Proportional versus additive de-vig on a lopsided book

Question

A match is quoted with a heavy favorite: Home 1.25, Draw 6.50, Away 12.00. De-vig this book with both the proportional method and the additive (equal-margin) method, and explain why they disagree.

Accepted Answer

Step 1: raw implied probabilities and overround. \frac{1}{1.25} = 0.8000, \quad \frac{1}{6.50} = 0.1538, \quad \frac{1}{12.00} = 0.0833. S = 0.8000 + 0.1538 + 0.0833 = 1.0372, \quad 	ext{overround} = 3.72\%. Step 2: proportional method (divide each by S): P	ext{Home} = \frac{0.8000}{1.0372} = 0.771, \quad P	ext{Draw} = \frac{0.1538}{1.0372} = 0.148, \quad P	ext{Away} = \frac{0.0833}{1.0372} = 0.080. Step 3: additive method (subtract the same absolute amount (S-1)/3 = 0.0372/3 = 0.0124 from each raw probability): P	ext{Home} = 0.8000 - 0.0124 = 0.788, \quad P	ext{Draw} = 0.1538 - 0.0124 …

Proportional versus additive de-vig on a lopsided book

Your answer

More Market Making questions