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 — Wt0 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 = Wt0 ■ X with X = ln(Wt1 ∣Wt0 ) VaR can also be expressed in terms of the critical return
X*:
VaR = Wt 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 = Wt0 ■ c ■ σ ■ -jh . (4)
More intriguing information
1. Housing Market in Malaga: An Application of the Hedonic Methodology2. Experimental Evidence of Risk Aversion in Consumer Markets: The Case of Beef Tenderness
3. Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box
4. The name is absent
5. Structural Influences on Participation Rates: A Canada-U.S. Comparison
6. Private tutoring at transition points in the English education system: its nature, extent and purpose
7. STIMULATING COOPERATION AMONG FARMERS IN A POST-SOCIALIST ECONOMY: LESSONS FROM A PUBLIC-PRIVATE MARKETING PARTNERSHIP IN POLAND
8. The name is absent
9. Surveying the welfare state: challenges, policy development and causes of resilience
10. Palvelujen vienti ja kansainvälistyminen