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BondYield: Large difference from expected yield for low-priced bonds near maturity #1168

Open amir656 opened 3 years ago

amir656 commented 3 years ago

Hi! Hope you all are having a nice day:)

Summary

The bondYield function returns incorrectly large yields when using the Compounded interest rate convention near the maturity date for low-priced bonds.

Example

Consider this bond which matures on 05-24-2021 and pays a semi-annual coupon of 8.25.

# Schedule
start_date = ql.Date(24, 05, 2011)
maturity_date = ql.Date(24, 05, 2021)
tenor = ql.Period(ql.Semiannual)
calendar = ql.UnitedStates()
payment_rescheduling=4
is_monthend=False
first_coupon_date = ql.Date(24, 11, 2011)
penultimate_coupon_date = ql.Date(24,11,2020)
settleDate=ql.Date(20, 05, 2021)
sched = ql.Schedule(start_date, maturity_date, tenor, calendar, payment_rescheduling, payment_rescheduling, ql.DateGeneration.Backward, is_monthend, first_coupon_date, penultimate_coupon_date)
settlement_days = 2
face_amount=100.00
coupon = [8.25 / 100]
dc = ql.Thirty360()
bond = ql.FixedRateBond(settlement_days,
   face_amount,
   payment_schedule,
   coupon,
   dc)
clean_px = 16.25
compounded = 1
simpleThenCompounded = 3
freq = 2
twoWeeksBefore = ql.Date(10,5,2021)
acc = 1e-8
max_evals = 100
# Using the default max_evaluations we can get through 5 days
[(twoWeeksBefore + i, bond.bondYield(clean_px, dc, compounded, freq, twoWeeksBefore + i, acc, max_evals)) for i in range(5)]
[(Date(10,5,2021), 3150592317.9252234),
 (Date(11,5,2021), 15812986348.612047),
 (Date(12,5,2021), 103851877064.3612),
 (Date(13,5,2021), 960378231440.0281),
 (Date(14,5,2021), 13857535326530.285)]
# Now if I repeat the same computation with SimpleThenCompounded interest, we get much more reasonable numbers
[(twoWeeksBefore + i, bond.bondYield(clean_px, dc, simpleThenCompounded, freq, twoWeeksBefore + i, acc, max_evals)) for i in range(15)]
[(Date(10,5,2021), 107.7991154903855),
 (Date(11,5,2021), 115.92723557553819),
 (Date(12,5,2021), 125.41044776928481),
 (Date(13,5,2021), 136.61832111317415),
 (Date(14,5,2021), 150.0682523250789),
 (Date(15,5,2021), 166.5075921951177),
 (Date(16,5,2021), 187.05736689967924),
 (Date(17,5,2021), 213.47918906030782),
 (Date(18,5,2021), 248.70907967601676),
 (Date(19,5,2021), 298.03187660562776),
 (Date(20,5,2021), 372.0172555509892),
 (Date(21,5,2021), 495.3277931706121),
 (Date(22,5,2021), 741.9512195082841),
 (Date(23,5,2021), 1481.826184863572),
 (Date(24,5,2021), 0.0)]

Compounded interest is interacting with the solver in an outsized way when the price is low. The yield should be high for a bond trading at $16.25 and maturing in 2 weeks, but these values are way too high.

Validation

Estimating yield with this online calculator: https://dqydj.com/bond-yield-to-maturity-calculator/ We get a YTM of 3760.430 for 2 weeks from Maturity. Which is more in the ballpark given that we ~6X our money in 2 weeks (just considering the difference between clean_price and payment at maturity), so annualized, we’d have something like ~6*26 = 160x return. Not 3,414,330,317.53 for yield. For 1 week from Maturity, we get 7506.667 for estimated yield which is roughly double of the previous number, which makes sense given that you get the same return over half the time span.

