Search

Canvas Example MCQ — Q5

• A) Higher property income-growth expectations have no effect on cap rates.
• B) Higher property income-growth expectations result in lower cap rates.
• C) Higher Treasury / risk-free bond yields have no impact on cap rates.
• D) A higher property risk premium results in a lower cap rate.

Using the standard growth intuition, cap rate ≈ required return - expected growth. If expected growth rises while required return is unchanged, the cap rate falls.

Rule: Growth up -> cap rate down, ceteris paribus.

Canvas Example MCQ — Q6

• A) the same as when the bond was issued.
• B) higher than when the bond was issued.
• C) lower than when the bond was issued.
• D) negative.
• E) None of A-D is close; write the correct answer.

The coupon is fixed. New investors now require 5.88%, which is above the 5.35% coupon yield at issue, so the old bond must sell below par.

Rule: Yield up -> price down.

Canvas Example MCQ — Q7

• A) $1,000
• B) $963
• C) $1,037
• D) $588
• E) None of A-D is close; write the correct answer.

Price = 53.50/(1.0588) + ... + 53.50/(1.0588)^9 + 1000/(1.0588)^9 ≈ 963.76.

Rule: Discount every remaining coupon and the face value at the current market yield.

Old Exam — Oct 2023, Q4 · adapted

Given: Bond setup: face=$1,000, annual coupon=3%; yield 2.14% at issue with 10 years; three years later 7 years remain and yield=4.66%.

• A) 2.52%
• B) 19.27%
• C) ‒12.68%.
• D) ‒16.15%.
• E) None of the above (A, B, C, D) is close to be correct.

At issue: P≈30 annuity @2.14% for 10 years + 1,000/(1.0214)^10≈1,076.69. Three years later: 7 remaining payments discounted at 4.66% -> P≈902.75. Change=(902.75/1076.69)-1≈-16.15% -> D.

Rule: Fixed-rate bond: yield up -> price down. Price = PV(coupons)+PV(face).

Computer Lab 1 — Exercise 4 (bond valuation concept)

• A) Inversely — when YTM rises, bond price falls
• B) Directly — when YTM rises, bond price rises
• C) They are unrelated
• D) Price only depends on coupon rate, not YTM

A bond's price is the present value of its coupon and principal cash flows discounted at the YTM. A higher discount rate (YTM) reduces the present value of fixed future cash flows, so price falls as YTM rises.

Rule: Bond price and yield to maturity are inversely related because price is the PV of fixed cash flows discounted at the yield.

Computer Lab 2 — Exercise 3, Problem 12.14

• A) Expected return = 2.12%; No, it cannot equal 2.36% because default risk lowers expected return below the promised yield
• B) Expected return = 2.36%; Yes, YTM always equals expected return
• C) Expected return = 1.36%; equals the risk-free Treasury yield
• D) Expected return = 0.24%; the default-loss amount itself

r_d = YTM − p×L = 2.36% − 0.5%×48% = 2.36%−0.24% = 2.12%. The 2.36% YTM is the best-case (promised) return only if every payment is received; with any default risk, it cannot reflect the true expected return (which is lower).

Rule: Expected return on risky debt: r_d = YTM − p×L, always ≤ the promised YTM.

Computer Lab 2 — Exercise 3, Problem 12.15

• A) ≈21.25%
• B) ≈28.83%
• C) ≈4.55%
• D) ≈12.75%

Debt CAPM: r_d = 3.0%+0.31×5.0% = 4.55%. Default probability: p = (YTM−r_d)/L = (17.3%−4.55%)/60% = 12.75%/60% = 21.25%.

Rule: When YTM and the CAPM-implied expected return are known, solve for p via p = (YTM − r_d)/L.

Computer Lab 2 — Exercise 3, Problem 12.16

• A) ≈3.70% (default-adjustment) and ≈3.85% (debt CAPM) — both far below the 8.5% promised YTM
• B) 8.5% under both methods, since YTM is a market-determined fair rate
• C) ≈4.8% default-loss amount is itself the expected return
• D) ≈11.5%, since recession risk should raise expected return

Method 1: r_d = 8.5%−8.0%×60% = 8.5%−4.8% = 3.70%. Method 2 (CAPM): r_d = 3.0%+0.17×5.0% = 3.85%. Both are far below the promised 8.5% YTM, reflecting significant recession default risk.

