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13 questions · 1 formulas

Exact real return (Fisher)

Real = (1 + nominal)/(1 + inflation) − 1 (approx: nominal − inflation)

Trap: Exact vs approximate — check which the question asks.

Returns & CompoundingE-level★ High priority — official Canvas example

Nominal return 8%, inflation 3%. Approximate real return?

→ B) 5%

Canvas Example MCQ — Q22

A) 3%
B) 5%
C) 8%
D) 11%
E) None of A-D is close; write the correct answer.

8% - 3% = 5%.

Rule: Approximation: subtract inflation.

Returns & CompoundingE-level★ High priority — official Canvas example

Nominal return 8%, inflation 3%. Exact real return?

→ B) 4.85%

Canvas Example MCQ — Q23

A) 3.00%
B) 4.85%
C) 5.00%
D) 11.00%
E) None of A-D is close; write the correct answer.

1.08/1.03 - 1 = 0.04854 = 4.85%.

Rule: Exact Fisher adjustment divides gross returns.

Returns & CompoundingE-level★ High priority — official Canvas example

Required real return is 4% and inflation is 3%. Approximate nominal return?

→ C) 7%

Canvas Example MCQ — Q24

A) 1%
B) 4%
C) 7%
D) 12%
E) None of A-D is close; write the correct answer.

4% + 3% = 7%.

Rule: Reverse the approximation by adding inflation.

Returns & CompoundingE-level★ High priority — official Canvas example

Required real return 4%, inflation 3%. Exact nominal return?

→ C) 7.12%

Canvas Example MCQ — Q25

A) 4.00%
B) 7.00%
C) 7.12%
D) 12.00%
E) None of A-D is close; write the correct answer.

(1.04)(1.03)-1 = 1.0712-1 = 7.12%.

Rule: Exact nominal = product of gross real return and gross inflation.

Returns & CompoundingE-level★ High priority — official Canvas example

Nominal total return 4%, inflation 6%. Approximate real return?

→ A) -2%

Canvas Example MCQ — Q26

A) -2%
B) 2%
C) 4%
D) 10%
E) None of A-D is close; write the correct answer.

4% - 6% = -2%.

Rule: Positive nominal return can mean lost purchasing power.

Returns & CompoundingE-level★ High priority — official Canvas example

Salary rises 6% while inflation is 4%. Approximate real salary growth?

→ A) 2%

Canvas Example MCQ — Q27

A) 2%
B) 4%
C) 6%
D) 10%
E) None of A-D is close; write the correct answer.

6% - 4% = 2%.

Rule: Treat salary growth like any nominal growth rate.

Returns & CompoundingE-level★ High priority — official Canvas example

Salary rises from SEK 50,000 to 53,000 (6%) while inflation is 4%. Exact real salary growth?

→ A) 1.92%

Canvas Example MCQ — Q28

A) 1.92%
B) 2.00%
C) 4.00%
D) 6.00%
E) None of A-D is close; write the correct answer.

1.06/1.04 - 1 = 0.01923 = 1.92%.

Rule: Use exact real formula when requested.

Returns & CompoundingE-level★ High priority — official Canvas example

Stock 100->108, dividend 4, inflation 3%. Approximate real total return?

→ C) 9%

Canvas Example MCQ — Q29

A) 5%
B) 8%
C) 9%
D) 12%
E) None of A-D is close; write the correct answer.

Nominal total return = (108-100+4)/100 = 12%. Approximate real = 12%-3% = 9%.

Rule: First compute total nominal return, then adjust for inflation.

Returns & CompoundingE-level★ High priority — official Canvas example

Same stock: nominal total return 12%, inflation 3%. Exact real total return?

→ A) 8.74%

Canvas Example MCQ — Q30

A) 8.74%
B) 9.00%
C) 12.00%
D) 15.00%
E) None of A-D is close; write the correct answer.

1.12/1.03 - 1 = 0.08738 = 8.74%.

Rule: Do not use simple subtraction when exact is requested.

Returns & CompoundingE-level★ High priority — official Canvas example

Stock 100->98, dividend 7, inflation 2%. Approximate real total return?

→ B) 3%

Canvas Example MCQ — Q31

A) 1%
B) 3%
C) 5%
D) 7%
E) None of A-D is close; write the correct answer.

Nominal total = (98-100+7)/100 = 5%. Real ≈ 5%-2% = 3%.

Rule: Income can offset a price decline.

Returns & CompoundingE-level★ High priority — official Canvas example

Property begins at SEK 200m, ends at SEK 212m, NOI SEK 8m, inflation 12%. Which statement is correct?

→ B) The nominal total return is 10%, and the approximate real return is -2%.

Canvas Example MCQ — Q32

A) The nominal total return is 6%, and the real return is positive.
B) The nominal total return is 10%, and the approximate real return is -2%.
C) The nominal total return is 12%, and the approximate real return is 0%.
D) The nominal total return is 10%, and the exact real return is -2%.
E) None of A-D is close; write the correct answer.

Nominal total = (212-200+8)/200 = 20/200 = 10%. Approx real = 10%-12% = -2%. Exact real = 1.10/1.12-1 ≈ -1.79%.

Rule: Distinguish nominal gain from purchasing-power gain.

Bonds & Cap RatesE-levelVery high priority

From a risk-return perspective, how should an investor compare a Treasury bond investment with a multifamily property investment?

→ A) The property should offer a higher expected return/cap rate than the Treasury yield to compensate for added risk

Computer Lab 4 — Exercise 1, Task 5

A) The property should offer a higher expected return/cap rate than the Treasury yield to compensate for added risk
B) They should offer identical returns since both are low-risk
C) The Treasury should offer a higher return because it is less liquid
D) Property risk is irrelevant once a cap rate is quoted

Real estate carries vacancy, operating, regulatory, liquidity and asset-specific risks beyond those of government bonds, so investors typically require a risk premium—i.e., a cap rate/expected return above the Treasury yield.

Rule: Riskier assets require a return premium above the risk-free (Treasury) rate.

Returns & CompoundingE-levelVery high priority

Nominal return 8%, inflation 3%. The question asks for the EXACT real return.

→ B) 1.08/1.03 − 1

Formula Battle — method recognition (built from the Formula Book)

A) 8% − 3%
B) 1.08/1.03 − 1
C) 1.08 × 1.03 − 1
D) 8% + 3%

Fisher relation. Correct method: 1.08/1.03 − 1.

Rule: Real = (1+n)/(1+π) − 1