Fixed Income

For a discount bond, the correct ordering is coupon rate < current yield < YTM. At a discount, the capital gain component lifts YTM above current yield, and the coupon rate is lowest because it is computed on par.

• Option A is wrong because for a premium bond the ordering reverses: coupon rate > current yield > YTM.
• Option C is wrong because for a par bond all three are equal: coupon rate = current yield = YTM.

Callable bond price equals the straight bond price minus the value of the call option.

• Option B: $102.50 + 3.20 = 105.70$, incorrectly adds the call value (issuer’s option reduces the bond’s value).
• Option C: 100.00 - 3.20 = 96.80, subtracts the option from par instead of from the straight-bond price.

Greater reliance on short-term wholesale funding to finance long-term assets heightens refinancing and rollover risk, worsening credit quality.

• Option A is generally credit positive: stronger liquidity and longer maturities reduce near-term refinancing risk.
• Option C is generally credit positive: tighter covenants provide creditor protections and can limit risk-taking.

For a zero-coupon bond, Macaulay duration equals maturity. Modified duration is:

• Option B (4.000 years) forgets to convert Macaulay duration to modified duration (i.e., omits division by $1 + y$).
• Option C (3.883 years) incorrectly divides by $1 + \frac{y}{2}$ as if yields were compounded semiannually: $\frac{4}{1 + 0.03} = \frac{4}{1.03} = 3.883$

Coupon per period equals the annual coupon rate divided by the payment frequency, times par.

• Option A uses the full annual coupon without dividing by the semiannual frequency: $0.06 \times 1{,}000 = 60.00$
• Option B multiplies by the frequency instead of dividing: $0.06 \times 2 \times 1{,}000 = 120.00$

Spread per 100 of par:

Par blocks of 100 in $2,000,000:

Round-trip cost:

Therefore, the transaction cost is $2,500.

• Option A uses the quote as if it were per $1 of par: $0.125 \times 2{,}000{,}000 = 250{,}000$, overstating by a factor of 100.
• Option B uses only the half-spread: $0.0625 \times 20{,}000 = 1{,}250$, taking just one side of the spread instead of the full round-trip.

Compute annual debt service (interest-only) and then DSCR.

• Option A (0.625): inverts the ratio: $\frac{3{,}750{,}000}{6{,}000{,}000} = 0.625$.
• Option C (19.20): divides annual NOI by monthly debt service, mixing periods: monthly debt service $= \frac{3{,}750{,}000}{12} = 312{,}500$; $\frac{6{,}000{,}000}{312{,}500} = 19.20$.

First, linearly interpolate the 4.5-year swap rate:

I-spread:

• Option B (70 bps) results from incorrectly using only the 4-year swap rate without interpolation: $0.0370 - 0.0300 = 0.0070 = 70 \text{ bps}$.
• Option C (50 bps) results from incorrectly using only the 5-year swap rate without interpolation: $0.0370 - 0.0320 = 0.0050 = 50 \text{ bps}$.

Convert BEY to periodic rate and compound to an annual effective rate.

Periodic rate:

EAY:

• Option A compounds the full BEY without halving: $(1 + 0.072)^2 - 1 = 0.149184 = 14.92\%$.
• Option C simply reports the nominal BEY (7.20%) without converting to an effective annual rate.

OAS removes the value effect of the embedded option from the Z-spread.

• Option A is correct: Callable bonds have OAS < Z-spread (the call option reduces investor value), while putable bonds have OAS > Z-spread (the put option increases investor value).
• Option B is wrong because callable bonds have OAS < Z-spread, not greater.
• Option C is wrong because OAS equals Z-spread only for option-free bonds (or when the embedded option has zero value under the model), not generally for bonds with options.