Using value-at-risk to measure financial risk

Journal of Bank Cost & Management Accounting, The, 1996 by Duchac, Jonathan

I. INTRODUCTION

Over the past several decades portfolio and risk management techniques have adapted to increasingly complex financial instruments and risk scenarios. The rapid growth in derivative financial instruments and the derivatives losses reported in recent years have intensified concerns over reliably measuring financial instrument risk exposure. The massive derivative losses experienced by Gibson Greetings 20 million), Proctor and Gamble ($157 million), the Orange County Investment Pool ($1.7 billion), and Barings Bank ($1 billion) illustrate the devastating effects that unexpected shifts in market prices can have on portfolio values.(1) To protect against such huge losses from unexpected market shifts, risk managers and managerial accountants have focused on developing reliable techniques for measuring financial instruments risk exposure.

The most basic method for measuring financial instrument risk is to examine notional principal amounts.(2) This type of analysis, however, provides very lime insight into the risks associated with financial instruments because it does not consider market values, the volatility of market prices, or correlations between financial instruments. Duration analysis improves on the notional principal technique by concentrating on changes in market values associated with a single basis point change in yield.(3) While this technique considers current market values and the effects of changes in interest rates, it only considers the effects of a single basis point movement. Duration is also limited to relatively non-complex environments where a company has only long or short positions, and does not accommodate changes in interest rates at different points in the yield curve.

To overcome some of the limitations of notional principal and duration analysis, value-at-risk techniques have been developed. Value-at-risk is the estimated total loss that may be sustained o a financial instrument (or portfolio of instruments) from an adverse market movement, estimated for a given level of confidence over a specified holding period.(4) The output of a single market risk estimate denominated in a simple common denominator, dollars, makes this measure useful for internal reporting and managerial decision making. Managers can use this information for portfolio management and capital allocation decisions. Performance measures such as risk-adjusted returns can also be enhanced by this information. In a risk management context, managers can use value-at-risk models to further examine the effects that catastrophic changes in market values will have on financial instrument portfolios. Value-at-risk estimates are valuable to the external user as well. Moody's currently uses value-at-risk estimates as part of its volatility rating system for bond mutual funds and money market funds.(5)

The following section provides two simplistic and general examples of how value-at-risk is determined. This illustration should in no way be perceived as a standard. Rather, it is intended to provide a basic illustration of value-at-risk concepts and how the methodology works (i.e., the basic mechanics). In practice, value-at-risk models vary widely and are significantly more complex than those presented in this discussion. The examples are designed solely to provide some initial insights into value-at-risk and how it can be used to evaluate the risks of financial instruments.

II. MEASURING VALUE-AT-RISK

As discussed above, value-at-risk is the estimated maximum potential loss that will be sustained from an unfavorable movement in market prices. This estimate is determined for a given probability and holding period. While a number of financial institutions and consulting firms have developed their own specific techniques and methods for measuring value-at-risk, these methods are based on the same underlying theory and model. This technique can be applied to individual financial instruments or a portfolio of different instruments. The output of the value-at-risk model is a single number representing the risk of the instrument or portfolio.

Value-at-risk is a function of four factors: market value (price), the standard deviation in market value, a confidence interval, and a holding period.(6) For individual financial instruments, the relevant market value(s) is the current market price of the financial instrument. Price data can be generated Internally or obtained from external data sources (e.g., broker quotes). The relevant market value for portfolios of financial instruments, however, is based on the percentage of the portfolios market value taken up by each instrument.(7) Thus, the portfolio's market value is equal to the sum of the individual instrument's market value multiplied by the proportion of the total financial instrument portfolio invested in that instrument. This value serves as the starting point for determining the value-at-risk of the individual instrument or portfolio of instruments.

The second component in the value-at-risk calculation is the standard deviation of market price returns for the financial instrument or instruments being evaluated, which measures the volatility of the instrument's return(s). When a portfolio of financial instruments is being considered, correlation factors for the correlation between the market prices of the various financial instruments held in the portfolio must also be considered. Both the standard deviation and correlation factors are typically based on historical data over a specified period. Similar to market prices, this data can be generated internally or obtained from external data sources.