Find the hold on a two-way moneyline

Question

A moneyline market posts -120 on the favorite and +105 on the underdog. Give each implied probability, the bookmaker's hold (margin), and the de-vigged fair line.

Accepted Answer

Convert each American price to a probability. For minus odds -x, p = \frac{x}{x + 100}; for plus odds +x, p = \frac{100}{x + 100}: p{	ext{fav}} = \frac{120}{120 + 100} = \frac{120}{220} = 0.5455, \qquad p{	ext{dog}} = \frac{100}{105 + 100} = \frac{100}{205} = 0.4878. These sum to 0.5455 + 0.4878 = 1.0333. The hold is the excess over 100\%: 1.0333 - 1 = 0.0333, about 3.33\%. De-vig by dividing each by the sum: \frac{0.5455}{1.0333} = 52.8\%, \qquad \frac{0.4878}{1.0333} = 47.2\%. So stripped of margin, the market sees the favorite at about 52.8\% and the underdog at 47.2\%, which now add to …

Find the hold on a two-way moneyline

Your answer

More Market Making questions