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Canvas Example MCQ — Q39

• A) 5%
• B) 10%
• C) 20%
• D) 21%
• E) None of A-D is close; write the correct answer.

[(1.10)(1.10)]^(1/2)-1 = 1.10-1 = 10%.

Rule: Arithmetic and geometric means are equal when annual returns are identical.

Canvas Example MCQ — Q40

• A) 9.54%
• B) 10.00%
• C) 20.00%
• D) 20.95%
• E) None of A-D is close; write the correct answer.

√(1.20 x 1.00)-1 = √1.20 -1 ≈ 0.09545 = 9.54%.

Rule: Compound gross returns, not percentages directly.

Canvas Example MCQ — Q41

• A) 5%
• B) 10%
• C) 20%
• D) 21%
• E) None of A-D is close; write the correct answer.

(121/100)^(1/2)-1 = 1.10-1 = 10%.

Rule: CAGR uses beginning and ending wealth.

Canvas Example MCQ — Q42

• A) Arithmetic mean = 10%; geometric mean ≈ 9.54%.
• B) Arithmetic mean ≈ 9.54%; geometric mean = 10%.
• C) Both means are exactly 10%.
• D) Geometric mean return is 0%.
• E) None of A-D is close; write the correct answer.

Arithmetic = (20+0)/2 = 10%. Geometric = √1.20-1 ≈ 9.54%.

Rule: Volatility creates a compounding drag.

Canvas Example MCQ — Q44

• A) -2.50%
• B) 0.23%
• C) 2.50%
• D) 5.00%
• E) None of A-D is close; write the correct answer.

(1.10)(1+R2) = 1.05^2 = 1.1025. Thus 1+R2 = 1.1025/1.10 = 1.002273, so R2 ≈ 0.23%.

Rule: For a geometric target, set the product of gross returns equal to (1+target)^n.

Canvas Example MCQ — Q45

• A) Both investments have the same arithmetic and geometric means.
• B) Both have the same arithmetic mean, but Investment A has the higher geometric mean.
• C) Investment B has the higher arithmetic and geometric means.
• D) Investment B has the higher geometric mean because its first-year return is higher.
• E) None of A-D is close; write the correct answer.

A geometric = 10%. B geometric = √(1.30 x .90)-1 = √1.17-1 ≈ 8.17%. Greater variation lowers compound growth.

Rule: Same arithmetic mean does not imply same compound performance.

Canvas Example MCQ — Q46

• A) SEK 108,000
• B) SEK 124,000
• C) SEK 125,971
• D) SEK 132,000
• E) None of A-D is close; write the correct answer.

100,000 x 1.08^3 = 125,971.2.

Rule: Use compound growth from the geometric mean.

Canvas Example MCQ — Q47

• A) 18%
• B) 20%
• C) 22%
• D) 44%
• E) None of A-D is close; write the correct answer.

(144/100)^(1/2)-1 = √1.44-1 = 1.20-1 = 20%.

Rule: CAGR is the constant annual compound rate.

Canvas Example MCQ — Q48

• A) Arithmetic mean = 2.5%, geometric mean = 0%.
• B) Both arithmetic and geometric means are 2.5%.
• C) Arithmetic mean = 0%, geometric mean = 2.5%.
• D) The cumulative two-year return is 5%.
• E) None of A-D is close; write the correct answer.

Arithmetic = (25-20)/2 = 2.5%. Gross wealth = 1.25 x .80 = 1.00, so geometric mean = 0%.

Rule: Positive arithmetic mean can coexist with zero cumulative wealth growth.

Canvas Example MCQ — Q50

• A) -3.0%
• B) 2.0%
• C) 7.2%
• D) 12.5%
• E) None of A-D is close; write the correct answer.

1.20 x .90 x (1+R3) = 1.05^3 = 1.157625. Thus 1+R3 = 1.157625/1.08 = 1.071875 -> R3 ≈ 7.19%.

Rule: Set the product of gross returns equal to the target compound growth factor.

Old Exam — Oct 2022, Q9

Given: Historical HPI dataset question. Current adaptation: ending value = initial value x index_end/index_start; geometric quarterly return = (ending/beginning)^(1/n)-1.

• A) The geometric mean returns is 1.126 %, and the house was worth $6 772 849
• B) The geometric mean returns is 1.279 %, and the house was worth $ 7 749 444
• C) The geometric mean returns is 1.240 %, and the house was worth $ 7 485 119
• D) The geometric mean returns is 1.113 %, and the house was worth $ 6 692 431
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: D) The geometric mean returns is 1.113 %, and the house was worth $ 6 692 431. Current paper-exam use: if the needed index levels/returns are supplied, apply the relevant return, compounding or correlation formula by hand; do not depend on the old spreadsheet.

Rule: The old exam supplied a spreadsheet/software. For the 2026 paper exam, expect the necessary values/table/output to be printed. Use the method, not the historical data file.

Old Exam — Dec 2021 re-exam, Q11

Given: Historical REIT data; geometric monthly mean is compound growth rate.

• A) 1.05%.
• B) 0.93%.
• C) 12.05%.
• D) 2.25%.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: B) 0.93%.. Current paper-exam use: if the needed index levels/returns are supplied, apply the relevant return, compounding or correlation formula by hand; do not depend on the old spreadsheet.

Rule: The old exam supplied a spreadsheet/software. For the 2026 paper exam, expect the necessary values/table/output to be printed. Use the method, not the historical data file.

Computer Lab 2 — Exercise 2B(ii)

• A) 9.57%
• B) 7.99%
• C) 248.89%
• D) 12.04%

Arithmetic mean = Sum of returns / n = 248.89% / 26 = 9.57%.

Rule: Arithmetic mean = (R1+R2+...+Rn)/n — a simple average of each period's return.

Computer Lab 2 — Exercise 2B(iii)

• A) CAGR ≈ 7.99%; lower due to volatility drag, since losses and gains compound asymmetrically
• B) CAGR ≈ 9.57%; identical to the arithmetic mean by definition
• C) CAGR ≈ 28.40%; higher than the arithmetic mean because it compounds all years
• D) CAGR ≈ 7.3844%; equal to the growth-factor product read as a percentage

CAGR = 7.3844^(1/26) − 1 = 7.99%. Volatility drag: e.g., +50% then −50% averages to an arithmetic mean of 0%, but wealth goes 100→150→75, a geometric loss — so geometric mean is always ≤ arithmetic mean when returns vary.

Rule: Geometric mean (CAGR) ≤ arithmetic mean whenever returns are volatile; the gap is caused by 'volatility drag'.