Interestingly the website also utilizes a solver (the non-estimated value below) and the solver is getting outsized estimates similar to Quantlib For 2 weeks from Maturity: 3630247600369.387 from the compounded calc above: (Date(17,5,2021), 3414330317.5386267) For 1 week from Maturity: 6.58934881522009e+22 from the compounded calc above: (Date(17,5,2021), 4.742958503364403e+18)

Screen Shot 2021-08-25 at 7 45 47 AM Screen Shot 2021-08-25 at 7 34 17 AM
boring-cyborg[bot] commented 3 years ago

Thanks for posting! It might take a while before we look at your issue, so don't worry if there seems to be no feedback. We'll get to it.

amir656 commented 3 years ago

More context

The issue appears to take into affect within 120 days of maturity. I expanded on my example above to create some plots

# Setup bond
start_date = ql.Date(24, 5, 2011)
maturity_date = ql.Date(24, 5, 2021)
tenor = ql.Period(ql.Semiannual)
calendar = ql.UnitedStates()
payment_rescheduling=4
is_monthend=False
first_coupon_date = ql.Date(24, 11, 2011)
penultimate_coupon_date = ql.Date(24,11,2020)
settleDate=ql.Date(20, 5, 2021)
payment_schedule = ql.Schedule(start_date, maturity_date, tenor, calendar, payment_rescheduling, payment_rescheduling, ql.DateGeneration.Backward, is_monthend, first_coupon_date, penultimate_coupon_date)
settlement_days = 2
face_amount=100.00
coupon = [8.25 / 100]
accrual_daycount = ql.Thirty360()
bond = ql.FixedRateBond(settlement_days,
   face_amount,
   payment_schedule,
   coupon,
   accrual_daycount)
# Yield arguments
dc = accrual_daycount
clean_px = 16.25
compounded = 1
simpleThenCompounded = 3
freq = 2
acc = 1e-8
max_evals = 100
# Sometimes yield fails even with 1000 evals
def try_bond_yield(clean_px, dc, comp, freq, settleDate, acc, max_evals):
    try:
        return bond.bondYield(clean_px, dc, comp, freq, settleDate, acc, max_evals)
    except:
        return np.nan

Some plotting logic

def ql2pddate(dt):
  return pd.to_datetime(pd.datetime(dt.year(), dt.month(), dt.dayOfMonth()))

def plot_yield_curve(clean_px, comp, first, last, plot=True):
    # plots 
    yield_curve_1000_eval = [(maturity_date - i, try_bond_yield(clean_px, dc, comp, freq, maturity_date - i, acc, 1000)) for i in range(180)]
    x_1000s, y_1000s = [ql2pddate(y[0]) for y in yield_curve_1000_eval], [y[1] for y in yield_curve_1000_eval]
    if plot:
        plt.plot(x_1000s[first:last], y_1000s[first:last], marker='*')
    return y_1000s[first:last]

def plot_simple_vs_compounded(px, start, stop):
    fig = plt.figure(figsize=(8, 6))
    fig.suptitle('%d - %d  days from Mat at px %d' % (stop, start, px))
    ySimple = plot_yield_curve(px, simpleThenCompounded, start, stop)
    yComp   = plot_yield_curve(px, compounded, start, stop)
    print('%d - %d  days from Mat at px %d, \nSimple, Compounded: %s' % (stop, start, px, zip(ySimple, yComp)))
for px in [100 / 4, 100/3, 100/2, 100 / 1.1]:
    for s in range(0, 151, 30):
        plot_simple_vs_compounded(px, s, s+30)

