Financial Decision Making - 10522/10522M
Topic 5- Share price Behaviour and Informational
Efficiency - Outline Answers
MULTIPLE CHOICE - Choose the one alternative that best completes the statement or
answers the question.
1) An equity has annual returns of 6 per cent, 14 per cent, -3 per cent, and 2 per cent for the past
four years. The arithmetic average of these returns is _____ per cent while the geometric
average return for the period is _____ per cent.
A) 4.57; 4.75
B) 4.75; 4.57
C) 6.33; 6.19
D) 6.19; 6.33
E) 6.33; 6.33
Answer: Use formulas to estimate the Arithmetic average
𝑅1 + 𝑅2 + ⋯ + 𝑅𝑇
𝑅̄𝐴 =
𝑇
and Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) ⋯ × (1 + 𝑅𝑇 )](1/𝑇) − 1
where 𝑅1 , 𝑅2 , 𝑅3 , 𝑅4 are 6%, 14%, -3% and 2%, respectively. T=4.
2) An equity had returns of 16 per cent, 4 per cent, 8 per cent, 14 per cent, - 9 per cent, and -5
per cent over the past six years. What is the geometric average return for this time period?
A) 4.26 per cent
B) 4.67 per cent
C) 5.13 per cent
D) 5.39 per cent
E) 5.60 per cent
Answer: Use formulas to estimate the Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) ⋯ × (1 + 𝑅𝑇 )](1/𝑇) − 1
where 𝑅1 , 𝑅2 , 𝑅3 , 𝑅4 … … … .. are 16%, 4%, 8% and 14%, -9% and 5% respectively. T=6.
1
, Topic 5 - Share price behaviour and informational efficiency
3) An equity had the following prices and dividends. What is the geometric average return on
this equity?
A) -15.87 per cent
B) -14.56 per cent
C) -13.33 per cent
D) -12.91 per cent
E) -11.48 per cent
Answer: First estimate the holding period return for each year 2,3,4.
𝑃𝑡 + 𝐷𝑡 − 𝑃𝑡−1
𝑅𝑡 =
𝑃𝑡−1
Pt = price/value of the security at the end of period t
Dt = any dividend payment from the security during t
Pt-1 = price at the beginning of t ,adjusted to the same basis as Pt
Then use formulas to estimate the Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) × (1 + 𝑅3 )](1/3) − 1
2
Topic 5- Share price Behaviour and Informational
Efficiency - Outline Answers
MULTIPLE CHOICE - Choose the one alternative that best completes the statement or
answers the question.
1) An equity has annual returns of 6 per cent, 14 per cent, -3 per cent, and 2 per cent for the past
four years. The arithmetic average of these returns is _____ per cent while the geometric
average return for the period is _____ per cent.
A) 4.57; 4.75
B) 4.75; 4.57
C) 6.33; 6.19
D) 6.19; 6.33
E) 6.33; 6.33
Answer: Use formulas to estimate the Arithmetic average
𝑅1 + 𝑅2 + ⋯ + 𝑅𝑇
𝑅̄𝐴 =
𝑇
and Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) ⋯ × (1 + 𝑅𝑇 )](1/𝑇) − 1
where 𝑅1 , 𝑅2 , 𝑅3 , 𝑅4 are 6%, 14%, -3% and 2%, respectively. T=4.
2) An equity had returns of 16 per cent, 4 per cent, 8 per cent, 14 per cent, - 9 per cent, and -5
per cent over the past six years. What is the geometric average return for this time period?
A) 4.26 per cent
B) 4.67 per cent
C) 5.13 per cent
D) 5.39 per cent
E) 5.60 per cent
Answer: Use formulas to estimate the Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) ⋯ × (1 + 𝑅𝑇 )](1/𝑇) − 1
where 𝑅1 , 𝑅2 , 𝑅3 , 𝑅4 … … … .. are 16%, 4%, 8% and 14%, -9% and 5% respectively. T=6.
1
, Topic 5 - Share price behaviour and informational efficiency
3) An equity had the following prices and dividends. What is the geometric average return on
this equity?
A) -15.87 per cent
B) -14.56 per cent
C) -13.33 per cent
D) -12.91 per cent
E) -11.48 per cent
Answer: First estimate the holding period return for each year 2,3,4.
𝑃𝑡 + 𝐷𝑡 − 𝑃𝑡−1
𝑅𝑡 =
𝑃𝑡−1
Pt = price/value of the security at the end of period t
Dt = any dividend payment from the security during t
Pt-1 = price at the beginning of t ,adjusted to the same basis as Pt
Then use formulas to estimate the Geometric average,
𝑅̄𝐺 = [(1 + 𝑅1 ) × (1 + 𝑅2 ) × (1 + 𝑅3 )](1/3) − 1
2
