ASSESSMENT OF MARKET RISK IN HOG PRODUCTION USING VALUE-AT-RISK AND EXTREME VALUE THEORY

Value-at-Risk

2.1 Definition

Briefly stated VaR measures the maximum expected loss over a given time period at a given confidence level that
may arise from uncertain market factors. Call W the value of an asset or a portfolio of assets and V = W₁ — W_t0 the
random change (revenue) of this value during the period h = At = t₁ —1₀ , then VaR is defined as follows:

VaR = E(V ) — V*                                                          (1)

E(V) means the expectation of V and the critical revenue V * is defined by:

∫ f (v)dv = Prob (V ≤ V*) = p                                                      (2)

-■S'

Using the identity V = W_t0 ■ X with X = ln(W_t1 ∣W_t0 ) VaR can also be expressed in terms of the critical return

X*:

VaR = W_t 0 (E(X) — X*)                                                     (3)

E(X) and X* are defined analogous to E(V) and V*. From (2) it is obvious, that the calculation of VaR boils down to
finding the p-quantile of the random variable V, i.e. the profit-and-loss-distribution. Alternative methods exist to
achieve this. A brief summary is given in the next section.

2.2 Methods of VaR calculation

The literature offers three standard procedures for VaR estimation, namely the variance-covariance-method (VCM),
Monte Carlo simulation (MS) and historical simulation (HS), all showing specific advantages and disadvantages. A
detailed treatment of these methods can be found in Jorion (1997) and Dowd (1998). This paper only provides some
basics thereby focusing on deficiencies that we try to overcome later.

Variance-Covariance-Method

The VCM (also called parametric approach or delta-normal method) determines VaR directly as a function of the
volatility of the portfolio return σ. If normality of the returns is assumed, VaR can be determined as:

VaR = W_t0 ■ c ■ σ ■ -jh .                                                                          (4)

<<   1   2   3   4   5   6   >>

More intriguing information