosis). A lognormal distribution has positive skewness.

PTS:	3	DIF:	Difficult	REF:	1.4.5.4 Return distributions

	11.	An investor purchased an asset for $32 000 at the beginning of the year. This investment is worth $36 000 at the end of the year. What is the return for the year on the investment?
A.	12.5%	
B.	14%	
C.	16%	
D.	18%	

ANS:	A
Rearranging equation 1.1, page 11, the return for the year = (36000 – 32000)/32000 = 0.125
Hence, the return for the year is 12.5%.

PTS:	1	DIF:	Easy	REF:	1.4.1.1 Measuring return 

	12.	An investor purchased an asset for $1675. This investment is worth $1742 after three months. What is the simple annualised return for the investment (simple annual return)?
A.	12%	
B.	14%	
C.	16%	
D.	18%	

ANS:	C
Rearranging equation 1.1, page 11, the three-month return is equal to (1742 – 1675)/1675 = 0.04. The return for the three-month period is 4%. Hence, the simple annualised return on the investment is 0.04 × 4 = 0.16 or 16%.

PTS:	2	DIF:	Moderate	REF:	1.4.1.1 Measuring return

	13.	An investor purchased an asset for $1675. This investment is worth $1742 after three months. What is the effective annualised return for the investment?
A.	15%	
B.	17%	
C.	19%	
D.	21%	

ANS:	B
Using equation 1.1, page 11, the periodic (three-month) return is calculated as (1742 – 1675)/1675 = 0.04. The return for the three-month period is 4%. The effective annual return can be calculated using equation 1.2, page 12 as follows: [(1 + 0.04)4 – 1] = 0.17 or 17%.

PTS:	2	DIF:	Moderate	REF:	1.4.1.1 Measuring return

	14.	An investment was purchased for $2985. After seven months this investment was worth $3245. What is the continuously compounded return on the investment over the seven-month period?
A.	7.61%	
B.	8.35%	
C.	8.95%	
D.	9.13%	

ANS:	B
Using equation 1.5, page 14, the continuously compounded return over the seven-month period is r = ln(3245/2985) = 0.0835 or 8.35%.

PTS:	2	DIF:	Moderate	REF: 1.4.1 Return definitions

Year	Return (%)	
Year 1	7%	
Year 2	17%	
Year 3	–2.4%	
Year 4	2%	

	15.	The value of an investment at the end of each of four years is shown above. What is the arithmetic cumulative return over the four years?
A.	23.6%	
B.	17%	
C.	-2.14%	
D.	 2%	

ANS:	A
Using equation 1.11, page 18, the arithmetic cumulative return for the investment over the four years is calculated as (0.07 + 0.17 – 0.024 + 0.02) = 0.236 or 23.6%.

PTS:	2	DIF:	Moderate	REF:	1.4 Performance measures

	16.	The value of an investment at the end of each of four years is shown above. What is the arithmetic average return over the four years?
A.	-5.75%	
B.	4.00%	
C.	4.25%	
D.	5.90%	

ANS:	D
Using equation 1.11, page 18, the arithmetic cumulative return for the investment over the four years is calculated as (0.07 + 0.17 – 0.024 + 0.02) = 0.236 or 23.6%. As per example 1.10, page 18, the arithmetic average return is found by dividing the cumulative return by the number of years, or 0.236/4 = 0.059 or 5.90% per annum.

PTS:	2	DIF:	Moderate	REF:	1.4 Performances measures

	17.	The value of an investment at the end of each of four years is shown above. What is the geometric cumulative return over the four years?
A.	15.1%	
B.	24.63%	
C.	18.7%	
D.	19.7%	

ANS:	B
Using equation 1.12, page 18, the geometric return over the four years is calculated as: [(1 + 0.07)(1 + 0.17)(1 – 0.024)(1 + 0.02) – 1] = 0.2463 or 24.63%  (Example 1.9)

PTS:	2	DIF:	Moderate	REF:	1.4.3 Calculating return

	18.	The value of an investment at the end of each of four years is shown above. What is the geometric average return over the four years?
A.	4.0%	
B.	4.67%	
C.	5.26%	
D.	5.66%	

ANS:	D
Using the equation in example 1.10, page 19, the geometric average return over the four years is calculated as [(1 + 0.07)(1 + 0.17)(1 – 0.024)(1 + 0.02)]1/4 – 1 = 0.0566 or 5.66% per annum.

