CFA Level 1 - Fixed Income Session 16 - Reading 67 Introduction to the Measurement of Interest Rate Risk - LOS h (Notes, Practice Questions, Sample Questions) 1. A 7% coupon bond with semiannual coupons has a convexity in years of 80. The bond is currently priced at a yieldto maturity (YTM) of 8.5%. If the YTM decreases to 8%, thepredicted e ect due to convexity on the percentage changein price would be: A) +20 basis points. B) +50 basis points.C) +40 basis points. Explanation: A — Convexity adjustment: +(Convexity)(changein i)2Convexity adjustment = +(80)(-0.005)(-0.005) = +0.0020 or 0.20% or+20 basis points 2. Why is convexity a good thing for a bond holder? Because when compared to a low convexity bonds a high convexitybond: A) is usually underpriced. B) has better price changes regardless of the direction of theyield change. C) is more sensitive to interest rate changes, increasing thepotential payo
Explanation: B — Relative to a bonds with low convexity, theprice of a bond with high convexity will increase more whenrates decline and decrease less when rates rise 3. How does the convexity of a bond inﬂuence the yield on the bond? All else the same, for a bond with high convexityinvestors will require: A) a lower yield. B) a higher or lower yield depending on the bond's duration.C) a higher yield. Explanation: A — Convexity is to the advantage of the bondholder because a high-convexity bond's price will decreaseless when rates increase and will increase more when ratesdecrease than a low-convexity bond's price 4. For a given change in yields, the di erence between the actual change in a bond’s price and that predicted using theduration measure will be greater for: A) a bond with less convexity.B) a short-term bond. C) a bond with greater convexity Explanation: C — Duration is a linear measure of therelationship between a bond’s price and yield. The truerelationship is not linear as measured by the convexity. Whenconvexity is higher, duration will be less accurate inpredicting a bond’s price for a given change in interest rates.Short-term bonds generally have low convexity 5. With respect to an option-free bond, when interest-rate changes are large, the duration measure will overestimate the: A) fall in a bond's price from a given increase in interest rates.
B) increase in a bond's price from a given increase in interestrates.C) ﬁnal bond price from a given increase in interest rates. Explanation: A — When interest rates increase by 50-100 basispoints or more, the duration measure overestimates thedecrease in the bond’s price 6. Convexity is more important when rates are: A) unstable. B) high.C) low. Explanation: A — Since interest rates and the price of bondsare inversely related, unstable interest rates will lead tolarger price ﬂuctuations in bonds. The larger the change inthe price of a bond the more error will be introduced indetermining the new price of the bond if only duration isused because duration assumes the price yield relationshipis linear when in fact it is a curved convex line. If durationalone is used to price the bond, the curvature of the linemagniﬁes the error introduced by yield changes, and makesthe convexity adjustment even more important 7. If a bond has a convexity of 120 and a modiﬁed duration of 10, what is the convexity adjustment associated with a 25basis point interest rate decline? A) -2.875%.B) -2.125%. C) +0.075% Explanation: C — Convexity adjustment: +(C) (Δi)2Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075%
8. A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage pricechange is closest to: A) -4.50%.B) -4.94%. C) -4.06%. Explanation: C — Recall that the percentage change in prices= Duration e ect + Convexity e ect = [-duration × (change inyields)] + [convexity × (change in yields)2] = (-4.5)(0.01) +(43.6)(0.01)2 = -4.06%. Remember that you must use the decimalrepresentation of the change in interest rates whencomputing the duration and convexity adjustments 9. A bond has a modiﬁed duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25basis points? It goes: A) down 1.46%. B) up 4.00%.C) down 15.00%. Explanation: A — ΔP/P = (-)(MD)(Δi) +(C) (Δi)2= (-)(6)(0.0025) + (62.5) (0.0025)2 = -0.015 + 0.00039 = - 0.01461 10. A bond has a modiﬁed duration of 7 and convexity of 50. If interest rates decrease by 1%, the price of the bond will mostlikely: A) increase by 6.5%.B) decrease by 7.5%. C) increase by 7.5%. Explanation: C — Percentage Price Change = –(duration) (?i) +convexity (?i)2therefore