VAR (Value At Risk)

   VAR is defined as the maximum possible amount of loss for a given financial portfolio held by a firm (financial organization, traders, investors, speculators) with a given confidence interval.  To be more specific, let's say that a risk management report states that 95% - 1 day VAR is 5.34 million US dollars. What does it means ?  It means that there are approximately 5 days out of 100 trading days resulting in a loss of more than 5.34 million US dollars. (This is just a definition!   You will see below that this definition is really meaningless without additional statement).   So, one can get a rough idea of how much a portfolio can lose. So, that is great ! It is so simple! This is one of the reason why VAR is established as the most popular tool in describing financial risk. The strength comes from its ability to express the risk value in one simple number.  Its simplicity has many drawbacks as well.

   Most importantly, is it always true ?  In other words, should management regard this number as an absolute guideline?  The answer is NO!   (For example, argument given by Mr. Nassim Taleb against Dr. Joridon- the author of "Value-AT-Risk")  When you look at actual history of any given portfolio, you can quickly discover that some times you lose only 1-2 days more than 95%-1day VAR out of 100 days (VAR is "OVER-ESTIMATING" the actual market risk).  On the other hand, you lose 10-15 days more than 95%-1day VAR out of 100 days (VAR is "UNDER-ESTIMATING" the actual market risk).  What is wrong? 

   There is nothing wrong with VAR's definition itself. It is the underlying assumption that is the problem. Most VAR system uses Variance -Covariance Method (See below for the explanation) which ignores the non-linear nature of option books. Therefore, it becomes meaningless. Also, VAR (unless one uses historical simulation or Gaussian simulation with jumps) uses an assumption that the market prices/rates follow s Gaussian process. This creates a problem even for Monte Carlo which uses correlated Gaussian random deviates. In reality, the market does not quite follow the simple Gaussian distribution. Historical simulation gives the "exact price/rate" movement of the past history (whether 260 days or 760 days). However, this approach is quite useless as well in case you have extremely volatile market which only occurs once every 50 years. So what one can do?


     First, one should restate the VAR as "If the market follow the Gaussian process at least for 1 day given today's prices/rates, then using the correlation matrix obtained from the past, one will most likely lose only 5 days more than 95%-1 day VAR out of 100 trading days". Then the above confusion will be solved.  Then next question, manager can ask is, "What happens if the market does not follow Gaussian process?", "What happens if the market crashed? Any jumps?", "Any unexpected Political, Socio Economical News?", "How much loss do we most likely to lose under these circumstances?"   Well, it is where stress test comes in. But stress test, by nature is static (not dynamic). Therefore, one can not really implement systematically. So, what is the solution?  Moreover, even if there is no jump, what method is the best method?     

   The answer is still under intensive research.   Meanwhile, please enjoy the following technological advances in financial risk management history.

Summary of Major VAR Calculation Methods

Simple Volatility Multiplication Method(maybe 1970??-Now)

Variance-Covariance Method (1996-Now)

Higher Order Variance Covariance Method (Late1996-Now)

Simulation Method (Historical Simulation) (1996-Now)

Simulation Method (Monte Carlo Method) (1996-Now)

Simulation Method (Speeded Up Monte Carlo Method) (1997-Now)

CVAR (Credit Value At Risk)

    For the past 10 years, the issue of credit risk has been getting many attentions. Many firms such as J.P.Morgan (CreditMatrix, Credit manager), CS First Boston (CreditRisk+), and KMV (EDF- Expected Default Frequency Method) have come up with their own ways of quantifying the credit risk. However, there seems to be no consensus on how one can incorporating credit risk with market risk. Credit risk is an very important risk one must quantify given the recent Asian crisis (Japan, China), and emerging markets crisis which plagued many financial institution. 

TVAR (Total Value At Risk)

   This name is more like my own creation than anything else. To my best knowledge, there is no word "TVAR" in financial literatures. I will explain this terminology in the coming update

To Go Back to the Previous Page  ====>Click Here !!!

Copyright (c) 1998 Kazuhiro Iwasawa ---------All Right Reserved.