PTS:	2	DIF:	Moderate	REF:	1.4.3 Calculating return

Asset	Price at
start of period ($)	Price at
end of period ($)	
A	$3.25	$4.25	
B	$4.12	$3.85	

	
19.	      Given the prices for A and B at the start and end of the period, calculate the continuously compounded return on an equally weighted portfolio consisting of assets A and B.
A.	8.20%	
B.	9.60%	
C.	10.00%	
D.	12.8%	

ANS:	C
Using equation 1.5, page 14, the continuously compounded return for share A is ln(4.25/3.25) = 0.268 or 26.8%, and for share B is ln(3.85/4.12) = –0.068 or –6.8%. Using equation 1.15, page 23, the equally weighted (continuously compounded) return on the portfolio is 0.5(26.8) + 0.5(–6.8) = 10%.

PTS:	2	DIF:	Moderate	REF:	1.4.4 Portfolio 

	20.	Given the prices for A and B at the start and end of the period, if an investor holds 1000 shares in asset A and 5000 in asset B, what is her value-weighted return on the portfolio?
A.	–3.12%	
B.	–2.23%	
C.	–1.12%	
D.	2.56%	

ANS:	B
Using equation 1.5, page 14, the continuously compounded return for share A is ln(4.25/3.25) = 0.268 or 26.8%, and for share B is ln(3.85/4.12) = –0.068 or –6.8%. The total value of the portfolio is (1000 ´ 3.25 + 5000 ´ 4.12) = 23850, of which 3250/23850 = 0.136 is invested in asset A, and 0.864 is invested in asset B. Using equation 1.14, page 22, the value-weighted (continuously compounded) return on the portfolio is 0.136(26.8) + 0.864(–6.8) = –2.23%.

PTS:	2	DIF:	Moderate	REF:	1.4.4 Portfolio

	21.	Given the prices for A and B at the start and end of the period, calculate the price-weighted return on a portfolio consisting of assets A and B.
A.	7.22%	
B.	7.85%	
C.	8.02%	
D.	8.65%	

ANS:	C
Using equation 1.5, page 14, the continuously compounded return for share A is ln(4.25/3.25) = 0.268 or 26.8%, and for share B is ln(3.85/4.12) = –0.068 or –6.8%. The total cost (in terms of price) of the portfolio is 3.25 + 4.12 = $7.37, of which 3.25/7.37 = 44.1% is invested in asset A, and 55.9% is invested in asset B. Using equation 1.16, page 23, the price-weighted (continuously compounded) return on the portfolio is 0.441(26.8) + 0.559(–6.8) = 8.02%.

PTS:	2	DIF:	Moderate	REF:	1.4.4 Portfolio

Asset	Number of shares	Initial price ($)	End price ($)	
A	2000	6.00	6.10	
B	5000	3.00	2.25	
C	3000	12.00	11.50	
D	12 000	8.50	8.85	

	22.	An investor purchased the investment above. What is the value-weighted return on the portfolio?
A.	–1.2%	
B.	1.2%	
C.	2.3%	
D.	2.5%	

ANS:	B
We must first calculate the continuously compounded return for each of the four shares. Using equation 1.5, page 14, the return for asset A is ln(6.10/6.00) = 0.165, for asset B is ln(2.25/3.00) = –0.288, for asset C is ln(11.50/12.00) = –0.043 and for asset D is ln(8.85/8.5) = 0.040. The total value of the portfolio is (2000 ´ 6.00 + 5000 ´ 3.00 + 3000 ´ 12.00 + 12000 ´ 8.50) = 165000. The value weights for each of the assets A, B, C and D, respectively, are for asset A (2000 ´ 6.00)/165000 = 0.073, for asset B = (5000 ´ 3.00)/165000 = 0.091, for asset C = (3000 ´ 12.00)/165000 = 0.218 and for asset D = (12000 ´ 8.50)/165000 = 0.618. Using equation 1.14, page 22, the value-weighted return is calculated as R = (0.073)(0.165) + (0.091)(–0.288) + (0.218)(–0.043) + (0.618)(0.040) = 0.012 or 1.2%.