Results at px of 25

30 - 0  days from Mat at px 25, 
Simple, Compounded: [(0.0, 0.0), (928.0521153930413, 9.007373981992987e+99), (464.5336008072691, 1.4408049693914344e+50), (310.02796300788884, 3.630421486687343e+33), (232.77554534862855, 1.8224059781154334e+25), (186.42441652523542, 1.910151094587377e+20), (155.5239327326953, 9.148661915185024e+16), (133.4523895120958, 389173291773368.0), (116.89893463296846, nan), (104.02420575420334, nan), (93.72458543338414, nan), (85.29777172144429, 2609928229.3713245), (78.2755632582976, nan), (72.33382069675642, 105628711.91714627), (67.24101588834068, 29963844.071501397), (62.82736156825105, 10054819.060280109), (58.965517234418236, 3867514.1315884525), (55.55810492035721, 1664596.7816048036), (52.529386153709765, 786808.338447464), (49.8195674422999, 402427.63535591634), (47.380813948609166, 220103.22725215848), (45.17440229598184, 127504.1680811393), (43.16864966114176, 77620.70543839353), (41.337383319835254, 49337.11494631205), (39.658792652946254, 32566.354062425376), (38.114556725926874, 22222.598372822657), (36.68917324637504, 15616.534031912346), (35.36943652622516, 11264.685232095877), (34.14402741743858, 8317.276915165425), (33.00318803919287, 6270.782553833916)]
60 - 30  days from Mat at px 25, 
Simple, Compounded: [(31.938461544082877, 4817.606685586468), (30.942482307339546, 3764.5903017404444), (30.0088054040111, 2987.3599341044037), (29.131767116930376, 2403.983359318566), (28.306370027256712, 1959.3483781126315), (27.528187889155483, 1615.6667457929266), (26.793286218811204, 1346.568124126999), (26.09815591612784, 1133.3486608270705), (25.439657248333724, 962.5413281458281), (24.81497249389394, 824.3136914556432), (24.22156573704633, 711.3934854585416), (23.657148427098853, 618.3368126092073), (23.119649995028382, 541.0224082267935), (22.607192478354712, 476.2973563800693), (22.118068661674208, 421.7257255122738), (21.650723030880016, 375.40808508491995), (21.203735376668313, 335.8504550827832), (20.775806348316493, 301.868140039999), (20.365744874650183, 272.51445633452596), (19.97245710176118, 247.02741090697677), (19.59493671264297, 224.78945455381904), (19.232256277673727, 205.29684755236315), (18.883559759163468, 188.13615575964855), (18.548055676424944, 172.96608066519372), (18.204573156833284, 159.0617117383212), (18.22501120829758, 159.50331191956795), (17.913746816069846, 147.51143636135657), (17.61363150864227, 136.79218673689508), (17.324078564179416, 127.17849337447367), (17.044541734392745, 118.528935117048)]
90 - 60  days from Mat at px 25, 
Simple, Compounded: [(16.774511817731444, 110.72328233036238), (16.51351351162849, 103.65889794455187), (16.261102736647402, 97.247816256273), (16.016864052251904, 91.41436018846929), (15.78040835316584, 86.09318849462142), (15.55137089106412, 81.22768806406195), (15.32940938252228, 76.76864475065649), (15.114202230869308, 72.67313948510531), (14.905447088332405, 68.9036283229319), (14.702859380881664, 65.4271723792076), (14.506171011632787, 62.21479103126028), (14.315129232916041, 59.240916794438036), (14.129495514122338, 56.482933996953435), (13.949044579575524, 53.92078753038206), (13.773563522959213, 51.53664950803581), (13.602850910569433, 49.31463467903293), (13.436716077191274, 47.24055667771487), (13.27497837705718, 45.30171858083502), (13.11746655711104, 43.486732479243855), (12.964018146272537, 41.785363664317835), (12.814478906717422, 40.1883957009084), (12.668702283379446, 38.68751320813839), (12.526549011556167, 37.27519995268258), (12.387886566212988, 35.944649801415565), (12.252588831499725, 34.68968903934742), (11.865710784398482, 31.324716584972194), (11.742725731213444, 30.320804086606557), (11.622558193426578, 29.368980115410043), (11.50511325980683, 28.46568825345328), (11.390300229604868, 27.60766765315281)]
