The Original Draft Copy of VaR and VaR Derivatives


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The Original Draft Copy of VaR and VaR Derivatives

  1. 1. ARMS ADVANCED RISK MANAGEMENT SOLUTIONS PTE LTD Mailing Address: Tanglin P.O. Box 0391, Singapore 912414 Headquarters Address: 400 Orchard Road, #17-06 Orchard Towers, Singapore 238875 Tel: (65)734-9803, 734-9804, 738-1747; Fax: (65)734-0392 (Sales & Technical Support) (Administration) (Management) July 27, 1996 VaR and VaR Derivatives Pretty soon you may hear the following conversation between an eager structured derivatives dealer with his or her curious customer: Dealer: “Why don’t you try selling some VaR (Value at Risk) Calls to finance the cost to purchase the VaR Puts? You may adjust the confidence levels, which are your strike prices, so that you can have a zero-cost VaR Range Forward.” “What is my downside protection vs. my upside profit potential?” the customer asked. Dealer: “It depends on whether you use spot level or forward level as your benchmark (the expected return). Let’s assume that you choose to use your portfolio implied forward as the benchmark, then your two strike levels would be quite symmetrical, such as 80% vs. 20% or 70% vs. 30% etc. In the lingo of a two-tail distribution, your portfolio’s P&L could be locked in to be within two standard deviations to each side of your expected return. For example, your portfolio’s profit and loss could be confined to plus and minus five million US Dollars on the horizon date.” Customer: “Will I have to stop trading during this period?” 1 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  2. 2. ARMS Dealer: “Well, our pricing will be much better for a ‘locked-up’ portfolio. But we can make a price for a dynamic portfolio as well if that suits you better.” In a couple of years’ time a conversation like this may not sound as exotic as it may sound now. VaR has been gaining its status as the de facto measure for market risk. It is not only the regulators who are getting to endorse it one after another, all private sector financial institutions are also embracing it. In what many view as the driving factor for the beginning of a new risk management industry, the VaR revolution has gradually been penetrating all levels of management of many financial institutions throughout the world. I. What is VaR (Value at Risk)? The VaR approach represents a set of methodologies to measure market risks. The concept is not new. In fact, many financial institutions around the world have been practicing some sort of Value at Risk (money at risk or dollar at risk, as they were known by different names before) procedures to manage their trading books in the past. However, the systemic approach of the VaR concept was first brought to the financial world’s attention by the Group of Thirty (G30) in their Recommendations for Derivatives Practices and Principles published in July, 1993. As it stands right now, the VaR is only used to measure market risk, although proposals have been raised to implement the same concept to measure credit and even operational risks. VaR is basically a statistical estimate which measures, at a certain confidence interval (say 95%), the amount of value (5 million) in a certain currency (Hong Kong Dollar) that a portfolio or an organization may stand to lose within a certain horizon time period (10 days) due to the potential changes in the market prices of the underlying assets. The possible time horizons for analysis could be only one day for most trading positions or it could be a month or longer for an investment portfolio. 2 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  3. 3. ARMS VaR has become significant because it represents the first collective effort by the market participants and regulators to create a standardized approach to assess risks, whether it is for a particular security, an investment portfolio or the entire balance sheet of an organization. However, it is very important to emphasize that VaR is only a statistical estimate usually based on an assumed distribution of some historical time series data. It is a forecast number and can not by nature be accurately determined with 100% degree of confidence. The common types of methodologies used to calculate this estimate number are: 1. Historical Price Modeling In historical price modeling, one tries to construct a distribution of portfolio returns from a series of changes in portfolio values based on a given time series of historical market prices of basic component instruments such as FX, interest rates, stocks and commodities at the beginning and the end of a given time horizon. From the distribution of the portfolio returns we can calculate the potential portfolio loss, at a certain confidence interval, for a particular holding period. Having the time series of portfolio returns, many statistical techniques could be used to construct the distributions to determine the probability of loss for the portfolio. For example, if we assume the portfolio returns follow a normal distribution through time, the VaR under any level of confidence can be easily calculated from the product of a confidence level factor and the standard deviation of the portfolio returns distribution. (See Figure 1) 2. Estimated Variance and Covariance Method A more pragmatic and convenient approach is to create a series of historical variance and covariance matrix data on simplified financial instruments and then apply them to those component securities in a portfolio. Most portfolio risk factors can be broken down into equivalent simplified instruments such as FX spot rates, money market rates, government bond prices, swap rates, stock market indices and commodities prices. 