Exercises
Explore how bonds are valued and how changes in interest rates, maturity, credit quality, and embedded features affect their prices. This quiz covers coupon payments, yield measures, premium and discount bonds, duration, convexity, yield curves, reinvestment risk, credit spreads, callable bonds, and bond ladders. The questions combine calculations, visual interpretation, and practical investment scenarios.
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Bond prices and market yields generally move in opposite directions. A higher discount rate reduces the present value of the bond's fixed future payments.
The annual coupon equals face value multiplied by the coupon rate: $1,000 × 6% = $60.
Yield to maturity is the discount rate that makes the present value of all promised coupons and principal equal to the bond's current price.
A bond trades at a premium when its market price exceeds its face value. Here, $1,040 is greater than $1,000.
Current yield equals annual coupon income divided by market price: $60 ÷ $1,200 = 5%.
A normal yield curve slopes upward because longer-maturity bonds generally offer higher yields than shorter-maturity bonds.
Macaulay duration is the weighted average time required to receive a bond's cash flows, with present values used as the weights.
The duration estimate is −5.2 × 0.005 = −0.026, or approximately a 2.6% price decrease.
With other factors equal, longer-maturity bonds have greater duration and price sensitivity because their cash flows are received farther in the future.
Positive convexity places the actual price-yield curve above its duration tangent. For a yield increase, the actual loss is generally smaller than the linear estimate.
Reinvestment risk arises because interim coupon payments may be reinvested at rates below the yield originally expected.
A wider credit spread raises the corporate bond's required yield relative to Treasuries. Higher required yields reduce the bond's present value.
BBB− is the lowest S&P investment-grade rating. Ratings of BB+ and below are generally classified as speculative grade.
When rates fall, an issuer may call a high-coupon bond and refinance the debt at a lower interest cost. This creates call and reinvestment risk for investors.
A zero-coupon bond makes only one payment at maturity, so the weighted average time to receive its cash flow equals its maturity.
The dirty price is the total settlement price paid by the buyer. It equals the quoted clean price plus interest accrued since the last coupon date.
A bond ladder distributes holdings across regularly spaced maturity dates. Maturing principal can provide liquidity or be reinvested at current rates.
The approximate real return equals the nominal return minus inflation: 7% − 3% = 4%.
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