Rule: Under recession-level default risk, promised YTM substantially overstates the investor's true expected return; two independent methods (default-adjustment, debt CAPM) should roughly agree.

Computer Lab 2 — Exercise 3, Problem 12.17

• A) YTM≈4.80%; spread≈0.80%
• B) YTM≈4.50%; spread≈0.50%
• C) YTM≈4.00%; spread≈0.00%
• D) YTM≈6.90%; spread≈2.90%

Required expected return via CAPM: r_d = 4.0%+0.10×5.0% = 4.50%. YTM = r_d + p×L = 4.50%+0.5%×60% = 4.50%+0.30% = 4.80%. Spread over AAA = 4.80%−4.00% = 0.80%.

Rule: Set promised YTM = required expected return (from debt CAPM) plus the expected default-loss compensation (p×L).

Computer Lab 2 — Exercise 3 concept

• A) Promised YTM is generally higher than expected return, because YTM assumes all payments are received with certainty
• B) Promised YTM is generally lower than expected return
• C) They are always identical regardless of default risk
• D) Expected return exceeds YTM only for investment-grade bonds

YTM is calculated assuming every promised payment is made in full and on time. If there's any default probability, the investor's actual expected return (accounting for potential losses) must be lower than the promised YTM.

Rule: Promised YTM ≥ expected return whenever there is positive default probability; the gap widens as credit quality worsens.

Computer Lab 3 — Problem 3 (Most likely)

• A) Because annual NOI (10% of price) plus an unchanged resale price means a 10% discount rate makes NPV exactly zero
• B) Because IRR always equals NOI/Purchase price regardless of other cash flows
• C) Because the sale price must always equal the purchase price for any IRR to exist
• D) Because flat NOI implies zero IRR

NOI/Purchase price = 200,000/2,000,000 = 10%, exactly matching a constant 'coupon-like' yield, and with the exit value unchanged, the investment behaves like a perpetual-income bond returning exactly 10% — so NPV(10%)=0 trivially.

Rule: When periodic income is a constant percentage of invested capital and the capital value is returned unchanged at the end, the IRR equals that constant income yield.

Computer Lab 4 — Exercise 1, Task 1

• A) True
• B) False
• C) True only for government bonds
• D) False — prices and yields move together

Bond prices and yields move inversely. A sharp fall in prices corresponds to a sharp rise in required yields, since price is the present value of fixed cash flows discounted at the yield.

Rule: Bond price and yield always move in opposite directions.

Computer Lab 4 — Exercise 1, Task 2

• A) About 28 basis points; yes, a marked rise
• B) About 280 basis points; yes, a marked rise
• C) About 2.8 basis points; no, negligible
• D) About 28 basis points; no, this is a fall

5.00% − 4.72% = 0.28 percentage points = 28 basis points, a measurable rise in yields over about one month.

Rule: 1 percentage point = 100 basis points.

Computer Lab 4 — Exercise 1, Task 3

• A) Yes, because coupon rate = YTM implies price = face value
• B) No, it is issued at a discount
• C) No, it is issued at a premium
• D) Cannot be determined without knowing maturity

When the coupon rate equals the market YTM at issuance, the present value of the coupon and principal cash flows discounted at that same yield equals the face value, so price = par.

Rule: Coupon rate = YTM ⇒ Price = Par; Coupon > YTM ⇒ Premium; Coupon < YTM ⇒ Discount.

Computer Lab 4 — Exercise 1, Task 4

• A) -7.11%
• B) +7.11%
• C) -5.00%
• D) -11.11%
• E) 0%, price is unaffected by YTM changes

P1 = 40×[1-(1.05)^-9]/0.05 + 1000/(1.05)^9 ≈ 928.92. %ΔP = (928.92-1000)/1000 = -7.11%.

Rule: When YTM rises above the coupon rate, a fixed-coupon bond's price falls; recompute with remaining years, not original maturity.

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.

