Value at Risk

Klienwort Wasserstein both published reports on climate change and the Pan-European utility sector. WestLB has published a report on the scope of financial value at risk in the economy overall and by specific industries. UBS, Credit Suisse First Boston, and Citigroup have published reports on the implications of carbon trading. Goldman Sachs has published an environmental and social index for the global oil and gas industry.31... 

Recently, risk started to be defined in terms of another point measure introduced by J.P. Morgan, value at risk or VaR (Jorion, 2000). This is defined as the difference between the expected profit and the profit corresponding to 5% cumulative probability. Many other mean-risk models use measures such as tail value at risk, weighted mean... 

Risk is considered a univariate numerical measure like variability or value at risk (VaR), which is the difference between the project expected outcome and the profit corresponding to (typically) 5% cumulative probability. Opportunities at high profit levels are rarely discussed or considered. 

Value at risk (VaR) Discussed in detail by Jorion, 2000, this was introduced by J.P. Morgan (Guldimann, 2000) and is defined as the expected loss for a certain... 

Finally, sometimes the risks of low liquidity measured by the cash flow at risk (CFAR) are more important than the value at risk (Shimko, 1998). 

Risk-adjusted return on capital (RAROC) This is the quotient of the difference between the expected profit of the project adjusted by risk and the capital (or value) at risk of an equivalent investment and the value at risk. This value is a multiple of the... 

Table 12.3 Value at risk for the alternative solutions. Gas commercialization in Asia...

Jorion P. 2000. Value at Risk. The New Benchmark for Managing Financial Risk, 2nd edition. McGraw Hill, New York. 

Recently, Duarte (1999) has suggested that value-at-risk approaches be used to derive efficient frontiers. TTiis approach differs from MV analysis in that it uses Monte Carlo simulation to determine the dollar value of the portfolio that is at risk with a particular degree of statistical confidence. That... 

Duarte also proposes a generalized approach to asset allocation that includes mean semi-variance, mean absolute deviation, MV, and value-at-risk as special cases. While cleverly broad, Duarte s method relies on simulation teclmiques and is computationally burdensome. In addition, because simulation approaches do not have explicit analytical solutions, the technique loses some of the precision of MV analysis. For example, one can examine solution sensitivities from the second-order conditions of MV problems, but this is not so easy with the simulation. It remains to be seen whether simulation approaches receive widespread acceptance for solving portfolio problems. Nonetheless, simulation techniques offer tremendous potential for future applications. 

While MV analysis stiU represents the current paradigm, other approaches to portfolio optimization exist and may eventually displace it. Value-at-risk simulation methodologies may ultimately prove more than tangential. Even so, for many practitioners there is stiU a long way to go before forecasting techniques, asset identification, md time horizon considerations are satisfactorily inte-... 

Saunders, A., Allen, L., 2002. Credit Risk Measurement New Approaches to Value at Risk and Other Paradigms, second ed. John Wiley Sons, New York. 

Golub, B. W., and L. M. Tilman, Measuring Yield Curve Risk Using Principal Components Analysis, Value at Risk, and Key Rate Durations, Journal of Portfolio Management (Summer 1997), pp. 72-84. RiskMetrics-09/30/96—Spot ZC 3M-30Y 3 92.8/4.8/1.27... 

Monte Carlo simulations are an alternative to parametric and historical approaches to risk measurements. They approximate the behavior of financial prices by using computer-generated simulations of price paths. The underlying idea is that bond prices are determined by factors that each have a specific distribution. As soon as these distributions (e.g., normal distributions) have been selected, a sequence of values for these factors can be generated. By using these values to calculate bond prices (and thus portfolio returns), the method creates a set of simulation outcomes that can be used for estimating value at risk. 

Butler, C. 1998. Mastering Value-at-Risk. London FT Prentice Hall. 

It should therefore be kept in mind that even if there is consensus on the valuation of risk expressed in a certain metric, such as Value-at-Risk (VaR), Fatal Accident Risk (FAR) and Potential Loss of Lives (PLL), the judgements about risk acceptance or tolerability could still be controversial. 

Figure 7.2 Pareto front and compromise decisions. Vertical line is naive approach. CVaR, conditional-value-at-risk.

Tyrrell RockafeUar R, Uryasev S. Optimization of conditional value-at-risk. J Risk 2000 2 21-42. 

Value-at-risk (VaR) Rare Severe Hurricane, strike, fire, terrorist attack... 

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