introduction to risk management defense resources management institute naval postgraduate school...
TRANSCRIPT
INTRODUCTIONTO
RISK MANAGEMENT
Defense Resources Management InstituteNaval Postgraduate School
Monterey, California
WHAT IS RISK?
• Arabic - Fortuitous and favorable.
• Greek - Fortuitous and neither favorable nor unfavorable.
• Latin (risicum) - the challenge that a barrier reef presents to a sailor.
• French (risque) - mainly negative connotation, but sometimes positive.
• Oxford Dictionary - “... the chance of hazard, bad consequences, loss, etc....”
DEFINITIONS I
DEFINITIONS II
• Economic risk - the chance of loss due to ….
• Business risk - the chance of loss associated with …
• Market risk - the chance that a portfolio of investments can
lose money because…..
• Inflation risk - the danger that a general increase in prices ...
• Interest-rate risk - market risk due to interest rate fluctuations
• Credit risk - the chance that of a default on a loan ...
• Liquidity risk - the difficulty in selling a fixed asset ...
• Derivative risk - the chance of financial loss due to increased
volatility ….
• Cultural risk - the chance of loss because of product market …..
CHANCERandom Occurrence
BAD CONSEQUENCESense of Loss
Hirschey & Pappas, Fundamentals of Managerial Economics Dryden Press, 1998
ALITTLE BIT
OFPROBABILITY
• It’s a number – it’s JUST A NUMBER!
• It’s a number between 0 and 1 ( 0 ≤ P ≤ 1)
• It quantifies the likelihood of an event
• It’s a function of experience, judgment, subjective assessment, available data
• It’s uses all information you think is relevant to the determination of the likelihood of occurrence of an event
PROBABILITY
Probability Rules
Probability = 0 if “never/impossible”
Probability = 1 if “always/certain”
If we are collectively exhaustive and
mutually exclusive then
the probabilities over the outocmes
SUM to 1.
Probability Rules
• If mutually exclusive then :
P(A or B) = P(A) + P(B)
• If independent :
P(A and B) = P(A) x P(B)
Probability from Data
• Given data we can always derive approximate probabilities using relative frequency.
• Relative frequency can be used as an estimate of the probability of the observed value
• Taken all together, these can represent the underlying PROBABILITY DISTRUBUTION FUNCTION
1.99 3.92 2.16 3.83 2.99 2.91 3.45 2.98 2.60 2.35 1.87 1.50 2.09 2.03 1.52 2.90 2.76 2.50 2.95 1.532.17 1.51 1.64 3.71 2.25 1.53 1.69 2.16 2.11 4.29 1.99 3.12 1.53 2.37 1.87 1.72 5.89 1.84 2.01 5.262.24 6.89 3.70 4.86 7.17 1.56 1.54 1.57 1.51 3.51 4.95 5.06 7.06 2.95 4.63 2.35 1.59 1.84 1.93 1.811.73 6.48 3.63 1.64 2.89 3.20 2.33 5.04 1.69 3.15 1.92 1.94 1.72 2.25 2.02 1.64 3.74 3.95 3.77 4.282.50 1.94 3.75 2.30 3.88 3.57 1.63 5.25 3.33 7.33 1.53 1.81 1.52 1.95 2.55 2.01 2.16 3.04 1.72 1.522.21 1.88 5.71 2.43 3.59 1.88 1.73 5.27 1.99 2.30 2.67 4.13 2.66 4.46 3.18 7.63 5.86 1.83 2.98 1.632.38 1.54 2.73 1.88 2.61 3.39 3.25 2.59 4.32 4.20 3.05 2.52 5.31 5.49 4.05 1.61 3.69 2.86 1.88 6.822.57 2.68 1.69 1.98 1.58 2.78 2.06 4.24 2.44 2.76 1.71 6.16 1.70 1.55 1.93 6.54 6.17 2.33 6.38 2.253.80 2.29 2.33 1.78 6.73 