Computer Lab 4 — Exercise 1, Task 6

• A) 200 bps
• B) 20 bps
• C) 2 bps
• D) 1.5 bps (ratio of the two rates)

Spread = Cap Rate − Government Bond Yield = 6.0% − 4.0% = 2.0 percentage points = 200 basis points.

Rule: Cap rate spread = Cap Rate − Government Bond Yield; 1 percentage point = 100 bps.

Computer Lab 4 — Exercise 1, Task 7

• A) Spread = Cap Rate − Government Bond Yield
• B) Spread = Cap Rate + Government Bond Yield
• C) Spread = Government Bond Yield − Cap Rate
• D) Spread = Cap Rate × Government Bond Yield

Simple algebra: subtract Government Bond Yield from both sides of Cap Rate = Government Bond Yield + Spread.

Rule: Always isolate the unknown term via basic algebraic rearrangement.

Computer Lab 4 — Exercise 1, Task 8

• A) 75 bps; a relatively small premium given office property's additional risks
• B) 675 bps; an unusually large premium
• C) 75 bps; abnormally large for office property
• D) 0.75 bps; essentially no premium

Spread = 5.75% − 5.00% = 0.75 percentage points = 75 basis points, which is a comparatively modest premium relative to the vacancy, leasing, operating and liquidity risks of office property, making Treasuries relatively attractive by comparison.

Rule: Compare the computed spread's economic magnitude to the asset's risk profile, not just its sign.

Computer Lab 4 — Exercise 1, Task 9a

• A) Property values fall
• B) Property values rise
• C) Property values stay constant
• D) NOI automatically rises to offset the higher cap rate

With V = NOI/Cap Rate and NOI held fixed, an increase in the cap rate (the denominator) decreases V.

Rule: Cap rate expansion (↑cap rate) → ↓value, all else equal.

Computer Lab 4 — Exercise 1, Task 9b

• A) Property values rise
• B) Property values fall
• C) Property values stay constant
• D) Values fall only if interest rates also fall

With V = NOI/Cap Rate and NOI fixed, a lower cap rate (smaller denominator) increases V.

Rule: Cap rate compression (↓cap rate) → ↑value, all else equal.

Computer Lab 4 — Exercise 1, Task 10

• A) False — cap rates compressed roughly 2010-2022, then expanded materially 2022-2024 before stabilizing
• B) True — cap rates fell continuously over the whole period
• C) True, but only for industrial property
• D) False — cap rates expanded continuously the whole period

The lab source indicates general compression from about 2010 to 2022, followed by material expansion from 2022 to 2024, then stabilization — so no single continuous trend describes the whole period.

Rule: Check whether a described trend holds for the entire stated period or only part of it.

Computer Lab 4 — Exercise 1, Task 11

• A) Narrowed, mainly because the 10-year Treasury yield rose while average cap rates stayed broadly stable
• B) Widened, mainly because cap rates fell sharply
• C) Narrowed, mainly because cap rates fell sharply
• D) Widened, mainly because the Treasury yield fell

Since Spread = Cap Rate − Treasury Yield, and the Treasury yield rose while the average cap rate stayed roughly stable, the spread shrank (narrowed).

Rule: To determine spread direction, track Cap Rate and Treasury Yield separately, then take the difference.

Computer Lab 4 — Exercise 1, Task 12

• A) Industrial — expectations shifted from compression toward no change
• B) Multifamily
• C) Retail
• D) Office

The lab identifies industrial property as having the most pronounced shift, moving away from expectations of cap rate compression toward expectations of no change.

Rule: Sector-specific expectations can shift independently of the broad market trend.

Computer Lab 4 — Exercise 1, Task 13

• A) Lower inflation expectations, weaker growth, expected Fed cuts, and a lower term premium
• B) Persistent inflation and heavy Treasury issuance
• C) Higher-for-longer policy rate expectations and strong private capital demand
• D) Stronger economic growth and rising inflation expectations

A major decline in the long yield generally requires a lower expected path of future short-term rates (driven by lower inflation/growth expectations and anticipated rate cuts) and/or a lower term premium.

Rule: Long yield = expected average future short rates + term premium; both components must fall for a substantial yield decline.