For one composite bond, duration and convexity are checked against full repricing before a barbell meets a bullet; the GF540 Unit 5 problem ends where the estimates fail. Searches like "gf 540 unit 5 assignment example", "gf540 unit 5 sample" and "gf540 unit 5 example" land here.
What a finished GF540 Unit 5 duration and convexity problem looks like
Four problems building on one another. The first takes a composite corporate bond with a 4.5 percent semiannual coupon, twelve years to maturity and a 5 percent yield, priced at 955.29, and computes a Macaulay duration of 9.33 years and a modified duration of 9.10. The second adds convexity of 101.3 and tests both estimates: for a 100 basis point rise, duration alone predicts a fall of 9.10 percent, the convexity-adjusted figure is 8.60 and full repricing gives 8.62. At 200 basis points the duration estimate misses by close to two points either way. The third repeats the work for a zero of the same maturity, whose modified duration of 11.71 shows why coupons shorten sensitivity. The fourth builds a barbell of two- and twenty-year bonds matching a ten-year bullet's duration of 7.80 and compares convexity, 119.2 against 73.6.
How a GF540 Unit 5 example is structured
The problems run from calculation to limitation, and each ends with a sentence on what its answer means. Duration is built from a cash flow table: each period's payment, its present value, its weight in the price and the weight times time, summed and converted from half-years to years. Modified duration follows from dividing by one plus the periodic yield, with the unit stated as percent price change per 100 basis points. Convexity uses the same table with an extra column. The repricing comparison is set out as a three-column table for shifts of plus and minus 100 and 200 basis points: estimate by duration, estimate with convexity, actual. Effective duration, computed from the up and down prices, confirms 9.12. The barbell problem ends the set with a paragraph on nonparallel shifts, credit spreads and embedded options, three things a single duration number cannot see.
Weights that sum to the price
Each discounted cash flow is divided by 955.29 so the time weights total one, making the Macaulay figure a weighted average the reader can verify line by line.
Half-years converted to years
Semiannual periods produce a duration of 18.66 periods, halved to 9.33 years, a conversion the problem shows because it is so often skipped.
Estimate against repricing
At a 100 basis point rise the duration estimate is off by about half a point and convexity closes nearly all of that gap; at 200 the gap widens.
Coupons shorten sensitivity
The zero's modified duration of 11.71 against the coupon bond's 9.10 shows how earlier cash flows pull the weighted average forward in time.
Equal duration, unequal risk
The barbell carries more convexity than the bullet yet can lose ground if the curve steepens, a risk invisible to any single duration figure.
Where marks go in GF540 Unit 5
Duration problems are marked on units and on the admission of limits. Macaulay duration left in half-years doubles the answer, and modified duration reported where Macaulay was asked, or the reverse, misses by a small but gradable margin. Modified duration described as the bond's life rather than as price sensitivity signals a definitional gap graders catch at once. Convexity computed per period squared and never annualized distorts the adjustment by a factor of four. A comparison that tests the estimate at only one small shift hides the curvature the unit is teaching. The most common loss at this level, though, is a correct set of numbers with no statement of what duration misses, when the prompt usually asks for exactly that: nonparallel moves, spread changes and options that alter the cash flows.
Get a GF540 Unit 5 example written to your instructions
Share the bond terms and yield shifts your GF540 Unit 5 problem uses, the rubric, and whether effective duration or a curve scenario is required. The set is worked from a cash flow table, estimates are tested against full repricing, and the limits paragraph answers your prompt's own wording. First custom sample free; turnaround sits around 24-48h.
GF540 Unit 5 questions, answered
What is the difference between Macaulay and modified duration?
Macaulay duration is a weighted average time to receive the bond's cash flows, measured in years. Modified duration divides it by one plus the periodic yield and becomes a sensitivity: the approximate percent price change for a one percentage point move in yield. The sample gives both figures and labels which one each later calculation relies on, since mixing them is a common source of lost marks.
Why add convexity if duration already estimates the change?
Duration draws a straight line through a curved price-yield relationship, so its error grows with the size of the move. Convexity adds the curvature back. In the sample, the adjustment brings the estimate for a 200 basis point rise from 18.21 percent down to 16.18 percent, close to the actual 16.33. For small shifts the correction is minor, which is why several sizes are tested.
My bond is callable. Does the same method work?
Not directly. A call changes the cash flows when rates fall, so modified duration, which assumes fixed cash flows, overstates sensitivity. Effective duration, computed by repricing the bond at higher and lower yields with the call taken into account, is the usual answer. The sample shows the effective calculation on a plain bond so the method carries over to your callable issue.