Inequalities

1 article

Agmons inequality Alexandrov fenchel inequality Babenko beckner inequality Bells original inequality Bennetts inequality Bergers inequality for einstein manifolds Bernoullis inequality Blaschke lebesgue inequality Blaschke santal inequality Boole inequality Borell brascamp lieb inequality Borell tis inequality Brascamp lieb inequality Brezis gallouet inequality Brs inequality Brunn minkowski inequality Burkholders inequality Cantellis inequality Castelnuovo severi inequality Cauchy interlacing theorem Chebyshev markov stieltjes inequalities Chebyshevs sum inequality Chernoffs inequality Chsh inequality Chung erd's inequality Clausius duhem inequality Eatons inequality Eilenbergs inequality Emerys inequality Erd's mordell inequality Etemadis inequality Fannes audenaert inequality Feffermans inequality Fekete szeg inequality Fr chet inequalities Fritz carlson Gaussian correlation inequality Gausss inequality Gibbss inequality Ginibre inequality Griffiths inequality Hadamards inequality Hadwiger finsler inequality Hardy littlewood inequality Hardy littlewood maximal inequality Hardy littlewood sobolev inequality Hardys inequality Heisenbergs inequality Hermite hadamard inequality Hoeffding inequality Hoeffdings lemma Hoffman wielandt inequality Holley inequality Inequalities in information theory Inequality of arithmetic and geometric means Ingletons inequality Isoperimetry Jordans inequality Kantorovich inequality Khabibullins conjecture on integral inequalities Kolmogorov inequality Krafts inequality Landau kolmogorov inequality Large sieve inequality Lebedev milin inequality Leggett garg inequality Lenglarts inequality Levinsons inequality Littlewoods 4 3 inequality Littlewoods inequality Loomis whitney inequality Mahlers inequality Markov brothers inequality Markov inequality Mashreghi ransford inequality Minkowskis inequality Muirheads inequality Nesbitts inequality Newtons inequalities Ojasiewicz inequality Onos inequality Pedoes inequality Popovicius inequality on variances Pr kopa leindler inequality Prophet inequality Ptolemys inequality Pus inequality Rayleigh faber krahn inequality Rearrangement inequality Remez inequality Rosss conjecture Rushbrooke inequality Samuelsons inequality Schur test Schurs inequality Shapiro inequality Shearers inequality Stochastic gronwall inequality Sylvesters rank inequality Szeg inequality Three spheres inequality Tsirelsons inequality Tur ns inequalities Vitales random brunn minkowski inequality Vysochanski petunin inequality Weitzenb cks inequality Welch bounds Youngs inequality for products

Analysis / Calculus LicenceExplication9 min

The Back Half Pays 20.227 Percent, and the Fifth Root Cancels

Because the horizons are ten and five, both sides of the no-arbitrage equation are fifth powers and the root disappears, leaving 1 + f = 1.15 squared over 1.10 = 529/440, so f = 89/440 exactly. Reflecting 10 percent around 15 to get 20 is low by exactly (b - a) squared over (1 + a), a square over a positive number, which is why the reflection can never overshoot for any pair of rates. Under continuous compounding the same problem is linear and 20 percent is exactly right, so the instinct is correct machinery pointed at the wrong convention.