At the horse races one Saturday afternoon Gavin Jones studies the racing form and concludes that the horse No Arbitrage has a $25 %$ chance to win and is posted at 4 to 1 odds. (For every dollar Gavin bets, he receives $\$ 5$ if the horse wins and nothing if it loses.) He can either bet on this horse or keep his money in his pocket. Gavin decides that he has a square-root utility for money.

(a) What fraction of his money should Gavin bet on No Arbitrage?

(b) What is the implied winning payoff of a $\$ 1$ bet against No Arbitrage?