PTS:	3	DIF:	Difficult	REF:	1.4.1.2 &1.4.4.1

	23.	An investor purchased the investment above. If continuously compounded returns are used, what is the equal-weighted return on the portfolio?
A.	–12.6%	
B.	–10.5%	
C.	–3.2%	
D.	2.3	

ANS:	C
We must first calculate the continuously compounded return for each of the four shares. Using equation 1.5, page 14, the return for asset A is ln(6.10/6.00) = 0.165, for asset B is ln(2.25/3.00) = –0.288, for asset C is ln(11.50/12.00) = –0.043 and for asset D is ln(8.85/8.5) = 0.040. Using equation 1.15, page 23, the equal-weighted return is calculated as R = [(0.165) + (–0.288) + (–0.043) + (0.040)]/4 = –0.0.0315 or –3.2%.

PTS:	2	DIF:	Moderate	REF:	1.4.1.2 & 1.4.4.1

Asset	Expected return
(E(R))	Standard deviation 
(s)	
A	10%	9%	
B	12%	8%	
C	15%	12%	
D	13%	11%	

	24.	Which of the four investments has the highest coefficient of variation?
A.	Asset A	
B.	Asset B	
C.	Asset C	
D.	Asset D	

ANS:	A
Using equation 1.10, page 18, the coefficient of variation (CV) can be calculated by dividing the standard deviation by the expected return. That is, the CV of asset A is 0.09/0.10 = 0.9, for asset B is 0.08/0.12 = 0.67, for asset C is 0.12/0.15 = 0.8 and for asset D is 0.11/0.13 = 0.85. Therefore, asset A has the highest coefficient of variation.

PTS:	2	DIF:	Moderate	REF:	1.4.2 Deviation

25.    	Given no other information other than the expected returns and risk, which asset would a risk-averse investor prefer?
A.	Asset A	
B.	Asset B	
C.	Asset C	
D.	Asset D	

ANS:	B
For two assets with the same expected return, a risk-averse investor will prefer the investment with the lower standard deviation, and for two investments with the same standard deviation will prefer the investment with the highest return. In this case, since the investments have different risks and expected returns, the coefficient of variation can be used. All other things equal, for a risk-averse investor a lower coefficient of variation is desirable, as this indicates less risk for each unit of expected return. Using equation 1.10, page 20, the coefficient of variation (CV) can be calculated by dividing the standard deviation by the expected return. That is, the CV of asset A is 0.09/0.10 = 0.9, for asset B is 0.08/0.12 = 0.67, for asset C is 0.12/0.15 = 0.8 and for asset D is 0.85. Therefore, asset B has the lowest coefficient of variation, hence will be the most preferred by a risk-averse investor.

PTS:	2	DIF:	Moderate	REF:	1.4.2 Deviation

	26.	The price at the start of the period for asset A is $5 and for asset B is $6. At the end of the period, asset A has fallen to $4 and asset B has risen to $6.50. Calculate the continuously compounded return on a price-weighted portfolio consisting of shares A and B.
A.	–5.8%	
B.	–4.9%	
C.	–2.5%	
D.	2.5%	

ANS:	A
Using equation 1.5, page 14, the return on asset A is ln(4/5) = –0.223 and for asset B is ln(6.5/6) = 0.080. The total cost (i.e. price) of the portfolio is $5 + $6 = $11, of which 5/11 = 0.455 is due to asset A and 6/11 = 0.545 is due to asset B. Hence, by equation 1.16, page 23, the price-weighted return on the portfolio (R) is equal to (0.455)(–0.223) + (0.545)(0.080) = –0.058 or –5.8%.