120 - 90  days from Mat at px 25, 
Simple, Compounded: [(11.27803238933187, 26.791924397288923), (11.16822680543035, 26.0157060283607), (11.06080410161854, 25.276478764828504), (10.955688276439375, 24.571907260378744), (10.852806539431601, 23.89983638629925), (10.752089136635945, 23.25827502333044), (10.653469165485529, 22.64538140121145), (10.55688249324282, 22.059450002113522), (10.462267545619984, 21.49889977957441), (10.36956521934464, 20.962263455664377), (10.278718758182883, 20.448177938440626), (10.189673636584235, 19.9553756785206), (10.102377421040256, 19.482676739498856), (10.016779730364785, 19.028981733926056), (9.93283208830766, 18.593265325881156), (9.850487826548285, 18.174570401388856), (9.769702043114194, 17.7720026663146), (9.69043152742395, 17.384725879052127), (9.61263458306265, 17.01195733038631), (9.53627109304303, 16.65296385387051), (9.461302361083803, 16.307058089674015), (9.387691065977311, 15.973595155244624), (9.315401227941681, 15.65196951576882), (9.233687183981981, 15.317970688388897), (9.24439812340771, 15.341612142587442), (9.174648226757485, 15.041987947576079), (9.106119169993903, 14.752593382023942), (9.03877970198084, 14.472954184614931), (8.972599624962449, 14.202623452570336), (8.90754975633492, 13.94117970243611)]
150 - 120  days from Mat at px 25, 
Simple, Compounded: [(8.843601894148462, 13.688225199405869), (8.780728761622512, 13.443384360124575), (8.718903952202927, 13.20630229631919), (8.658101975413011, 12.976643437604313), (8.598298116834396, 12.754090331362686), (8.539468468346698, 12.53834244863333), (8.481589868397808, 12.32911510187548), (8.424639915512008, 12.126138484783517), (8.368596886292032, 11.929156765629166), (8.31343970852777, 11.737927154725327), (8.25914802415685, 11.552219166984415), (8.20570202441319, 11.371813878443135), (8.15308254272761, 11.196503249715011), (8.10127099733065, 11.026089418927091), (8.050249314377762, 10.860384187028636), (8.00000000455426, 10.699208416756658), (7.950506064376465, 10.54239148582451), (7.901750991281004, 10.3897708850252), (7.853718789154392, 10.241191660617186), (7.806393869968472, 10.096506066734317), (7.759761135106775, 9.955573171733699), (7.71380590885786, 9.818258393605198), (7.66851390683653, 9.684433272092683), (7.623871253056724, 9.553975065270892), (7.570927707631011, 9.414104197631199), (7.579864475915971, 9.426766453785536), (7.5364804437245505, 9.302695266406019), (7.493706422207487, 9.181654242622399), (7.45152999720737, 9.063540694514227), (7.409939081982592, 8.948256345435144)]
180 - 150  days from Mat at px 25, 
Simple, Compounded: [(7.368921949425173, 8.835707098925965), (7.32846714819052, 8.72580274418203), (7.288563574534567, 8.618456912834581), (7.249200346731892, 8.513586707260227), (7.210366949394391, 8.411112684207989), (7.172053079311627, 8.310958600451912), (7.1342487382267965, 8.213051288814365), (7.096944151360821, 8.117320477592887), (7.06012982143935, 8.023698694678613), (7.023796477709125, 7.9321211257299336), (6.98793507809798, 7.842525425033883), (6.95253682732572, 7.754851728521137), (6.917593119286002, 7.669042391775722), (6.883095596163194, 7.585042013576893), (6.84903605586492, 7.502797261537635), (6.815406552781466, 7.42225679553526), (6.782199311075668, 7.343371155797666), (6.749406707155613, 7.26609277134539), (6.717021358185754, 7.190375715421114), (6.68503602582619, 7.116175812096162), (6.653443646871658, 7.043450428254403), (6.6222373393540614, 6.972158438658729), (6.591410333459605, 6.902260221353808), (6.5609560872227135, 6.833717533220607), (6.530868164638099, 6.76649341590255), (6.501140275393793, 6.700552275799206), (6.471766315271987, 6.635859677230215), (6.4427402505611315, 6.572382382974624), (6.414056265387728, 6.510088274501678), (6.385708605268885, 6.448946343919088)]

