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Reducing Risk

diversification - putting resources into different risky situations  

  • can't lose on all investments
  • invesments not too closely correlated >> eliminates some risk
  • negatively correlated - good results for 1 investment means bad results for another investment
  • positively correlated - investments moving in the same direction, in response to economic changes

insurance - uses risk premiums  

  • insurance cost = expected loss
  • law of large numbers - aility to avoid risk by operating on a large scale
  • if insurance premium = expected payout, then actuarially fair
    • insurance companies need to profit >> charge more than expected losses

Dan has a wealth utility function of U = lnw. He currently has $1200, but there's a 1/8 chance that his car will blow up and he'll lose $1000. However, he could pay insurance 30 cents on the dollar to cover his potential losses. How much insurance should he pay?  

  • you want to maximize expected utility
  • x = amount he covers w/ insurance
    • he'll pay 0.3x for the insurance
  • if his car doesn't blow up, he'll have w = 1200 - 0.3x
  • if his car does blow up, he'll have w = (1200-1000) - 0.3x + x
    • gets back the x amount he covers
    • be sure to include the 0.3x amount that he still paid
  • EU = (7/8) ln(1200 - 0.3x) + (1/8) ln(200 + 0.7x)
    • d(EU)/dx = 0 = (-2.1/8) / (1200 - 0.3x) + (0.7/8) / (200 + 0.7x)
    • (2.1/8) / (1200 - 0.3x) = (0.7/8) / (200 + 0.7x)
    • 2.1 / (1200 - 0.3x) = 0.7 / (200 + 0.7x)
    • 420 + 1.47x = 840 - 0.21x
    • 1.68x = 420
    • x = $250

value of complete information - difference between expected value of choice w/ and w/o complete information  

  • calculates how much firm would pay for extra information/predictions for sales
  • also dependent on whether firm is risk averse/neutral/loving
Subject: 
Economics
Subject X2: 
Economics

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