# Value at Risk

**Topics:**Normal distribution, Risk, Risk management

**Pages:**7 (2035 words)

**Published:**January 11, 2013

In recent years the needs for professional skills in the modelling and management of credit risk have rapidly increased and credit risk modelling has become an important topic in the field of finance and banking. While in the past most interests were in the assessments of the individual creditworthiness of an obligor, more recently there is a focus on modelling the risk inherent in the entire banking portfolio. This shift in focus is caused in greater part by the change in the regulatory environment of the banking industry. Banks need to retain capital as a buffer for unexpected losses on their credit portfolio. The level of capital that needs to be retained is determined by the central banks. In 2007 a new capital accord, the Basel II Capital Accord, will become operative. This accord will be the successor of the Basel I accord. The capital accords are named after the place where the Bank for International Settlements (BIS) is settled, namely Basel, Switzerland. The BIS gives recommendations concerning banks and other financial institutes on how to manage capital. The influence and reputation of the Basel Committee on Banking Supervision is of such nature that its recommendations are considered worldwide as “best practice”.

Due to these changes in the banking and finance industry the use of risk measures in credit portfolio management has increased dramatically. One of the most used risk measures is Value at Risk (VaR). The wide use of VaR as a tool for risk assessment, especially in financial service firms, and the extensive literature that has developed around it, push us to dedicate this chapter to its examination.

In its most general form Value at Risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) is the given probability level[1].

There are three methods of calculating VAR: the historical method, the variance-covariance method and the Monte Carlo simulation.

The historical method simply re-organizes actual historical returns, putting them in order from worst to best. It then assumes that history will repeat itself, from a risk perspective. The QQQ started trading in Mar 1999, and if we calculate each daily return, we produce a rich data set of almost 1,400 points. Let's put them in a histogram that compares the frequency of return "buckets". For example, at the highest point of the histogram (the highest bar), there were more than 250 days when the daily return was between 0% and 1%. At the far right, you can barely see a tiny bar at 13%; it represents the one single day (in Jan 2000) within a period of five-plus years when the daily return for the QQQ was a stunning 12.4%.

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The red bars are the lowest 5% of daily returns (since the returns are ordered from left to right, the worst are always the "left tail"). The red bars run from daily losses of 4% to 8%. Because these are the worst 5% of all daily returns, we can say with 95% confidence that the worst daily loss will not exceed 4%. Put another way, we expect with 95% confidence that our gain will exceed -4%. That is VAR in a nutshell. With 95% confidence, we expect...

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