3.69 1.72 3.74 3.10 7.02 2.97 2.30 1.77 6.81 4.46 2.19 1.75 2.97 2.22 5.021.78 2.36 1.71 1.86 4.14 2.09 1.86 3.94 4.17 3.34 1.87 1.54 2.60 2.97 4.30 2.76 3.20 4.72 2.18 1.881.67 2.46 1.59 1.74 1.66 2.02 1.81 3.85 5.31 2.21 4.19 3.48 4.77 2.21 3.62 2.00 1.86 2.46 3.46 3.762.49 2.44 3.70 1.66 4.28 4.75 2.03 1.91 3.84 2.18 3.56 1.66 2.63 2.01 2.93 2.76 3.10 4.98 1.85 5.001.52 1.58 1.79 2.25 5.16 3.65 1.92 4.43 2.54 2.48 1.81 2.24 3.41 2.38 2.57 3.69 1.68 2.78 4.86 3.843.17 4.09 3.94 2.19 7.11 1.65 3.06 2.22 2.32 2.02 2.92 4.12 8.93 2.03 1.69 3.24 1.53 5.52 1.60 1.724.88 3.90 5.13 2.26 2.48 2.84 1.58 3.48 1.55 2.33 1.64 6.69 2.18 1.67 3.27 1.85 3.56 1.81 3.07 1.942.96 2.71 1.92 6.79 3.85 4.07 1.88 2.48 1.51 2.64 2.65 3.37 2.02 2.88 2.04 4.43 1.73 3.50 3.05 3.352.37 1.59 5.02 4.92 2.35 2.20 2.83 2.98 3.35 2.15 2.41 2.09 2.38 2.00 2.01 3.79 1.92 3.97 5.22 3.041.61 1.83 1.72 7.11 2.16 1.60 2.48 5.98 6.21 2.69 3.52 1.68 5.75 2.23 1.56 1.99 3.59 1.84 5.67 1.836.46 2.17 2.85 2.64 2.00 5.43 5.88 2.44 4.73 2.28 3.27 1.95 4.02 2.71 1.80 2.87 1.79 1.62 1.64 2.811.79 3.99 3.17 3.16 3.32 2.15 3.66 2.46 3.65 1.89 3.15 2.23 2.73 1.83 4.33 2.80 2.57 3.38 3.49 2.245.39 1.88 3.95 2.81 2.55 1.56 4.53 1.89 1.67 3.11 4.41 5.83 3.70 2.85 3.59 3.34 4.11 2.48 5.77 2.474.12 1.82 6.37 1.69 5.46 5.89 2.17 3.23 3.75 6.50 5.73 5.71 2.14 1.70 6.14 3.00 3.55 4.95 3.46 1.893.26 4.33 3.30 2.08 2.80 2.35 4.27 2.83 1.90 6.58 5.38 3.10 2.50 2.18 3.79 1.73 1.53 3.46 2.49 1.581.96 3.83 7.10 3.67 4.63 1.79 3.30 3.65 3.05 1.96 1.76 2.72 5.70 1.62 1.50 3.58 3.55 2.51 3.70 1.561.53 2.89 2.10 2.15 1.63 1.65 2.83 4.90 2.59 4.08 2.77 1.92 4.10 3.27 4.39 1.77 3.54 4.52 7.18 3.932.36 1.86 1.85 1.70 1.90 2.32 3.14 2.72 1.58 2.44 3.30 1.67 3.66 3.10 3.34 3.06 2.68 2.80 6.16 3.231.53 1.89 2.52 3.80 1.57 2.11 1.64 1.94 1.55 2.22 2.14 1.96 4.43 1.77 2.69 4.41 1.92 2.44 3.25 1.882.79 2.12 2.50 2.04 2.16 4.34 2.29 1.55 1.52 2.40 4.07 2.13 2.13 2.62 2.10 2.90 2.17 2.68 4.32 3.106.53 4.24 1.75 2.14 2.93 2.00 4.26 2.93 1.63 2.35 2.00 2.44 2.80 2.17 3.31 3.41 1.71 2.61 1.62 4.295.34 4.30 2.17 1.84 6.87 4.09 2.19 5.49 4.94 1.83 4.55 1.99 4.57 3.83 4.10 2.48 1.71 2.45 4.69 2.662.30 5.08 4.96 3.40 2.33 1.61 4.40 2.31 2.11 1.72 2.97 4.39 2.92 1.89 1.85 3.59 3.11 1.95 2.37 4.262.58 5.16 4.18 2.14 2.03 4.10 1.81 2.06 4.11 5.38 1.84 2.68 2.91 1.83 2.34 6.26 5.83 3.60 2.50 2.733.48 4.52 3.12 1.94 1.83 2.22 4.07 2.82 1.53 2.16 4.32 6.31 1.93 5.01 2.38 4.08 2.13 3.36 2.14 2.152.00 5.48 3.32 3.00 4.83 3.32 6.96 1.66 1.55 2.17 2.88 2.99 3.79 3.22 1.52 2.02 2.28 1.93 1.71 2.147.76 2.10 2.24 2.60 1.60 2.31 4.85 5.51 3.31 2.90 4.17 2.97 5.12 2.08 2.05 3.20 2.60 5.08 1.90 2.792.34 2.91 2.00 2.78 2.16 1.67 3.12 4.11 2.59 6.21 3.37 3.23 2.84 3.74 2.24 2.95 2.03 2.37 2.48 3.423.77 2.16 3.23 1.56 1.69 2.82 2.37 4.64 3.35 1.53 3.64 1.90 1.76 3.14 3.22 2.61 3.64 2.51 2.44 3.971.53 1.90 3.60 2.16 3.11 3.60 2.71 4.65 4.28 4.39 1.67 2.78 1.82 5.69 2.41 3.77 2.12 1.58 4.15 2.033.87 2.89 1.86 1.75 4.05 2.90 1.75 1.62 3.36 1.78 2.36 2.26 1.82 2.87 3.59 2.76 1.74 3.29 1.55 1.654.33 1.90 1.71 2.74 1.88 3.16 2.09 2.56 3.94 5.10 1.51 3.66 