Topic14_Uncertainty

# 33 di ifi ti diversification if government offers a

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Di ifi ti Diversification If government offers a lucrative contract to If government offers a lucrative contract to either firm A or B with 50-50% probability, then investing in both the firms eliminates the risk. In this case the two events are perfectly negatively correlated. Even if the two events are imperfectly negatively correlated, risk will be reduced. But if the events are perfectly positively correlated, diversification cannot reduce risk. 34
Reducing Risk – The Stock M k t Market If you invest all money in one stock, then you If you invest all money in one stock, then you take on a lot of risk. If that stock loses value, you lose all your investments. You can spread risk out by investing in may different stocks or investments. Ex: Mutual funds: S&P 500 or NYSE. However a systematic risk (price of all However, a systematic risk (price of all stocks fall during recession but increase during expansion) cannot be avoided. 35

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R d i Ri k I Reducing Risk – Insurance Risk averse people are willing to pay to Risk averse people are willing to pay to avoid risk. If the cost of insurance (premium) equals the If the cost of insurance (premium) equals the expected loss, risk averse people will buy enough insurance to recover fully from a enough insurance to recover fully from a potential financial loss. A risk averse person is willing to pay a risk A risk averse person is willing to pay a risk premium to avoid risk. 36
R d i Ri k I Reducing Risk – Insurance Example: Insuring against Break Ins Assume wealth = \$50 K and loss = \$10 K in case of break Ins case of break Ins. If Prob. of break in = 0.1, E(Loss) = 0.1* 10 =1 K. 1 K. Assume full insurance against loss and pay premium = E(Loss) = 1 K. This is called acturially fair premium . The insurance firm makes zero profits with this 37 insurance premium.

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Th D i i t I The Decision to Insure E(X) with insurance = 0.1*(50 – 1) + 0.9*(50 – 1) = 49 K – 1) = 49 K. With insurance, risk is eliminated as Variance or Standard Deviation = 0 38 or Standard Deviation 0.
R d i Ri k I Reducing Risk – Insurance For risk averse consumers guarantee of For risk averse consumers, guarantee of same income regardless of outcome has higher utility than facing the probability of risk. For the same expected wealth, expected utility with insurance is higher than without utility with insurance is higher than without (for a risk averse individual). Thus when fair insurance is offered risk Thus when fair insurance is offered, risk averse person fully insures . 39

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R d i Ri k F i I Reducing Risk – Fair Insurance With fair Insurance total premiums raised = With fair Insurance, total premiums raised = E(Loss) = E(coverage). So insurance companies usually offer less So insurance companies usually offer less than fair insurance to cover their operating costs. costs. A monopoly insurance company could charge up to the risk premium —the maximum the policy holders are willing to pay.
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• Spring '10
• E.Fowler
• Utility, Ri, Behavioral Economics of Risk

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