Chapter 10: Risk Management Objective •Risk and Financial Decision Making •Conceptual Framework for Risk Management •Efficient Allocation of Risk-Bearing 10.1 What is Risk? 10.2 Risk and Economic Decisions 10.3 The Risk Management Process 10.4 The Three Dimensions of Risk Transfer 10.5 Risk Transfer and Economic Efficiency 10.6 Institutions for Risk Management 10.7 Portfolio Theory: Quantitative Analysis for Optimal Risk Management 10.8 Probability Distributions of Returns 10.9 Standard Deviation as a Measure of Risk Standard Deviations of Portfolios 0.20 Standare Deviation 0.19 σ = 0.2000 0.18 σ = 0.1421 0.17 0.16 0.15 0.14 0.13 Portfolio Size σ* = 0.1342 Theoretical Minimum 10 Equation for Homogeneous Diversification with n Stocks σ port = σ stock n( n − 1) + ρ n n Returns on GENCO & RISCO State of Return on Return on ProbEconomy RISCO GENCO ability Strong 50% 30% 0.20 Normal 10% 10% 0.60 Weak -30% -10% 0.20 Probability Distributions of Returns of Genco and Risco 0.6 0.5 0.4 Probability 0.3 0.2 0.1 50% Genco 30% Risco 10% -10% Return -30% Equations: Mean µ r = E [ r ] = P1r1 + P2 r2 + P3 r3 + Pn rn = P ⋅r n = ∑ Pi ri i =1 µ rGENCO = 0.2 × 0.3 + 0.6 × 0.10 + 0.2 × (−0.10) µ rGENCO = 0.10 = 10% Also : µ rRISCO = 10% σr Equations: Standard Deviation = E [( r − E [ r ] ) ] = P1 ( r1 − µ r ) + P2 ( r2 − µ r ) + + Pn ( rn − µ r ) = n ∑ Pi ( ri − µ r ) 2 i =1 σ rGENCO = 0.2 × ( 0.30 − 0.10 ) + 0.6 × ( 0.10 − 0.10 ) + 0.2 × (−0.10 − 0.10) 2 σ rGENCO = 0.016 = 0.1265 Also : σ rRISCO = 0.2530 Distribution of Returns on Two Stocks 3.5 Probability Density 3.0 2.5 NORMCO 2.0 VOLCO 1.5 1.0 0.5 0.0 -100% -50% 0% Return 50% 100% Two More Return Densities 1.8 1.6 1.4 Probability Density VOLCO ODDCO 1.2 1.0 0.8 0.6 0.4 0.2 -100.00% -50.00% 0.0 0.00% 50.00% Return 10 100.00%