2.61 1.55 3.99 1.63 2.71 2.26 1.97 1.753.14 5.34 2.07 2.45 2.02 2.19 2.39 3.36 4.53 2.83 2.10 1.89 1.99 4.01 5.40 2.64 3.86 2.35 4.04 2.361.76 4.86 5.00 1.86 3.69 1.98 2.42 1.80 1.78 2.54 1.78 2.22 3.14 4.44 1.77 2.17 3.53 1.56 2.63 3.332.09 2.36 4.09 2.88 2.08 2.39 1.96 3.02 8.14 4.45 1.52 2.80 2.59 3.77 3.23 6.42 1.59 2.28 3.36 4.043.14 1.73 1.97 3.66 1.69 2.48 3.02 1.53 1.62 3.02 5.35 3.98 2.15 4.16 2.89 3.23 2.25 1.84 2.40 3.207.90 2.55 1.64 3.19 2.31 1.63 2.40 1.78 3.27 4.14 2.40 5.72 2.73 3.47 4.22 3.26 2.82 2.13 2.11 1.914.12 3.15 1.68 1.92 2.70 1.60 2.21 1.62 2.56 1.69 3.23 2.85 3.74 3.62 2.65 4.85 1.54 5.59 1.98 1.984.39 3.24 2.45 2.17 3.67 3.08 5.67 3.95 2.23 1.95 2.49 1.95 3.18 4.07 1.56 1.76 3.57 2.05 1.87 3.201.52 1.58 3.06 2.77 2.46 1.62 3.48 2.29 3.64 3.67 6.39 4.75 2.59 3.92 2.01 6.03 2.01 3.74 1.76 1.731.87 1.79 4.77 2.37 3.12 5.96 1.54 5.40 1.62 2.36 1.76 2.39 2.59 2.85 3.44 4.07 1.60 2.35 3.37 1.511.51 2.05 2.33 3.73 3.95 5.87 1.77 2.65 1.66 1.62 2.07 2.04 1.88 2.02 5.11 2.43 1.92 3.45 1.80 6.20
Earthquakes
1.50 1.58 1.67 1.77 1.86 1.95 2.06 2.17 2.31 2.44 2.60 2.80 2.97 3.20 3.41 3.69 3.98 4.30 4.95 5.831.50 1.58 1.67 1.77 1.87 1.95 2.06 2.17 2.31 2.44 2.60 2.80 2.98 3.20 3.42 3.69 3.99 4.32 4.96 5.831.51 1.58 1.67 1.77 1.87 1.96 2.07 2.17 2.32 2.44 2.60 2.80 2.98 3.20 3.44 3.69 3.99 4.32 4.98 5.861.51 1.58 1.67 1.77 1.87 1.96 2.07 2.17 2.32 2.44 2.61 2.80 2.98 3.22 3.45 3.69 4.01 4.32 5.00 5.871.51 1.58 1.68 1.77 1.87 1.96 2.08 2.17 2.33 2.45 2.61 2.80 2.99 3.22 3.45 3.70 4.02 4.33 5.00 5.881.51 1.58 1.68 1.78 1.87 1.96 2.08 2.18 2.33 2.45 2.61 2.81 2.99 3.23 3.46 3.70 4.04 4.33 5.01 5.891.51 1.59 1.68 1.78 1.88 1.97 2.08 2.18 2.33 2.45 2.61 2.81 3.00 3.23 3.46 3.70 4.04 4.33 5.02 5.891.51 1.59 1.69 1.78 1.88 1.97 2.09 2.18 2.33 2.46 2.62 2.82 3.00 3.23 3.46 3.70 4.05 4.34 5.02 5.961.52 1.59 1.69 1.78 1.88 1.98 2.09 2.18 2.33 2.46 2.63 2.82 3.02 3.23 3.47 3.71 4.05 4.39 5.04 5.981.52 1.59 1.69 1.78 1.88 1.98 2.09 2.19 2.33 2.46 2.63 2.82 3.02 3.23 3.48 3.73 4.07 4.39 5.06 6.031.52 1.60 1.69 1.78 1.88 1.98 2.09 2.19 2.34 2.46 2.64 2.83 3.02 3.23 3.48 3.74 4.07 4.39 5.08 6.141.52 1.60 1.69 1.79 1.88 1.98 2.09 2.19 2.34 2.47 2.64 2.83 3.04 3.23 3.48 3.74 4.07 4.39 5.08 6.161.52 1.60 1.69 1.79 1.88 1.99 2.10 2.19 2.35 2.48 2.64 2.83 3.04 3.24 3.48 3.74 4.07 4.40 5.10 6.161.52 1.60 1.69 1.79 1.88 1.99 2.10 2.20 2.35 2.48 2.65 2.83 3.05 3.24 3.49 3.74 4.07 4.41 5.11 6.171.52 1.60 1.69 1.79 1.88 1.99 2.10 2.21 2.35 2.48 2.65 2.84 3.05 3.25 3.50 3.74 4.08 4.41 5.12 6.201.52 1.61 1.70 1.79 1.88 1.99 2.10 2.21 2.35 2.48 2.65 2.84 3.05 3.25 3.51 3.75 4.08 4.43 5.13 6.211.53 1.61 1.70 1.80 1.89 1.99 2.11 2.21 2.35 2.48 2.66 2.85 3.06 3.26 3.52 3.75 4.09 4.43 5.16 6.211.53 1.61 1.70 1.80 1.89 1.99 2.11 2.21 2.35 2.48 2.66 2.85 3.06 3.26 3.53 3.76 4.09 4.43 5.16 6.261.53 1.62 1.71 1.80 1.89 2.00 2.11 2.22 2.35 2.48 2.67 2.85 3.06 3.27 3.54 3.77 4.09 4.44 5.22 6.311.53 1.62 1.71 1.81 1.89 2.00 2.11 2.22 2.36 2.48 2.68 2.85 3.07 3.27 3.55 3.77 4.10 4.45 5.25 6.371.53 1.62 1.71 1.81 1.89 2.00 2.12 2.22 2.36 2.49 2.68 2.86 3.08 3.27 3.55 