PTS:	2	DIF:	Moderate	REF:	1.4.4 Portfolio measurement

27.	      The returns for two assets, A and B, are 5% and 8% respectively. If a price-weighted portfolio were formed when shares in A were $9 and shares in B were $3, what is the continuously compounded price-weighted return for the portfolio?
A.	3.25%	
B.	4.75%	
C.	5.75%	
D.	6.25%	

ANS:	C
The total cost (i.e. price) of the portfolio is $9 + $3 = $12, of which 9/12 = 0.75 is due to asset A and 3/12 = 0.25 is due to asset B. Hence, by equation 1.16, page 23, the price-weighted return on the portfolio (R) is equal to (0.75)(5%) + (0.25)(8%) = 5.75%.

PTS:	1	DIF:	Easy	REF:	1.4.4.1 Portfolio formation methods

	28.	The returns for two assets, A and B, are 5% and 8% respectively. If an investor holds 25% of her wealth in asset A, what is the continuously compounded return of a value-weighted portfolio comprising assets A and B?
A.	3.25%	
B.	6.25%	
C.	6.75%	
D.	7.25%	

ANS:	D
Using equation 1.16, page 23, the value-weighted return on the portfolio (R) is equal to (0.25)(5%) + (0.75)(8%) = 7.27%.

PTS:	1	DIF:	Easy	REF:	1.4.4.1 Portfolio formation methods

29.	    Loredana has invested equal amounts in each of the shares of company A, company B and company C, which she purchased one year ago at prices of $10, $2 and $1, respectively. Loredana has recently sold her shares in company B for $2.50 and in company C for $1.15. If Loredana wishes to earn a continuously compounded return of 20% for the year, on her equally weighted portfolio, at what price will she need to sell her shares in company A?
A.	$11.55	
B.	$12.26	
C.	$12.67	
D.	$13.34	

ANS:	C
Using equation 1.5, page 14, the continuously compounded return for asset B is ln(2.5/2) = 0.223, and for asset C is ln(1.15/1) = 0.140. If we denote x as the return Loredana needs to earn on asset A, and she wishes to earn 20% on the equally weighted portfolio, then using equation 1.15, page 23, we know that the equally weighted portfolio return is: (1/3)(x) + (1/3)(0.223) + (1/3)(0.140) = 0.20. Solving the equation for x yields an answer of x = 23.7%. Therefore, Loredana must earn a return on asset A of 23.7%. Denoting P as the selling price, then using equation 1.5, ln(P/$10) = 0.237. Hence, P = 10e0.237, which equals $12.67. As a check, using equation 1.5, ln(12.67/10) = 23.7.

PTS:	3	DIF:	Difficult	REF:	1.4.4.1 Portfolio formation methods

30.	      Charles invests in a price-weighted portfolio of two shares, ABC and XYZ. His funds manager sends him a statement of his performance at the end of each year for his tax return. Unfortunately, some of the form was illegible, and all he could discern was that the price-weighted portfolio return was 10%, the returns on ABC and XYZ were 8% and 16%, respectively and that the purchase price of ABC was $10. Given this information, at what price did Charles purchase the shares in company XYZ?
A.	$2.50	
B.	$3.33	
C.	$3.75	
D.	$4.25	

ANS:	B
Given that there are only two shares in the portfolio, the weights in each asset must sum to unity. That is, if we define the (unknown) price weight in asset B as wb, then the weight in asset A is 1 – wb. Using equation 1.16, page 23, we know the price-weighted return on the portfolio is 10%, which can be expressed as 0.10 = (1 – wb)(8%) + wb(16%). Solving yields wb = 25%. We can now solve for the selling price of asset B. We know that the price-weight of asset B is calculated as the purchase price of asset B divided by the combined purchase prices of both assets A and B, and that the weight must be 25%. Hence if we denote the purchase price of asset A as P, we know that P/(10 + P) = 0.25. Hence, P = 2.5 + 0.25P, which can be solved to yield P = 3.33. To verify the answer is correct, we now know that the price of assets A and B are $10 and $3.33 (and hence a combined cost (i.e. price) of $13.33), respectively. Hence, the price-weighted return on the portfolio should be (10/13.33)(8%) + (3.33/13.33)(16%) = 10.0% as required.

PTS:	3	DIF:	Difficult	REF:	1.4.4.1 Portfolio formation methods