3 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  4. 4. ARMS The total cash flows of any portfolio, linear or non-linear, can be converted into present-valued zero-coupon cash flows for simple instruments, and delta or spot equivalent amount for derivatives in a process called cash flows mapping. This is a way to standardize the component cash flows of most portfolios to facilitate the process of calculating VaR. Once we have the portfolio cash flows exposure broken down into standardized maturity time buckets, it becomes much easier to compute VaR of the total portfolio through the use of volatility and correlation data of these standardized maturity time buckets. The main advantage of this methodology to produce VaR risk reports is its simplicity, although to some extent at the expense of lost accuracy. For derivatives, other than the component delta risks, none of the other derivatives risks such as gamma, theta and vega are captured in this computation process. One of the dangers of not taking into account these non-linear risk factors is that this methodology fails to distinguish a long-dated option from a short-dated option for example. A risky situation often referred to as the short short-dated deep-outs (sold short-dated deep out-of-the-money options) would sometimes generate severe unpleasant surprises during some adverse market conditions. It is the same short Gamma risk that the exchange-listed margin system such as SPAN fails to cope with. Despite its shortcomings in handling derivatives, this methodology is currently proposed by many such as J. P. Morgan‘s RiskMetrics (See below) due to its superiority in its extreme ease of implementation. 3. Structured Monte Carlo Simulation In a Monte Carlo simulation, a set of randomly generated market prices of the basic instruments will be used to construct a distribution of portfolio returns from a series of changes in portfolio values instead of the historical prices. By nature the methodology is much more forward looking than the method which has to rely on the historical prices. It avoids the type of criticism such as “Driving by looking at the rear-view mirror.” about the historical price modeling methodology. 4 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  5. 5. ARMS Implied volatility currently traded in the market place may be utilized for the structured random numbers generating in the computation process. The forward looking characteristics of the implied volatility is widely viewed as a better choice over the historical volatility. However, due to the lack of liquid correlation derivatives products markets and computational difficulties, the correlation can not easily be implied from any market prices. In practice, a combination of implied volatility and historical correlation have often been used. The major drawback of the structured Monte Carlo simulation technique is the computational complexity. With the continual progress in the computing technology, this simulation methodology will continue to gain more and more favorable support from the market participants. 4. Stress Analysis The memories of the October stock markets crash in 1987 as well as the bond market massacre in February of 1994 are still vivid in many market participants’ mind. After all, it is the extreme scenarios that caused the various catastrophes to many financial institutions. A VaR calculated solely on a set of historical prices may not give the complete picture of what might happen to an investment portfolio. The G30recommended the use of stress simulations in addition to the statistically-based Value at Risk methodologies. In a stress analysis, instead of using historical market prices or a randomly-generated data, a set of arbitrary scenario prices can be created to test the performance of the portfolio. The non-linear risks in the portfolio should be captured through the use of any widely available analytical pricing software for derivatives. In practice, the stress analysis method is quite straight forward and has been in use extensively by derivatives traders to manage their trading books in the past. For example, it is very common for an option trader to run a report 5 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  6. 6. ARMS at the end of the day to see what is the P&L impact on his/her portfolio if the spot moves up or down 2%, or if the volatility moves up or down by 1%. II. The Impact of the RiskMetrics Data Sets RiskMetrics is a particular approach developed by JP Morgan based on the estimated variance-covariance method to quantify market risk. The market risk is defined as the maximum loss of a portfolio, given a confidence interval and time horizon. The methodology is derived from, but not exactly the same as, J. P. Morgan’s own in-house market risk management systems. JP Morgan made the concept and the data sets available in October 1994 for the professed motivation of promoting greater transparency of market risk, providing a benchmark for market risk measurement and making sound advice available to the public. The RiskMetrics products include the VaR methodology and the three data sets which are composed of daily and monthly volatility and correlation estimates on over 400 instruments and a separate regulatory data set which complies with the requirements of the 1995 Basle Committee proposals for using internal models to calculate regulatory capital requirements on market risks. Since its inception, the RiskMetrics methodology has been put in the public domain and the data sets with daily updating have been made available free to the public through the Internet. They have been intentionally left to the end users as well as third party consultants and advisers to implement and further improve on. Since JP Morgan did not provide any software tools for the implementation of RiskMetrics (pre 4:15), it appeared a great opportunity for many financial software vendors. However, up to now, only a handful of 6 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  7. 