3.77 4.10 4.46 5.26 6.381.53 1.62 1.71 1.81 1.89 2.00 2.12 2.22 2.36 2.49 2.68 2.87 3.10 3.27 3.56 3.77 4.10 4.46 5.27 6.391.53 1.62 1.71 1.81 1.90 2.00 2.13 2.22 2.36 2.49 2.68 2.87 3.10 3.29 3.56 3.79 4.11 4.52 5.31 6.421.53 1.62 1.71 1.81 1.90 2.00 2.13 2.23 2.36 2.50 2.69 2.88 3.10 3.30 3.57 3.79 4.11 4.52 5.31 6.461.53 1.62 1.72 1.81 1.90 2.00 2.13 2.23 2.36 2.50 2.69 2.88 3.10 3.30 3.57 3.79 4.11 4.53 5.34 6.481.53 1.62 1.72 1.82 1.90 2.01 2.13 2.23 2.37 2.50 2.70 2.88 3.10 3.30 3.58 3.80 4.12 4.53 5.34 6.501.53 1.62 1.72 1.82 1.90 2.01 2.14 2.24 2.37 2.50 2.71 2.89 3.11 3.31 3.59 3.80 4.12 4.55 5.35 6.531.53 1.63 1.72 1.82 1.90 2.01 2.14 2.24 2.37 2.50 2.71 2.89 3.11 3.31 3.59 3.83 4.12 4.57 5.38 6.541.54 1.63 1.72 1.83 1.91 2.01 2.14 2.24 2.37 2.51 2.71 2.89 3.11 3.32 3.59 3.83 4.13 4.63 5.38 6.581.54 1.63 1.72 1.83 1.91 2.01 2.14 2.24 2.37 2.51 2.71 2.89 3.12 3.32 3.59 3.83 4.14 4.63 5.39 6.691.54 1.63 1.72 1.83 1.92 2.01 2.14 2.24 2.37 2.52 2.72 2.90 3.12 3.32 3.59 3.84 4.14 4.64 5.40 6.731.54 1.63 1.73 1.83 1.92 2.02 2.14 2.25 2.38 2.52 2.72 2.90 3.12 3.33 3.60 3.84 4.15 4.65 5.40 6.791.54 1.63 1.73 1.83 1.92 2.02 2.15 2.25 2.38 2.54 2.73 2.90 3.12 3.33 3.60 3.85 4.16 4.69 5.43 6.811.55 1.64 1.73 1.83 1.92 2.02 2.15 2.25 2.38 2.54 2.73 2.90 3.14 3.34 3.60 3.85 4.17 4.72 5.46 6.821.55 1.64 1.73 1.83 1.92 2.02 2.15 2.25 2.38 2.55 2.73 2.91 3.14 3.34 3.62 3.86 4.17 4.73 5.48 6.871.55 1.64 1.73 1.84 1.92 2.02 2.15 2.25 2.39 2.55 2.73 2.91 3.14 3.34 3.62 3.87 4.18 4.75 5.49 6.891.55 1.64 1.73 1.84 1.92 2.02 2.15 2.26 2.39 2.55 2.74 2.91 3.14 3.35 3.63 3.88 4.19 4.75 5.49 6.961.55 1.64 1.74 1.84 1.92 2.02 2.16 2.26 2.39 2.56 2.76 2.92 3.14 3.35 3.64 3.90 4.20 4.77 5.51 7.021.55 1.64 1.74 1.84 1.93 2.03 2.16 2.26 2.40 2.56 2.76 2.92 3.15 3.35 3.64 3.92 4.22 4.77 5.52 7.061.55 1.64 1.75 1.84 1.93 2.03 2.16 2.28 2.40 2.57 2.76 2.93 3.15 3.36 3.64 3.92 4.24 4.83 5.59 7.101.56 1.65 1.75 1.84 1.93 2.03 2.16 2.28 2.40 2.57 2.76 2.93 3.15 3.36 3.65 3.93 4.24 4.85 5.67 7.111.56 1.65 1.75 1.85 1.93 2.03 2.16 2.28 2.40 2.57 2.76 2.93 3.16 3.36 3.65 3.94 4.26 4.85 5.67 7.111.56 1.65 1.75 1.85 1.94 2.03 2.16 2.29 2.41 2.58 2.77 2.95 3.16 3.36 3.65 3.94 4.26 4.86 5.69 7.171.56 1.66 1.75 1.85 1.94 2.03 2.16 2.29 2.41 2.59 2.77 2.95 3.17 3.37 3.66 3.94 4.27 4.86 5.70 7.181.56 1.66 1.76 1.85 1.94 2.04 2.16 2.29 2.42 2.59 2.78 2.95 3.17 3.37 3.66 3.95 4.28 4.86 5.71 7.331.56 1.66 1.76 1.86 1.94 2.04 2.16 2.30 2.43 2.59 2.78 2.96 3.18 3.37 3.66 3.95 4.28 4.88 5.71 7.631.56 1.66 1.76 1.86 1.94 2.04 2.17 2.30 2.43 2.59 2.78 2.97 3.18 3.38 3.66 3.95 4.28 4.90 5.72 7.761.57 1.66 1.76 1.86 1.95 2.05 2.17 2.30 2.44 2.59 2.78 2.97 3.19 3.39 3.67 3.95 4.29 4.92 5.73 7.901.57 1.67 1.76 1.86 1.95 2.05 2.17 2.30 2.44 2.59 2.79 2.97 3.20 3.40 3.67 3.97 4.29 4.94 5.75 8.141.58 1.67 1.76 1.86 1.95 2.05 2.17 2.31 2.44 2.60 2.79 2.97 3.20 3.41 3.67 3.97 4.30 4.95 5.77 8.93
Frequency Table
Richter Scale Number of Earthquakes
1.5 ≤ R < 2.5 474
2.5 ≤ R < 3.5 240
3.5 ≤ R < 4.5 158
4.5 ≤ R < 5.5 65
5.5 ≤ R < 6.5 38
6.5 ≤ R < 7.5 20
7.5 ≤ R < 8.5 4
8.5 ≤ R < 9.5 1
How Big? How Many?
