Tài chính doanh nghiệp - Lecture 2: The universal principle of risk management

Lecture 2The Universal Principle of Risk ManagementPooling and Hedging of RiskProbability and InsuranceConcept of probability began in 1660sConcept of probability grew from interest in gambling.Mahabarata story (ca. 400 AD) of Nala and Rtuparna, suggests some probability theory was understood in India then.Fire of London 1666 and InsuranceProbability and Its RulesRandom variable: A quantity determined by the outcome of an experimentDiscrete and continuous random variablesIndependent trialsProbability P, 0<P<1Multiplication rule for independent events: Prob(A and B) = Prob(A)Prob(B)Insurance and Multiplication RuleProbability of n independent accidents = PnProbability of x accidents in n policies (Binomial Distributon):Expected Value, Mean, AverageGeometric MeanFor positive numbers onlyBetter than arithmetic mean when used for (gross) returnsGeometric  ArithmeticVariance and Standard DeviationVariance (2)is a measure of dispersionStandard deviation  is square root of varianceCovarianceA Measure of how much two variables move togetherCorrelationA scaled measure of how much two variables move together-1 1Regression, Beta=.5, corr=.93DistributionsNormal distribution (Gaussian) (bell-shaped curve)Fat-tailed distribution common in financeNormal DistributionNormal Versus Fat-TailedExpected UtilityPascal’s ConjectureSt. Petersburg Paradox, Bernoulli: Toss coin until you get a head, k tosses, win 2(k-1) coins.With log utility, a win after k periods is worth ln(2k-1)Present Discounted Value (PDV)PDV of a dollar in one year = 1/(1+r)PDV of a dollar in n years = 1/(1+r)nPDV of a stream of payments x1,..,xnConsol and Annuity FormulasConsol pays constant quantity x foreverGrowing consol pays x(1+g)^t in t years.Annuity pays x from time 1 to TInsurance AnnuitiesLife annuities: Pay a stream of income until a person dies.Uncertainty faced by insurer is termination date T Problems Faced by Insurance CompaniesProbabilities may change through timePolicy holders may alter probabilities (moral hazard)Policy holders may not be representative of population from which probabilities were derivedInsurance Company’s portfolio faces risk