7. ARMS third parties software vendors around the world have been able to deliver a full-functioning system solutions to any potential end users of the RiskMetrics. What also makes the RiskMetrics data sets significant is the fact that the data sets are deliverable through the Internet. providing daily access to the updated database of all volatilities and correlations of the market risks basic elements such as FX, interest rates, equities and commodities. Without the Internet the VaR implementation would never have been made so easy and wide-spread. III. VaR Calculation Examples Let’s first assume that a US-based company called ARMS corporation has foreign exchange exposures in the following currencies: DEM, JPY, CHF and GBP (See Table 1). The risk management committee of the ARMS corporation is interested in finding out the Value at Risk from the potential currency fluctuation. For a corporation, unlike a bank which may require daily mark-to-market evaluation of its trading books, the FX exposure is usually managed on a monthly revaluation basis. Therefore, the risk management committee would be interested to know, with a certain level of confidence, what the potential maximum amount, in US dollars, more than which the corporation will not lose within a month is. Listed on Table 2 are the monthly correlation data from the RiskMetrics on 9th December, 1995. Table 3 is the variance and covariance data calculated from the RiskMetrics data. Figure 2 and 3 explain the diversified and undiversified VaR. The diversified VaR takes into account the correlation effect among the various currency pairs and therefore is lower than the undiversified VaR which is a simple sum of all the undiversified VaR of each individual currency pair. 7 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  8. 8. ARMS For a bank’s trading books, the revaluation time horizon could be just one day. Table 4 illustrates a typical portfolio of many interest rate sensitive instruments of a bank called ARMS Bank. If we can put each maturity segment into various time buckets whose volatility and correlation data are available from the RiskMetrics daily data set, we can easily calculate the diversified and undiversified VaR for ARMS Bank’s interest rate portfolio for a one day time horizon (Figure 4 and 5). IV. The Uses of VaR The traditional risk management cycle starts from understanding, identifying, assessing, measuring, monitoring, and controlling risks, to the final reporting of the risk management performance. The most tedious and logistically most challenging step is the measuring step. VaR provides us with a systemic way to approach the measuring task. Some of the benefits that VaR brings about are as follows: 1. Management Information. The VaR information could be used by regulators, senior management, independent risk management committee, internal and external auditors. VaR makes the reporting process transparent by making the information which is needed for decision making more specific and simple. 2. Setting Trader Limits. Many would agree that the risk of a long 10 million USD vs. DEM position today could be very different from that of the same position one year ago. This is just because the USD/DEM has different levels of volatilities at these two different time. Banks can therefore set trader’s limits in terms of VaR in addition to the current practice of maximum position exposure. The use of VaR has many advantages among which the most significant is that positions in different markets or on different products can now be compared with one another. The other advantage is that the traders may get trading limits 8 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  9. 9. ARMS which are higher than what they would have under the traditional position limit system. For example the simple sum of the each individual trader’s VaR could be larger than that allowed for their department due to the possible negative correlation between their positions. 3. Tracking Portfolio Risk Performance with a Benchmark Index. By computing the VaR of an index from its components one can track and compare it to the VaR of an investment portfolio in a similar way people track an index for its returns. 4. Resource Allocation. Having the VaR information, the risk takers can make better informed decisions about their trading or investment strategy. Position taking should be geared toward maximizing returns given a risk tolerance level. By calculating the incremental increase in VaR of any potential investment candidate, the risk taker can make a better decision for the optimal performance of their existing portfolio. 