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SA3- Incorporation of cost of capital in business planning (Method…

- - - - Variance/Standard deviation/semi-variance
        Widely understood and accessible
        But not monotonic e.g. Var(X) not always less than Var(Y) if X > Y
      - Value at Risk
        The loss at a certain level of probability.
        Not coherent as fails sub-additivity
      - Tail VaR
        The conditional mean of the loss distribution above the selected threshold set as a percentile of the loss distribution
      - Expected policyholder default
        Variant of Tail VaR where the threshold is set as company's surplus capital. Not coherent as fails linear homogeneity
      - Transformed loss measures
        These apply a transformation to the loss distribution to give more weight to the key focus area of the loss distribution for the decision maker.
        Attach an artificially inflated probability to the worst outcomes.
        Generally coherent
    - - Coherence:
        Monotonicity- if one portfolio always worth more than another it cannot be riskier
        Linear homogeneity- scaling a portfolio by a constant will change the risk by the same proportion
        Sub-additivity- combing two portfolios should not create more risk
        Translational invariance- adding a portfolio with a known, guaranteed outcome to an existing portfolio reduces the risk by the guaranteed outcome