A bank is considering adding life insurance underwriting to the services it offers. It has estimated that the expected return and standard deviation of its traditional services are 12 percent and 6 percent respectively. It has also estimated that the expected return and standard deviation of its new underwriting services are 18 percent and 10 percent respectively. The correlation between these services has been estimated to be 0.10 and the bank estimates that 90 percent of its business will be from traditional services and 10 percent from the new underwriting services. If the bank is expecting that the overall risk of the bank will be reduced by adding the life insurance underwriting to the bank, what type of effect are they expecting

Because of the violent nature of the sport, professional american football players are at risk of suffering concussions (or brain injuries) during the violent collisions that occur between players during the game. violent collisions involving hits to the head are particularly risky. suppose the commissioner of the national football league (nfl) institutes a rule requiring players to wear a new, lighter helmet that is designed to reduce head trauma during collisions between players on the field. while the new helmets the probability of a concussion resulting from each individual collision, at the same time the new helmets could also give football players an incentive to play more , which could potentially the amount of violent collisions and thus the number of concussions suffered by nfl players, all else equal.