Chapter 10 - Risk measurement

Question 1

Desirable features of risk measures

Answer 1

Coherence
   Monotonicity   L1< F(L2)
   Subadditivity    F(L1+L2)  =0
   Translation invariance    F(L + k)  = F(K) + k
Positive homogeneity   F(k.L) = k.F(L) 

Convexity
F(k.L1 + (1-k).L2) <=1)
ie diversification reduces capital requirement

Question 2

Types and approaches to risk measurement

Answer 2

Deterministic
Notional
Factor sensitivity approach
Scenario sensitivity approach

Probabilistic
   Deviation
    Value at Risk (VaR)
            Empirical
            Parametric
            Stochastic
    Probability of ruin
    Tail Value at Risk (TVaR)
    Expected Shortfall

Question 3

Risk discount rate should take into account

Answer 3

Cost of capital
Inflation
Interest rates
Rates of return on investments in the economy

Question 4

Dificulties with setting risk discount rate

Answer 4

Suitable reference invetsments may not exist
Difficult to determine risk-free rate
Shoudl allow for dredit risk - which is linked to other risks varying over time
May need to be varied by project
Difficult to set with allowance for uncertainty of future values