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Canvas Example MCQ — Q89

• A) approximately 30.9%
• B) approximately 50.0%
• C) approximately 69.1%
• D) approximately 84.1%
• E) None of A-D is close; write the correct answer.

z = -4.60 + .40(12) - .20(2) + .10(7) = 0.50. P = Φ(0.50) ≈ 0.6915 = 69.15%.

Rule: Compute the index first; then apply the standard normal CDF.

Canvas Example MCQ — Q90

• A) approximately -20.0 percentage points
• B) approximately -15.2 percentage points
• C) approximately -7.0 percentage points
• D) approximately +7.0 percentage points
• E) None of A-D is close; write the correct answer.

ME = -0.20 x 0.3521 = -0.07042, i.e. about -7.04 percentage points for a one-unit local increase in MARGIN.

Rule: Probit ME = coefficient x normal PDF at the current index.

Canvas Example MCQ — Q93

Given: Logit model for choosing an adjustable-rate mortgage. At FIXRATE=12, MARGIN=2, NETWORTH=3 the index is z = −0.80. MARGIN coefficient = −0.35. Logit: P = 1/(1+e^(−z)); marginal effect = b·P·(1−P).

• A) approximately -35.0 percentage points
• B) approximately -12.8 percentage points
• C) approximately -7.5 percentage points
• D) approximately +7.5 percentage points
• E) None of A-D is close; write the correct answer.

z=-0.80, P≈0.3100. ME = (-.35)(.31)(.69) = -.0749 ≈ -7.49 pp.

Rule: Logit ME = β x P(1-P).

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, Q8

Given: Historical HPI dataset question; keep the concept of comparing standard deviations.

• A) Slovenia with standard deviation of 24.97 %
• B) Slovenia with standard deviation of 58.79 %
• C) Croatia with standard deviation of 35.20 %
• D) Croatia with standard deviation of 24.05 %
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: D) Croatia with standard deviation of 24.05 %. 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, Q9

Given: Historical HPI index-growth question; current adaptation: V_end=V_start x Index_end/Index_start.

• A) SEK 8 549 279.
• B) SEK 2 454 658.
• C) SEK 4 323 050
• D) SEK 4 393 259.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: C) SEK 4 323 050. 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, Q10

Given: Historical correlation question. Correlation is a unit-free number between -1 and +1; 0.52 means 0.52, not 52%.

• A) 0.52
• B) 52.
• C) 0.52 %.
• D) 1.00 %.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: A) 0.52. 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.

Old Exam — Dec 2021 re-exam, Q12

Given: Historical REIT data; arithmetic monthly mean is simple average of monthly returns.

• 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: A) 1.05%.. 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 — Oct 2021, Q6

Given: Historical HPI dataset question; keep the concept of comparing arithmetic means across countries.

• A) Slovenia with arithmetic mean return of 9.30 %
• B) Israel with arithmetic mean return of 6.79 %
• C) Sweden with arithmetic mean return of 11.62 %
• D) Croatia with arithmetic mean return of 11.62 %
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: D) Croatia with arithmetic mean return of 11.62 %. 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 — Oct 2021, Q7

Given: Historical HPI dataset question; keep the concept of min/max simple returns.

• A) ‒17.4% and 192.7%
• B) ‒17.4% and 60.88%
• C) ‒17.4% and 120.78%
• D) ‒60.88% and 17.4%.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: A) ‒17.4% and 192.7%. 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 — Oct 2021, Q8

Given: Historical HPI dataset question; keep the concept of comparing pairwise correlations.

• A) Croatia and Slovenia.
• B) UK and US.
• C) Sweden and Norway.
• D) Israel and Slovenia.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: A) Croatia and Slovenia.. 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 — Oct 2021, Q9

Given: Historical REIT index-data question; current adaptation: ending value = initial value x ending total-return index / starting index.

• A) $24 641.
• B) $82 022.
• C) $104 224.
• D) $720 000.
• E) None of the above (A, B, C, D) is close to be correct.

Historical external-data result: B) $82 022.. 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 6 — Exercise 3, Model 1 interpretation · adapted

• A) A higher ARM margin makes choosing an adjustable-rate mortgage less attractive (negative sign); the raw coefficient is NOT a direct percentage-point probability effect
• B) A higher ARM margin makes an ARM more attractive, and -0.2675 means exactly a 26.75 percentage-point decrease in probability
• C) The coefficient has no interpretable meaning in a Probit model
• D) -0.2675 is the exact percentage-point change in probability for a one-unit increase in MARGIN

The negative sign indicates direction (higher MARGIN lowers the attractiveness/probability of choosing ARM), but Probit coefficients are index-scale, not probability-scale; the actual probability effect requires multiplying by φ(Xβ), the marginal effect formula.

Rule: Probit coefficient signs indicate direction only; the probability-scale marginal effect requires β_j×φ(Xβ).

Computer Lab 6 — Exercise 3, Task c

• A) ≈17.59%
• B) ≈82.41%
• C) ≈37.21%
• D) ≈93.12%

P = Φ(-0.9312) ≈ 0.1759 = 17.59%, reading the standard normal CDF at z = -0.9312.

Rule: Compute z=Xβ first, then look up Φ(z) for the predicted probability.

Computer Lab 6 — Exercise 4, Probit calc

• A) z = -2.26+2.74(0.35)+0.71(1) = -0.591
• B) z = -2.26+2.74(0.35) = -1.301
• C) z = -2.26+0.71 = -1.55
• D) z = 2.74(0.35)+0.71 = 1.669

z = -2.26 + 2.74×0.35 + 0.71×1 = -2.26 + 0.959 + 0.71 = -0.591.

Rule: Compute the full linear index z=Xβ by summing the intercept and all included terms with their given covariate values.

Computer Lab 6 — Exercise 4, Probit vs LPM nonlinearity

• A) Because Probit is nonlinear: the marginal/discrete effect of PIRAT depends on the predicted probability level itself, which differs by BLACK status even without an explicit interaction term
• B) Because the Probit model actually includes an interaction term between PIRAT and BLACK
• C) Because Probit coefficients differ by group automatically
• D) This is a calculation error; Probit should give identical effects just like LPM

Even without an interaction term, Probit's nonlinear Φ(·) link function makes the implied probability effect of any regressor depend on the overall linear index (and thus on BLACK, which shifts the index), unlike LPM where effects are mechanically constant across groups.

Rule: Nonlinear models (Probit/Logit) naturally produce covariate-dependent marginal effects even without explicit interaction terms, unlike the linear LPM.

Computer Lab 6 — Exercise 4, Logit calc

• A) ≈27.28%
• B) ≈72.72%
• C) ≈49.51%
• D) ≈9.05%

Λ(-0.9805) = 1/(1+e^0.9805) = 1/(1+2.6654) ≈ 1/3.6654 ≈ 0.2728 = 27.28%, matching the lab's reported value.

Rule: Logit predicted probability: Λ(z) = 1/(1+e^(-z)), computed directly from the linear index z.

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

• A) (160 − 100)/100/10
• B) (1.6)^(1/10) − 1
• C) 1.6 / 10
• D) ln(1.6) × 10

Multi-period growth compounds. Correct method: (1.6)^(1/10) − 1.

Rule: CAGR = (End/Start)^(1/n) − 1