Risk Sharing: Approximate Expression Three investors with risk tolerance equal to $5000, $10,000, and $15000 face the following deal. [ 0.25, -20000; 0.5, 0; 0.25, 30000 ] a. What is the risk...

Risk Sharing: Approximate Expression

Three investors with risk tolerance equal to $5000, $10,000, and $15000 face the following deal.

[ 0.25, -20000; 0.5, 0; 0.25, 30000 ]

a. What is the risk tolerance of the group?

b. Using the approximate expression, calculate the group certain equivalent.

c. What is the optimal fraction that each group member should take? What is the certain equivalent of each group member's optimal fraction?

d. The group has the option to include an additional investor. What is the group's preferred risk tolerance for this new investor?

e. What is the group certain equivalent and optimal share of each member if the preferred investor joined the group?