VOLUME 1, NUMBER 26/September 4, 1995
***************************************************************** DERIVATIVES 'R US is a weekly non-profit publication on the Internet user group misc.invest.futures that provides a simple non-technical treatment of various topics in derivatives. DRU is written by Don M. Chance, Professor of Finance at the Center for the Study of Futures and Options Markets at Virginia Tech. He can be contacted at dmc @ vt.edu or by phone at 540-231-5061 or fax at 540-231-4487. DRU is for educational purposes only and does not provide trading advice. Back issues of DRU available by anonymous ftp from fbox.vt.edu/filebox/business/finance/dmc/DRU or can be accessed using a Web browser at http://fbox.vt.edu:10021/business/finance/dmc/DRU. The file contents.txt can be viewed to see a list of old filenames and topics available for reading or downloading. *****************************************************************
***** IN MEMORIAM ****
Fischer Black, developer of the Black-Scholes option pricing model, died during the evening of August 31, 1995. He had fought cancer for more than a year. Black had entered academia after a brief career with a management consulting firm that followed receipt of his Ph.D. in applied mathematics. From the early 70s until around 1984, Black was a major contributor to scholarly work in finance. The intellectual and practical impact of his famous option pricing model tended to overshadow his numerous contributions in capital asset pricing theory, corporate finance and international finance. In 1984 Black left academia for Wall Street and though he never returned, he continued to contribute to the intellectual environment of finance.
Fischer Black was 57 years old.
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VALUE AT RISK
This week's topic, Value at Risk was suggested by a reader. Value at Risk is a concept developed in the field of risk management that defines the minimum amount of money that one could expect to lose with a given probability over a specific period of time. The concept has taken hold as a way to manage the position of a derivatives dealer or end user. Let's use VaR. as its abbreviation.
The VaR concept consist of three factors. One is a given time horizon. A derivatives user might be concerned about possible losses over one day, one week, one month, etc. Second, there is a tolerance level, stated as a percentage. Third, there is the actual value at risk itself, stated in dollars or whatever currency is appropriate. Consider for example a dealer with a $20 million position. He might find that his VaR for a one day period, with a one percent tolerance level is $200,000. This means that the dealer can expect to lose at least $200,000 in any given day about one percent of the time, or in other words, 2.5 times in a year (assuming 250 trading days). Of course, the user can specify any tolerance level or holding period, an indeed varying at least the holding period is a smart thing to look at.
The concept of VaR is a very appealing one. It can be developed for any kind of portfolio and can be aggregated across portfolios of different kinds of instruments. For example, a bank might have a portfolio of interest rate swaps, a portfolio of currency swaps and a portfolio of equity swaps, as well as its regular loan and bond portfolios. The VaR for each separate portfolio can be calculated and aggregated across all portfolios. Now I am not implying that this is a simple process; the correlations across portfolios should be accounted for, a point I'll hit later. VaR does, however, provide a consistent measure across portfolios. Thus, with appropriate consideration for all correlations, VaR can provide the bank with an overall measure of exposure.
VaR is also an easily monitored and easily-interpretable concept. It is stated in terms of dollars, or whatever currency is appropriate. Senior management and anyone without much technical knowledge of derivatives can still understand the concept.
I think VaR is a particularly appealing concept because it is consistent with the objective of shareholder wealth maximization, the central paradigm of business and finance. VaR represents the minimum potential loss in shareholder wealth with a given probability over a specific period of time.
Now let me say a few things about how one arrives at VaR. First the portfolio of securities and derivatives must be identified.
There are two primary methods of quantifying the risk. One is to identify the probability distribution of the overall portfolio's return. A portfolio of stocks would require knowledge of the mean's, variances and covariances of the component stocks. A portfolio of interest rate swaps would require knowledge of the probability distribution of whatever underlying interest rate variables are driving the swap values. Since not all of the swaps are likely to be driven by the same variables, the correlations between the different interest rates must also be considered. If all of these statistical parameters are known, it possible to generate the distribution of the overall portfolio. From that distribution, assuming it is normal, lognormal or some other reasonably tractable distribution, you can determine the probability of a loss of at least any chosen value. [Again, I don't mean to imply that this is simple. It can be quite difficult, but it is, generally feasible.] This can then be translated into the appropriate VaR. Alternatively, you can use Monte Carlo simulation, which generates sample values of prices, interest rates, etc. and from those values build the distribution of portfolio returns that leads to the calculated VaR. Monte Carlo simulation is especially useful if the probability distribution is not normal.
A good VaR system will account for all of the relevant risk factors (delta, gamma, vega, theta, rho, etc.). It is possible to design simplified systems that ignore risks like gamma, vega, etc. and in some cases, these simplified systems will suffice (e.g. if trading only stock index futures, gamma risk is irrelevant). Integrating credit risk into VaR is desirable but much more difficult. Nonetheless, credit risk is just as valid of a concern and should be properly accounted for in VaR.
Let me conclude by noting that while VaR seems to be a recent development, its origins go back a lot longer than you probably think. It is based on the Markowitz portfolio theory, which lays out the principles involved in managing multiple assets and was first published in 1952.
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DERIVATIVES QUOTE FOR THE WEEK
"A common misconception about risk management in some quarters is that the use of derivative securities constitutes speculation - that is, the addition of financial risk to the business risk of a firm's operations. Some folks think that condom use increases risk."
Walter Dolde
"The Trajectory of Risk Management"
Journal of Applied Corporate Finance
1993, Vol. 6, No. 3, pp. 33-41.
[However, you can't buy derivatives in gas stations]