Contemporary Risk Measures

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Chapter 17

• Contemporary Risk Measures

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Probability as a Risk Measure

• Probability the chance of occurrence associated
  with any possible outcome. Probabilities
  associated with any possible occurrence range
  from zero to one.
• If probability equals zero, event certainly will
  not occur
• A probability of one indicates certainty of
  occurrence

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Probability as a Risk Measure

• Decisions are divisible
• Certaintyonly one possible outcome decisions
  based solely on the decision makers preference
  between certain alternatives
• Risk-probabilities associated with various
  possible outcomes are either known or can be
  estimated
• Uncertaintyprobabilities are neither known or
  estimable implies unknown number of possible
  outcomes

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Probability as a Risk Measure

• Uncertainty is not measurable
• As better information becomes available,
  uncertain elements can be converted to risk
  factors by incorporating into analysis their
  associated probability distributions
• Analysts generate information to estimate the
  probability of occurrence of each risk

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Probability as a Risk Measure

• Estimating future cash flows from real estate
  ventures is part art and part science.
• No way to determine future, instead develop
  informed estimates
• Couple estimates with probability estimate
• Multiple law of probability used to determine the
  probability of occurrence of an event whose
  outcome depends in turn on the outcome of some
  prior event

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Interpreting Risk Measures

• Probabilistic estimates of possible investment
  outcomes provide valuable intelligence about
  relative risk
• Probability distribution array of all possible
  outcomes and their related probabilities of
  occurrence
• Discrete probability distribution
• Continuous probability distribution

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Figure 17.1
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Interpreting Risk Measures

• Expected Value of probability distribution of
  possible cash flows is the weighted average of
  the possible cash flows making up the
  distribution, with each value weighted by its
  attendant probability of occurrence
• n
• CF S CFiPi
• i1
• Where CF is the expected value of cash flow
  distribution, CFix is the value of the ith
  probability, and , Pi is the probability
  associated with that value.

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Interpreting Risk Measures

• Variance weighted average of the squared
  differences between each possible outcome and the
  expected outcome
• n
• V S (CFx CF)2 Px
• x1

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Interpreting Risk Measures

• V is variance
• CFx is value of the xth possible outcome
• CF is expected value
• Px is related probability

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Interpreting Risk Measures

• Square root of variance is standard deviation
• Standard deviation has other mathematical
  properties that make it useful as a measure of
  risk
• Once the mean and standard deviation are
  established, it is possible to determine the
  probability of occurrence of values over any
  desired interval within the distribution

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Figure 17.2
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Figure 17.3
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Figure 17.4
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Figure 17.5
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Figure 17.6