5. Investment & Trading Performance Evaluation. The information of VaR can help investment managers compare risk-adjusted performance across different portfolios. For example, to measure the cumulative trading revenues over time of different traders in similar markets and compare them on the basis of the following ratios: a. Sharpe Ratio: P&L / Volatility (of P&L), b. Risk Ratio: P&L / VaR, or c. Efficiency Ratio: VaR / Volatility (of P&L). In most of the dealing rooms environment, the performance of traders or position takers have been measured so far by returns only. The risk-adjusted performance are certainly much more meaningful for comparison purpose. By using the Efficiency Ratio, which gives the comparison of the estimated risks vs. realized volatility of profits, bank management can add another way to gauge the performance of its traders (i.e. their ability to manage risk). 9 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  10. 10. ARMS 6. Regulatory Compliance. Financial institutions and corporations will have to comply with capital adequacy requirements or risk disclosure requirements set by the respective local regulators. Some of the currently existing and pending regulatory requirements are as follows: a. The European Union’s Capital Adequacy Directive (EEC 6-93), which requires banks and investment firms to set capital aside to cover market risks took effect in January, 1996. b. The Basle Committee on Banking Supervision of the Bank for International Settlements consultative proposal “Internal Model-Based Approach to Market Risk Capital Requirements” will soon come into effect in 1997 (See below). c. The Security and Exchange Commission’s proposed amendments to Regulation S-X, Regulation S-K, and Form 20-F. The proposal requires registered corporations to provide quantitative information on market risks of derivatives and other financial instruments. V. VaR and the Regulatory Capital Charges for Banks In the January 1996 Amendment to the original 1988 Basle Capital Accord, BIS had proposed that the required capital charge for a bank’s market risk exposure could be derived from applying a multiplication factor between 3 and 4 to the VaR calculated from any of the bank’s internal models depending on how well the bank could satisfy the statistical testing requirements set by the BIS. In order to standardize the different methodologies utilized by various internal models, BIS also specified that the VaR generated from the internal models should use a minimum of 10 days holding period and should adopt a 99% confidence interval. 10 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  11. 11. ARMS When the proposal first came out, there were quite some criticism regarding how BIS came out with such a multiplication factor. Many felt the multiplier of 3 seemed to be an arbitrary number taken out of thin air. Many bankers even argued that a multiplier is unnecessary and that the capital charge should be equal to the Value-at-Risk figure (which means a multiplier of 1). At the time few of those comments were backed up by supporting data. Let’s try to run some test cases to see how the two ways of calculating capital charges compare: one from multiplying the VaR calculated from the internal model using the Estimated Variance-Covariance Methodology (with RiskMetrics data sets) and the other from calculating directly using the Standardized Methodology proposed by the BIS. (See Table 7) We used the software Outlook (Version 1.0) provided by Financial Engineering Associates, Inc. with the RiskMetrics daily data set (of April 30,1996) for calculating the VaR based on the Estimated Variance-Covariance Methodology. The VaR calculated from the daily data set by the conversion factor, 2.32 / 1.65 * √10 = 4.4464 was then adjusted. There may also be some inaccuracy introduced from the difference between the BIS volatilities forecasting approach (regular Moving Average) and the RiskMetrics approach (Exponentially Weighted Moving Average, or EWMA). However, due to the relatively quiet market behavior prior to the date of daily data set we used, any error introduced this way could be assumed to be minimal. For the calculation based on BIS Standardized Methodology, we used the software RiskBusters (Version 1.0), which is a proprietary product of Advanced Risk Management Solutions Pte Ltd. In order to compare apples with apples, specific risk charges (e.g. 2% on the market index portfolio) have been excluded in our calculation for capital charges from the BIS Standard Method. This is due to the inherent limitations of this particular internal model we used (RiskMetrics) which does not calculate the specific risks . (For portfolios that 11 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  12. 12. ARMS contain options, the capital charges from the Delta Plus method, i. e. Gamma, Vega etc. should also be excluded for comparison purposes.) The results showed that the capital charges based on the internal model VaR, multiplied by 3 could be higher than that calculated from the BIS Standardized Methodology for most undiversified portfolios. An internal model/standardised methodology (IM/SM) ratio has been created to indicate how effective the savings of required capital charge are by using the internal models as compared to the standard method. An IM/SM Ratio of less than 100% indicates that the internal model has created savings in required capital charge due to the diversification effect of running a bigger portfolio. If the IM/SM Ratio is larger than 100% then it means the bank has too small a portfolio to benefit from the diversification effect. It would be better off using the BIS Standard