Question

Assume you have initial wealth of $5000 and face a 40% chance of winning$2000 and a 60% chance of losing $1000. You are an expected utilitymaximizer with u(W) = 1-e^-.0005W. Calculate Risk premium? What will the risk premium be if intial wealth is increase to 1000$?

Answer 1

Utility function is given as:

uw) = 1-e-0.0005-

Expected income due to winning : I(E) = 5000+2000=7000

Expected income due to loosing: I(E) = 5000-1000=4000

Expected income: 7000 *0.4 + 4000*0.6 = 2800+2400 = 5200

if not involed with lottery then the fixed wealth = 5000.

Risk Premium is the maximum amount of money a risk averse person is willing to pay to avoid the risk.

Here Risk Premium = 5200-5000 = $200

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If wealth is 6000 now:

Expected income due to winning : I(E) = 6000+2000=8000

Expected income due to loosing: I(E) = 6000-1000=5000

Expected income: 8000 *0.4 + 5000*0.6 = 3200+3000 = 6200

if not involed with lottery then the fixed wealth = 6000.

Risk Premium = 6200-6000 = $200