Relative Frequency Table
Richter Scale Number of Earthquakes
1.5 ≤ R < 2.5 0.474
2.5 ≤ R < 3.5 0.240
3.5 ≤ R < 4.5 0.158
4.5 ≤ R < 5.5 0.065
5.5 ≤ R < 6.5 0.038
6.5 ≤ R < 7.5 0.020
7.5 ≤ R < 8.5 0.004
8.5 ≤ R < 9.5 0.001
How Big? How Many?
0.474
0.240
0.158
0.065
0.0380.020 0.004 0.001
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
[1.5 - 2.5) [2.5 - 3.5) [3.5 - 4.5) [4.5 - 5.5) [5.5 - 6.5) [6.5 - 7.5) [7.5 - 8.5) [8.5 - 9.5)
Relative Frequency Histogram
Prob. of an event = proportion of observations that corresponds to the event
= percent of observations that corresponds to the event
= portion of area of histogram that corresponds to the event
• Planning for retirement
• Two options for investment
• Each has a track record, the historical rates-of-return over a specified time period
• Each can be used to compute various statistics; e.g., average rate-of-return, etc.
AN INVESTMENT DECISION
AN INVESTMENT DECISION
Expected Value Std. Dev. Variance
A1 5.00% 1.25% 1.5625
A2 5.70% 2.75% 7.5625
Alternative 1
-2
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
time
Alternative 2
-2
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
time
r
n
n
r
Alternative 1
0
200
400
600
800
1000
1200
-0.30 -0.23 -0.16 -0.09 -0.02 0.05 0.12 0.19 0.26 0.33 0.40
Alternative 2
0
200
400
600
800
1000
1200
-0.30 -0.23 -0.16 -0.09 -0.02 0.05 0.12 0.19 0.26 0.33 0.40
What’s the likelihood of ?
What’s the likelihood of ?
r < 0
r < 0
I don’t want a rate ofreturn < 0!
I want a rate of return > 0!
THE FREQUENCY HISTOGRAM( The “KEY to it ALL’’ )
• The relative frequency histogram over the outcomes contains all relevant information.
• This information allows us to quantify risk.
• This is provides our most powerful tool for risk management.
A QUANTITATIVE
DEFINITION OF RISK
Risk is a COMBINATION of the answers to three questions:
(1) “What can go wrong?”
(2) “How likely is it to go wrong?”
(3) “If it does go wrong, what are the consequences?”
A QUANTITATIVE DEFINITION OF RISK
Adapted from S. Kaplan and B. John Garrick, “On the Quantitative Definition of Risk”, Risk Analysis, Vol.1, no.1, 1981
EXAMPLE: Hinterland Illegal Immigration
What can go wrong? recession;depression;economic collapse
How likely is it to go wrong? chances are 1 in a 10; a 10% chance; PF = .10
If it does go wrong, what happens to Drmecia? large numbers of illegalimmigrants ; increasing crime;failing social services; social unrest;
What can go wrong?
How likely is it to go wrong?
If it does go wrong, what are the consequences?
FuturescenarioF
Probabilityof FPF
Result dueto FY
A QUANTITATIVE DEFINITION OF RISK
THE ANSWER TO THE FIRST QUESTION
1. It all starts with the future scenario, F.
2. The F is uncertain so we need probability, PF.
3. F causes a result, an outcome of concern, Y.
4. Y is a function of F. We need to know this relation! The relation between Y and F is uncertain!!!
BEGINNING – MIDDLE – END
F → X → Y
F1, F2,… → X1 then X2 then… → Y1, Y2,…
X1 then X2 then….. XM
Y1
Y2
Y3
…YN
F1
F2
F3
…FK
THE “SYSTEM”
EXAMPLE: Hinterland Illegal Immigration
Illegal immigration is proportional to the ratio of per capita GDP.
GDPD/popD
GDPH/popH
Yillegal immigration =
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025
Year
Relative GDP per capita
0.0E+00
2.0E+04
4.0E+04
6.0E+04
8.0E+04
1.0E+05
1.2E+05
1.4E+05
1.6E+05
1980 1985 1990 1995 2000 2005 2010 2015 2020 2025
Annual Illegal Immigration
F =
G. H. Hanson (2009), “The Economics and Policy of Illegal Immigration in the U.S.”, Washington, D.C.: Migration Policy Institute
THE ANSWER TO THE SECOND QUESTION
X1 then X2 then….. XM PF PY
→ Math Model →Probability Distribution
for Future Scenarios
Probability Distributionfor
Outcomes of Interest
THE “SYSTEM”
SIMULATIONMODELING
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Val
ues
x 10
-̂6
I llegal Immigration [Millions]
Total Illegal Immigration (Baseline)
THE ANSWER TO THE SECOND QUESTION
PY
What number of illegal immigrants do you most want to avoid? 10000; 100000; 1000000; 10000000; 20000000.
What outcome do you most prefer to avoid: minor economic strain; substantial strain; or collapse of government social/educational services?