Method to calculate its required capital charges. It also means that it does not make economic sense for the bank to invest heavily in people, systems and the whole related infrastructure to calculate its required capital charges using any of the internal models. Whether the IM/SM Ratio is larger than one depends on the volatility forecast at the time for each individual instrument. From the analysis, it can be seen that the CAD FX spot, BEF interest rate and Aluminum all have lower capital charges from the internal model VaR due to the low volatility numbers in the RiskMetrics daily data set. The portfolio diversification effect will start to kick in once the number of instruments in a portfolio starts increasing. It can be observed that within each asset class (FX, equity, interest rate and commodity) the diversified VaR brings down the IM/SM Ratio dramatically (98% down to 61% for FX for instance). For the overall portfolio, the required capital charge based on the diversified VaR represents only 62% of the capital charge based on the BIS Standard Method. This is a significant savings in running a trading operation of this size. At least two meaningful conclusions can be drawn from this demonstrated portfolio diversification effect. 12 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  13. 13. ARMS First, it is definitely toward the advantage of the larger size banks to invest in the people, systems and other resources required to set up the VaR calculation techniques based on various internal models (Estimated Variance-Covariance Analysis, Historical Price Model and Structured Monte Carlo Simulation etc.) to ensure the bank’s trading operations will be run in the most efficient way by putting up only the minimum level of required capital to cushion for potential losses from the trading operations. Second, by allowing the banks to use correlation across the different asset classes to calculate diversified VaR, the regulators (the various central banks in each country) will encourage all financial institutions to run their operations in a more diversified way by growing bigger both in size and diversity. On one hand, this creates quite positive benefits for the financial institutions’ management in the future in terms of allowing them to take advantage of the cheapest form of hedging, i.e. through diversification. On another hand, the ramification of this incentive could be increased numbers of mergers and acquisitions in the financial industries at an accelerated pace. The barrier to entry for the financial industries will at the same time getting higher and higher for entrepreneurial start-ups. This is due to the larger absolute risk for the start-ups and hence larger required capital vs. the smaller incremental risk for the larger financial institutions to build the same operations. Once we are convinced that diversification brings efficient management for the banks’ trading operations, the next natural question would be: how big does the bank has to be in order to fully exploit the diversification effect? Well, similar question has been asked very frequently in the mutual fund industry about how many stocks that one needs to fully enjoy the diversification effect in running of a stock portfolio. The answer to that question is about 10 to 20 stocks By having more than 20 stocks the incremental risk reduction diminishes as each additional stock is added in the portfolio. The answer to our first question would be roughly about when a portfolio has achieved an IM/SM Ratio of around 40% - 50% based on our limited number of test runs of various portfolios of different sizes and types of component 13 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  14. 14. ARMS investment instruments. Further research would be necessary to come up with a more precise answer. VI. VaR Derivatives Imagine the following scenario: what would derivatives bankers do when a USD- based corporate treasurer finds out that his company’s AUD currency forward exposure could be easily offset through the negative correlation between his AUD exposure and the outstanding DEM exposure from the DEM 10 year bond his company issued a year ago? Because the diversified VaR that his company is exposed to is brought lower by this negative correlation, it does not make sense for him to go out and do a AUD option or forward trade to hedge off the AUD risk individually. In other words, the AUD currency exposure may have a negative incremental VaR to his company which has an existing DEM 10 year interest rate exposure. By doing a AUD option trade with his derivatives banker to hedge away the AUD exposure he could inadvertently be increasing the firm-wide VaR. Hence, for the derivatives bankers to survive, they need to find new ways to offer to their corporate customers the right risk management solutions instead of pushing the conventional derivatives products that his/her bank has to offer. With the exponential rate of growth of this newly established industry, the awareness and understanding of VaR will become much more wide-spread then anyone can imagine today. The ease of implementation will be further fostered by the availability of Internet and other systems technology. When the VaR gains its foothold into the corporate boardroom of many of the world’s corporation and financial institutions, treasurers will become less inclined to manage their treasury risks on an isolated basis. The demand for currency options or interest rate swaps for example, will be growing at a much slower rate, if not declining. In 14 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  15. 