Results at px of 90

30 - 0  days from Mat at px 90, 
Simple, Compounded: [(0.0, 0.0), (38.34399699420778, 163331394.74780124), (19.220514643214067, 18472.373753445343), (12.846036282009969, 891.4521293474448), (9.658808927576413, 194.48220789723712), (7.7464819983141275, 77.19090811928143), (6.471605261945843, 41.209326099979556), (5.560985814778549, 26.031809652524284), (4.878027143105639, 18.26314950225768), (4.346842344100015, 13.742880859775694), (3.9218992661669168, 10.864309569003993), (3.5742228882805422, 8.905214703582985), (3.2844965435632445, 7.502569565630651), (3.039347128396753, 6.45760116734708), (2.8292224831148602, 5.653875114759684), (2.6471176278139246, 5.019367213562171), (2.4877788696380074, 4.507478965913142), (2.3471886465836884, 4.086907526807911), (2.2222222166570584, 3.7359439897373763), (2.110412673283045, 3.4391153773988963), (2.0097864719733396, 3.1851286861770896), (1.9187460051361902, 2.9655687931282064), (1.8359841218193136, 2.7740494251916785), (1.7604210093676875, 2.605644597342208), (1.69115682889564, 2.4564992213613164), (1.62743569061313, 2.323556748651331), (1.5686180478284828, 2.204365034726947), (1.5141590400254477, 2.096935778647352), (1.4635916727566038, 1.9996410085098373), (1.4165133843439501, 1.9111358528545086)]
60 - 30  days from Mat at px 90, 
Simple, Compounded: [(1.3725752519414538, 1.8303002722295503), (1.3314733950520075, 1.7561943936948987), (1.2929419053741622, 1.6880240437655245), (1.2567471333964035, 1.625113834629777), (1.2226828881904641, 1.5668859897627443), (1.1905665581526872, 1.5128434474549373), (1.1602358000089756, 1.4625563431798878), (1.1315458634364481, 1.4156511927691642), (1.1043671869304585, 1.3718019597395439), (1.0785835413083285, 1.3307228081527103), (1.0540902968098722, 1.2921621743304579), (1.0307930336998288, 1.2558977653385197), (1.0086063165161603, 1.2217325337554064), (0.9874526740008637, 1.189491117740306), (0.9672616668388727, 1.1590170470440833), (0.9479691187685241, 1.130170207496747), (0.9295164399298516, 1.102824838617277), (0.911850026736205, 1.076867708609766), (0.8949207254642579, 1.052196607825512), (0.8786834102632298, 1.028719048731669), (0.8630965710138429, 1.006351172463495), (0.84812194872504, 0.98501672695048), (0.8337242067077054, 0.964646249847683), (0.8198706960669762, 0.9451763320231238), (0.8046879108010615, 0.924143522945377), (0.8065311947041024, 0.9265489731092563), (0.7936776681264655, 0.9087110291185153), (0.7812840605076422, 0.8916136967523771), (0.7693261799691119, 0.8752120997736063), (0.7577814945093001, 0.8594648964127601)]
90 - 60  days from Mat at px 90, 
Simple, Compounded: [(0.7466289924261929, 0.8443339469570911), (0.7358490583020797, 0.8297839853972464), (0.7254233701472381, 0.8157823888532607), (0.715334800129417, 0.802298928598682), (0.70556727355044, 0.7893055228430363), (0.6961057679583252, 0.7767760970202172), (0.6869361345226369, 0.7646863692176044), (0.6780451324770321, 0.753013726200899), (0.6694202591707504, 0.7417370737888086), (0.6610498066262818, 0.730836710269183), (0.6529226760547772, 0.7202941986706473), (0.6450284692834628, 0.7100923034158552), (0.6373573377505541, 0.7002148753467857), (0.6298999705911875, 0.690646736539258), (0.6226476044814022, 0.6813736746016205), (0.6155919208251714, 0.6723823057189026), (0.6087250561867952, 0.6636600631448019), (0.6020395577770952, 0.6551950936296024), (0.5955283437441112, 0.6469762344041526), (0.5891847394423724, 0.6389929679478252), (0.5830023712051153, 0.6312353418804705), (0.576975166344285, 0.6236939843776466), (0.5710974144860459, 0.6163600007840395), (0.5653636202348948, 0.6092250172304867), (0.559768603094506, 0.6022810559783215), (0.5437677605500459, 0.5825219914820909), (0.5386805298997641, 0.5762706105974913), (0.5337094770308735, 0.5701762663190686), (0.5288507069247964, 0.5642331087483337), (0.524100482800733, 0.5584356392141104)]
120 - 90  days from Mat at px 90, 