HOW YOU FEEL (about the possible Y)
= PREFERENCE
THE ANSWER TO THE THIRD QUESTION
1. It all starts with the future scenario, F.
2. The F is uncertain so we need probability, PF.
3. F causes a result, an outcome of concern, Y.
4. Y is a function of F. Given PF we can derive PY
5. How do you feel about the probable outcomes? Do you prefer to avoid some Y more than other Y?
THE ANSWER TO THE THIRD QUESTION
• Preferences < = > value function < = > v(Y) (1) v(Y) > 0 if Y is “good”
(2) v(Y) < 0 if Y is “bad”
• Value Function Charcteristics(1) reference point [defining GAINS from LOSSES]
(2) loss aversion [losses MORE IMPORTANT than GAINS]
(3) decreasing marginal values
THE ANSWER TO THE THIRD QUESTION
v(Y)
Losses ( - )convex
Gains ( + )concave
Illegal Immigration
Reference Point
A QUANTITATIVE DEFINITION OF RISK
1. It all starts with the future scenario, F.
2. The F is uncertain so we need probability, PF.
3. F causes a result, an outcome of concern, Y.
4. Y is a function of F. Given PF we can derive PY
5. Your preference info, v(Y), is the LAST PIECE!defines the consequences!
ProbabilityDistribution
(Outcome)
Decision MakerPreferencesAND
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Val
ues
x 10
^-6
I llegal Immigration [Millions]
Total Illegal Immigration (Baseline) v(Y)
Illegal Immigration, Y
AND
PY v(Y)AND
Risk
Fg(F)
Y
PF
g(F)
PY
v(Y)
Hinterland Economy Collapse Prob. of Economic Collapse
How does Drmecia “feel” about the Y?
Number of IllegalImmigrants
Prob. Dist. IllegalImmigrants
Y
v(Y)SPECIAL CASE OF PREFERENCE
Y
v(Y)
“I can’t bear the thought of experiencing loss! “
“Experiencing loss would be a catastrophe!”
In the limit the weight we assign to all outcomes <=> a losstends to - ∞.
In this case risk is very simple to quantify risk.
SPECIAL CASE OF PREFERENCE
ASSESSING THE RISK
PY
v(Y)
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
-3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5
+ -
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Valu
es x 1
0̂-6
Values in Millions
Total Illegal Immigration (Collapse)
0.20.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Valu
es x
10-̂
6
Values in Millions
Total Illegal Immigration (Collapse)
ASSESSING THE RISK
PY
v(Y)
-105
-85
-65
-45
-25
-5-3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.50.20.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Valu
es x 1
0̂-6
Values in Millions
Total Illegal Immigration Collapse)
RISK = P{ Y correspond to loss }
RISK = P{ Y ≥ reference point }
RISK = P{ Y you prefer to avoid }
RISK = P{ unacceptable Y }
ASSESSING THE RISK (SPECIAL CASE)
OVERALL C-RATING System for Readiness:
C-1 = MAE > 89% P{not capable} ≤ 0.11C-2 = MAE 80-89% 0.11 ≤ P{not capable} ≤ 0.20C-3 = MAE 70-79% 0.21 ≤ P{not capable} ≤ 0.30C-4 = MAE 50-69% 0.31 ≤ P{not capable} ≤ 0.50C-5 = MAE < 50% 0.50 ≤ P{not capable}
Senate Armed Services Committee, terminology used in arguments before the committee, Feb. 1997
Who uses this stuff?.......
AR 220 – 1 (2010), AFI 10-201 (2006), SORTS (US Department of Defense)
A QUANTITATIVEAPPROACH TO
RISK MANAGEMENT
The History of Risk Management
• 1950 B.C. – Code of Hamurabi – formalization of bottomry contracts containing a risk premium for chance of loss of ships and cargo.
• 750 B.C. – Greece – the use of bottomry contracts.
• 1285 A.D. – King Edward - forbids use of soft coal in kilns to manage air pollution in London.
• 1583 A.D. – 1st life insurance policy issued in England.
• 19th and 20th century – water and garbage sanitation, building codes, fire codes, boiler inspections, railroads, steamboats, autos.
• 1959 A.D. – H. Markowitz, stock portfolio diversification.
Identify Risks
Assess Risks
ImplementMonitor
Management Action
RISK MANAGEMENT PROCESS
What can go wrong F?
What is F and PF?
What are the outcomes [Y, and PY]?
What are the consequences, v(Y)?
What is the risk [quantified]? Prevent
Mitigate
Negotiate
Tools of Risk Management
• Prevention.
• Mitigation.
• Hedging.
• Diversification.
Why not plot P{ Y ≥ y* } versus y*, for any y* ?THE RISK CURVE
ASSESSING THE RISK
National policy often specifies a reference point.
Definition depends on a reference point.
Not everyone has the same reference point.
Determining the Outcome Distribution
• theoretical derivation
• direct assessment
• simulationGenerating your own data
EARTHQUAKES
Total cost
Number ofearthquakes
Cost perearthquake
Earthquakepolicy
Program Cost
FIXED
Earthquake cost
VARIABLESize of
earthquake
1.00 0.652 0.11 0.012 0.002 0.00P{ Total Cost ≥ y* }
THE RISK CURVE
0.00
0.20
0.40
0.60
0.80
1.00
0 10 20 30 40 50 60 70
y*
P{Y>
y*}
A1 : Do Nothing
A2 : New Building Codes
A3 : Retro-Fit & New Codes
The RISK CURVES
compared
P{ Total Cost ≥ x }
A1 (red)
A2 (blue)
A3 (green)
0.065
0.328
0.652
ACCEPTABLE RISK
“The perennial question free people ask with regard to defense is:
‘How much is enough?’ To this there can be no precise answer.
A country’s security is a function of the DEGREE OF RISK A
COUNTRY IS WILLING TO ACCEPT.”
Hitch & McKean, The Economics of Defense in the Nuclear Age, Atheneum, 1986
ACCEPTABLE RISK
Risk
Cost
AcceptableRisk
Required Budget
Too Risky
Proposed Budget
Ultimately, policy makers must decide how much the United States is willing to pay to lower the risks associated with de-
ploying forces abroad. But some might argue that defense planners occasionally focus on absolute requirements – the
minimum number of forces that they believe will meetDoD’s military needs – without fully weighing the
relative risks and costs of alternative levels.
