Question

Your firm forecasts that there is a 50% probability that the market will be up significantly next year, a 20% probability that the market will be down significantly next year, and a 30% probability that the market will be flat, neither up or down significantly. You are asked to evaluate the prospects of a new portfolio manager. The manager has a long bias and is likely to perform better in an up market. Based on past data, you believe that the probability that the manager will be up if the market is up significantly is 80%, and that the probability that the manager will be up if the market is down significantly is only 10%. If the market it flat, the manager is just as likely to be up as to be down. What is the unconditional probability that the manager is up next year?

Answer 1

P(market up)=0.5

P(market down)=0.2

P(market flat)=0.3

P( manager up | market up)= 0.8

P(manager up| market down)= 0.1

P( manager up| market flat)= 0.5 = P( manager down| market flat)

P( manager up)= P( market up)*P( manager up | market up) + P( market down) *P(manager up| market down) + P(market flat)* P( manager up| market flat)

= 0.5* 0.8 + 0.2*0.1 + 0.3*0.5

=0.57