Simple, Compounded: [(0.5194551962258578, 0.5527785673459293), (0.514911444599557, 0.5472568966236049), (0.5104659536691905, 0.5418658346040766), (0.5061155897152663, 0.5366008378441574), (0.5018573429507016, 0.5314575366309883), (0.4976883275208236, 0.5264317764557124), (0.49360579920799746, 0.5215196091858627), (0.4896071200223685, 0.5167172460306407), (0.4856897190167627, 0.5120210398362877), (0.48185118198440086, 0.5074275559046031), (0.47808916058661943, 0.5029334480605363), (0.4744013924066306, 0.49853556487996586), (0.47078573518421657, 0.4942308496222698), (0.46724008206841955, 0.49001639795172225), (0.4637624678453207, 0.485889395608592), (0.46035094500563145, 0.4818471807380438), (0.45700367170014566, 0.4778871684641123), (0.4537188614643336, 0.47400688512932776), (0.45049477754137524, 0.47020397875039593), (0.4473297916730166, 0.4664761449929476), (0.4442222933676352, 0.46282120119678977), (0.44117074043333526, 0.4592370405109645), (0.43817364757030014, 0.45572166231229305), (0.4343300078286887, 0.4513037551953078), (0.4352295912205418, 0.45227306597759726), (0.43233717468736177, 0.4488894279299975), (0.4294950681544543, 0.4455688891833543), (0.42670200344636444, 0.4423097500931978), (0.42395670214587455, 0.43911032871968747), (0.4212579659016652, 0.4359689785322428)]
150 - 120  days from Mat at px 90, 
Simple, Compounded: [(0.41860464932544234, 0.4328841639742582), (0.41599560742834846, 0.4298543836182357), (0.41342978075716497, 0.42687816451385024), (0.41090607428834436, 0.4239541386584044), (0.40842349567477704, 0.4210809236549263), (0.40598105345718855, 0.41825721366832264), (0.4035777915855646, 0.4154817658262916), (0.4012127894191504, 0.4127533576672792), (0.39888513250349167, 0.41007079677236724), (0.3965939701620817, 0.4074329588500356), (0.39433845342695717, 0.4048387330315351), (0.392117779403472, 0.4022870532474756), (0.389931143539477, 0.39977687311589727), (0.3877777726580382, 0.39730723658678546), (0.38565694012570045, 0.3948771345818848), (0.38356791264698503, 0.3924856462034941), (0.3815099979116585, 0.3901318510678054), (0.37948248306214966, 0.3878148992669344), (0.37748474345104693, 0.3855339232740164), (0.3755161302434206, 0.38328807326681613), (0.37357601561872406, 0.38107658794624805), (0.3716637798238993, 0.37889867060396665), (0.3697788564018011, 0.37675357764551626), (0.3679206605880122, 0.37464054777181155), (0.3653656536053226, 0.3718108344798327), (0.3660886299307761, 0.3725589135920297), (0.3642822415943861, 0.3705079684702635), (0.36250094337108146, 0.3684870203766585), (0.3607442545833349, 0.36649546196868427), (0.35901166179687977, 0.3645326204704047)]
180 - 150  days from Mat at px 90, 
Simple, Compounded: [(0.3573026692820787, 0.3625979293336631), (0.35561681671855455, 0.36069075119178295), (0.3539536437859297, 0.35881051949660775), (0.35231270786845675, 0.35695666769998075), (0.35069354864575863, 0.355128665152189), (0.3490957874043975, 0.3533259792467833), (0.34751896900715945, 0.35154806260778904), (0.345962703968305, 0.34979444169587093), (0.34442661645731015, 0.3480646087172148), (0.3429102923638582, 0.34635809689196323), (0.34141338361060625, 0.3446744400378525), (0.3399355073344946, 0.34301319150764975), (0.3384763365136887, 0.34137388458130363), (0.33703550666182047, 0.3397561240243674), (0.335612670083808, 0.3381594673862697), (0.3342075131771185, 0.3365835118391771), (0.33281972481733363, 0.3350278724498987), (0.3314489700391531, 0.3334921551479102), (0.33009495535380845, 0.331975983757329), (0.3287573682218956, 0.3304789864809274), (0.3274359323986769, 0.32900082693073757), (0.32613036181493765, 0.32754111560490135), (0.3248403628371, 0.32609955152471065), (0.3235656898680055, 0.32467576289293765), (0.3223060554526444, 0.32326946643550397), (0.3210612210622072, 0.32188030805981166), (0.3198309086259604, 0.3205080044917822), (0.31861488382604125, 0.3191522571607244), (0.31741289879763135, 0.3178127401592494), (0.3162247233805418, 0.31648919970283396)]

PDF: quantLibPlots.pdf

Where I think the issue might be

I did some digging myself. I believe it has do with how either the IRR objective function of newtonSafeSolver handles the corner case of being close to maturity and using the compounded compounding convention. Stack_trace:

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lballabio commented 6 days ago

The problem here is that we need to get a discount factor of around 0.2 over a time as short as 10 days, or T = 0.0277. The discount formula for quarterly compounded rates, $B = 1 / \left(1 + y/4\right)^{4t}$, decreases too slowly as a function of the yield. Simple and continuous compounding decrease more steeply and get the target (the dotted red line) for more reasonable values — if you can call reasonable a yield of 5000% — but quarterly compounded just takes too long.

plot

I'm not sure what we can do about this, or what kind of threshold we should add if we wanted to detect this and fall back on another calculation. I guess you can manually switch to SimpleThenCompounded as a workaround.