Moving U.S. Forces: Options for Strategic MobilityCongressional Budget Office, Feb. 1997
Who uses this stuff?.......
“Our armed forces remain capable, within an acceptable level of risk, of meeting the demands of our strategy.”
Maj. Gen. John J. Maher,Vice Director for Operations, Joint Staff:
testimony before House National Security readiness subcommittee,
Feb. 1997
Who uses this stuff?.......
“Computer security is basically risk management.”
Stephen H. Wildstrom,review of the book “Secrets and Lies by Bruce Schneier,
Businessweek Sept. 2000
Who uses this stuff?.......
“…. Managers have to decide what they are trying to protect and how much they are willing to spend, both in cost and
convenience, to defend it.”
“…we continue to believe the federal government can benefit from risk management.”
Raymond J. Decker,Director, Defense Capabilities and Management, GAO,
Testimony before the Senate Committee on Governmental Affairs Oct. 2001
Who uses this stuff?.......
“…. An effective risk management approach includes a threat assessment, a vulnerability assessment and a
criticality assessment ...”
Risk
Cost
RISK MANAGEMENT
old
new
Risk
Cost
RISK MANAGEMENT
Proposed Budget
new
Risk
Cost
RISK MANAGEMENT
AcceptableRisk
new
APPLICATION I
ENTERPRISE BUSINESSRISK
Correct
Correct
Error
P(correct) = 0.8
P(corrected) = 0.9
P(error) = 0.2
P(uncorrected) = 0.1
Data Entry
Reconciliation Check
P = .02
P = .18
P = .80SECNAV M-5200.35 March 2007
En
d U
ser
Ad
min
.S
up
po
rtS
po
nso
red
Pro
gra
mP
urc
has
eA
gen
tDirect or
Indirect/Reimb.?
Define Needs, prepare PurchaseRequisition Form
Forward to SPFA
Forwardto ASA
SPFA Reviews PR
FundsAvailable, etc.?
ASA reviews PR, confirms funds,
obtains approval
FundsAvailable, etc.?
SPFA assigns PR number and
form to PA
NO
NO
DIR.
YES
YES
INDIR.
En
d U
ser
Ad
min
.S
up
po
rtS
po
nso
red
Pro
gra
mP
urc
has
eA
gen
t
Purchaser reviews for
completeness of
documentation
All required info.present and adequate to
make procurement?
ASA /OA will Assign req., number and
task Purchaser
Clarify requirementswith end user
Screen request for mandatory
sources of supply,
prohibited or special items,
and authority to buy
NO
YESBuy from
mandatory source orgo open market?
En
d U
ser
Ad
min
.S
up
po
rtS
po
nso
red
Pro
gra
mP
urc
has
eA
gen
t
Place order with source, direct delivery point, and provide estimated
delivery date
Order completeand accurate?
Receive order (if delivery point)
Receive ordered items
and sign acknowledging
Reconcile with vendor
NO
YES
STOP
ReimburseOr
Direct Funds
0.9
0.9
0.9
0.9
0.9
0.1
0.1
0.1
0.1
0.1
ERROR
ERROR
ERROR
ERROR
ERROR
P = .1
P = .1
P = .09
P = .081
P = .0729
NOERROR
P = .3439
P = .6561
ASA
SPFA
Purchaser
ScreenRequest
ReceiptReview
What can go wrong?
How likely is it to go wrong?
ReimburseOr
Direct Funds
0.95
0.95
0.9
0.9
0.9
0.05
0.05
0.1
0.1
0.1
ERROR
ERROR
ERROR
ERROR
ERROR
P = .05
P = .05
P = .095
P = .0855
P = .07695
NOERROR
P = .30745
P = .69255
SPFA
ASA
Purchaser
ScreenRequest
ReceiptReview
ReimburseOr
Direct Funds
0.95
0.95
0.95
0.95
0.95
0.05
0.05
0.05
0.05
0.05
ERROR
ERROR
ERROR
ERROR
ERROR
P = .05
P = .05
P = .0475
P = .0451
P = .04287
NOERROR
P = .1855
P = .8145
SPFA
ASA
Purchaser
ScreenRequest
ReceiptReview
ReimburseOr
Direct Funds
0.99
0.99
0.99
0.95
0.99
0.01
0.01
0.01
0.01
0.01
ERROR
ERROR
ERROR
ERROR
ERROR
P = .01
P = .01
P = .0099
P = .009801
P = .009703
NOERROR
P = .0394
P = .9606
SPFA
ASA
Purchaser
ScreenRequest
ReceiptReview
APPLICATION II
COST RISKASSESSMENT
ESTIMATING SHIPBOARD HELICOPTER O&M COSTS
Life-cycle cost estimates for the helicopter are needed. The cost analysis staff is organized into four groups, one each for the four main components of the life-cycle cost: (1) R&D; (2) Procurement; (3) Operations and Maintenance; and (4) Salvage/Residual. As leader of the O&M cost estimating group you have decided to use a factor cost estimates since:
1. Relevant O&M cost data produce reliable CERs for the three components of
the O&M cost [POL, Parts, and “Other”] as functions of the procurement cost.
