Locking a profit by hedging after the odds move

Earlier you backed outcome XX of a two-outcome event, staking $100 at decimal odds of 3.003.00 (so you collect $300 if XX occurs, and lose your $100 otherwise). The market has since moved, and you can now back not-XX at decimal odds of 2.002.00. You want to hedge so your net profit is the same whichever outcome happens - a locked profit. How many dollars should you now stake on not-XX, and what is your guaranteed profit? Give the guaranteed profit (in dollars).

Show hints (2)+
  1. Write the net profit on each outcome as a function of the hedge stake hh (total out is 100+h100 + h), then set the two equal.
  2. Solving 200h=h100200 - h = h - 100 gives h=150h = 150; plug back in for the locked profit.

Answer

Reveal answer →

50

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude, Options Market-Making, ETF Market-Making

Related questions