Value at Risk and Expected Tail Loss

Value at Risk and Expected Tail Loss - Value at Risk and...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Value at Risk and Expected Tail Loss Conditional value at risk (CVaR) is also referred to as expected tail loss (ETL) [see Acerbi and Tasche (2001)]. It has gained significant importance in the risk management field and is our choice of downside risk measure. Let ( ) p Xt be the value of an investment at time p t which assumed to be known and let ( ) ( ) 1 pp XX t X t + =− be the future uncertain value of the investment profit or loss. Let ( ) X f x and ( ) X Fx be the probability density and distribution functions of this future uncertain investment value. Given a confidence level q ( 01 q < < ) and time period duration 1 tt + (i.e. month or quarter), value at risk (VaR) is that quantity ( ) * Xq such that. ( ) ( ) { } ( ) ** 1 pX PXt X q F X q q + ⎡⎤ ≤= = ⎣⎦ (5.1) Let ( ) ( ) * | X FxX Xq < be the conditional distribution for the future investment value given that ( ) 1 p + it is less than ( ) * . From basic probability theory, this conditional distribution is related to the unconditional distribution ( ) X in the following way.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

Value at Risk and Expected Tail Loss - Value at Risk and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online