2. The helicopter is a recently developed model and procurement cost is expected to be $3.7 million (+/- 3%).
3. Why not just use an O&M cost factor approach: annual O&M cost = 10% of acquisition cost?
POL ($/hr) vs Acquisition ($M): Summary Output
Regression StatisticsMultiple R 0.736R Square 0.542Adjusted R Square 0.522Standard Error 28.224Observations 25.000
Coefficients Standard Error t Stat P-valueIntercept 112.845 22.447 5.027 0.000
Acquisition cost 30.155 5.778 5.219 0.000
Parts ($/hr) vs Acquisition ($M): Summary Output
Regression StatisticsMultiple R 0.922R Square 0.851Adjusted R Square 0.844Standard Error 24.425Observations 25.000
Coefficients Standard Error t Stat P-value
Intercept -84.956 19.426 -4.373 0.000Acquisition cost 57.215 5.000 11.442 0.000
Other ($/hr) vs Acquisition ($M): Summary Output
Regression StatisticsMultiple R 0.685R Square 0.470Adjusted R Square 0.446Standard Error 21.751Observations 25
Coefficients Standard Error t Stat P-value
Intercept 45.2104 12.857 3.516 0.002Acquisition cost 10.1249 3.310 3.059 0.006
POL[$/hr] = 112.84 + 30.16 × ACQ + error
Other[$/hr] = 45.21 + 10.12 × ACQ + error
Parts[$/hr] = -84.96 + 57.21 × ACQ + error
PROBABILISTIC COST ESTIMATING
y = a + b x + eCost estimateis a RANDOMVARIABLE
There always is the model residual error
Slope coefficient issubject to estimation error
Intercept issubject toestimationerror
Future explanatory variable is not always known withcertainty
PROBABILISTIC COST ESTIMATING
y = a + b x + eWhat is the resulting distribution function?
What is the most appropriate distribution function?
What is the most appropriate distribution function?
What is the most appropriate distribution function?
What is the most appropriate distribution function?
PROBABILISTIC COST ESTIMATING
Triangular Density
0.00
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0.30
0.40
0.50
0.60
0.000 1.000 2.000 3.000 4.000 5.000 6.000
0.0
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0.4
0.6
0.8
1.0
1.2
1.4
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Empirical Distribution Function
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 2.0 4.0 6.0 8.0 10.0 12.0
X
Empirical Distribution Function
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 2.0 4.0 6.0 8.0 10.0 12.0
X
y = a + b x + e
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Lognormal Distributions
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
0.00 0.50 1.00 1.50 2.00 2.50
x
?
?
cPOL = a1 + b1×ACQ + e1
cParts = a2 + b2×ACQ + e2
cOther = a3 + b3×ACQ + e3
CO,M&S = [cPOL + cParts + cother ] × H
$164K ≤ CO,M&S ≤ $676
$164K ≤ CO,M&S ≤ $672
$158K ≤ CO,M&S ≤ $511
$190K ≤ CO,M&S ≤ $463K
APPLICATION III
PROJECTMANAGEMENT
FACILITIES FOR THE FLIGHT SIMULATOR DEPARTMENT(ACTIVITIES, TIME ESTIMATES, AND DEPENDENCIES)
#
ACTIVITY DESCRIPTION
REQUIRED
PRECEDING ACTIVITIES
ACTIVITY
DURATION DAYS
A
Demolish areas 1 & 2
----
10
B
Demolish area 3
----
20
C
Dismantle Basic Simulator
----
10
D
Construct Bomber Simulator area
A
70
E
Construct Fighter Simulator area
A
40
F
Upgrade utilities
B
60
G
Construct Basic Simulator area
B
6
H
Reassemble Basic Simulator
C
48
I
Install Bomber Simulator
D
10
J
Install Fighter Simulator
E,F
27
K
Install Basic Simulator
G,H
40
New Facilities for the Flight Simulator Department
ACTIVITY DESCRIPTION a m b te s 2 te s 2
A Demolish Areas 1 & 2 8 17 28 17.3 11.1 0.0 0.0B Demolish Areas 3 30 60 180 75.0 625.0 75.0 625.0C Dismantle Basic Simulator 7 15 22 14.8 6.3 0.0 0.0D Construct Bomber Sim Area 85 120 206 128.5 406.7 0.0 0.0E Construct Bomber Fighter Sim Area 37 50 62 49.8 17.4 0.0 0.0F Upgrade Utilities 75 90 135 95.0 100.0 95.0 100.0G Construct Basic Sim Area 4 8 11 7.8 1.4 0.0 0.0H Reassemble Basic Sim 58 70 102 73.3 53.8 0.0 0.0I Install Bomber Sim 9 15 22 15.2 4.7 0.0 0.0J Install Fighter Sim 38 52 100 57.7 106.8 57.7 106.8K Install Basic Sim 37 50 62 49.8 17.4 0.0 0.0
Project estimated completion time = 227.7Variance = 831.8
Standard Deviation = 28.84
Critical Path
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
140 160 180 200 220 240 260 280 300 320 340 360
Shortest Time to Completion
P = 0.482
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
140 160 180 200 220 240 260 280 300 320 340 360
Shortest Time to Completion
P = 0.048
SUMMARY
• RISK is a factor in every decision with significant uncertainty
• RISK is a combination of the answers to 3 questions– what can go wrong?– how likely is it to go wrong?– if it does go wrong, what are the conse-
quences?
• RISK is quantified using PROBABILITY.
– use it to express the riskiness an
alternative.
– use it to find the least risky alternative.
• THINK about the RISK vs COST
tradeoff curve.
SUMMARY
• MANAGING RISK requires the information provided by the tradeoff curve!
– THINK about where you want to be on the curve.
– THINK about changing the tradeoff curve!
• USE THE MODEL to help find how to change things!
SUMMARY