15. ARMS its place, it will be the growing demand for some integrated risk management tools such as the VaR derivatives. Would VaR derivatives be the light at the end of the tunnel for many of today’s conventional derivatives operations? We had already seen the development of increasing applications of the multi-assets or correlation derivatives developed for the corporate users such as the currency basket options, the quanto swaps, and the commodity-linked interest rate caps in the past few years before the big bang of the market risk management for the banks themselves started. It should not be a question of whether but a question of when. What are VaR derivatives? Few can give a precise answer now. Could they take the forms as most of us know derivatives to be such as VaR Forward, VaR Calls, VaR Puts, VaR Swaps, VaR Caps, VaR Floors or some derivatives strategies such as VaR Range Forward and VaR Participating Forward? Irrespective of its future forms, the basic definition of VaR derivatives should be no different from the definition of derivatives else where. They are financial contracts where the profit and loss are determined by the cash flows of the underlying instrument, in this case, the VaR. Let’s try to look at this following scenario: A GBP based customer holding a portfolio composed primarily of European currency denominated securities is interested in buying some sort of insurance on his portfolio as he does not have (or unwilling to put up) the enough capital (GBP 2.4 million, using a multiplier of 3) to support his investment portfolio exposure . Let’s assume his daily VaR is GBP 0.8 million (e.g. 95% confidence interval) based on a portfolio size of GBP 600 million. If he can buy insurance for the next year for the GBP 0.3 million portion of his daily VaR which will leave him with only GBP 0.5 million for which he has to come up with the required capital charge (GBP 1.5 million now). 15 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  16. 16. ARMS Assume there are three global banks interested in offering the VaR derivatives to assume the potential daily loss of GBP 0.3 million (the same 95% confidence interval), and they all have different accounting currencies, i.e. one is a Japanese bank (JPY based), one is a German bank (DEM based) and the last one is an American bank (USD based). The pricing from all the three banks would be quite different due to the different accounting currencies and their different composition of their own bank’s portfolios. Table 8 shows the VaR obtained from a computer simulation for three hypothetical banks, each with one of the accounting currencies listed above. The portfolios of the banks were constructed so that each was weighted more heavily towards the instruments of its respective home currency. The diversified and undiversified VaR and the capital charge in accordance with the BIS standardized methodology (SM) guidelines were then calculated. This was done first for each bank’s portfolio on a stand-alone basis, then for the combined portfolio consisting of each bank’s portfolio and the customer’s portfolio which generates a VaR of only GBP 0.3m. Across the three banks, the diversified VaR shows the smallest increase when the customer’s portfolio is added to the bank’s portfolio. The undiversified VaR and BIS SM capital charge show greater increases as these measures do not allow for the correlation between different assets. Considering diversified VaR in particular, the hypothetical German bank has the greatest increase in VaR when it takes on the customer’s portfolio. This would be the same as expected as the portfolio constructed for the hypothetical German bank has the highest proportion of instruments denominated in European currencies. This would have had the strongest correlation with the customer’s sterling-based portfolio. Similarly, the fact that the hypothetical Japanese bank suffered the smallest VaR increase can be explained by the low correlation between the yen-denominated and the sterling-denominated instruments. Indeed, on a VaR per unit of cash flow basis, the hypothetical Japanese bank exhibits a decrease in VaR. For the hypothetical American bank, given its dollar-based portfolio, the change in 16 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  17. 17. ARMS VaR that results from adding the customer’s portfolio lies in between that of the other two banks. While a decrease in the absolute VaR is not illustrated in this example, theoretically there could be a situation that for one out of the three competing banks, by adding the customer’s portfolio to the bank’s own portfolio would create a negative incremental VaR while for the other two banks a positive incremental VaR. If this happens, does this mean the bank with negative incremental VaR addition should actually pay the customer for assuming his downside risk while the other two banks are charging him? What does this all mean for the future bank risk management business? Would there be more cross border transactions with companies searching around the world (maybe through the Internet search engine) to find banks with the most negatively-correlated portfolios? Would it be the banks which have largest and most diversified portfolios who would become the eventual winners in this new game of risk management business? Or would it be the ones who are currently most isolated and undiversified to benefit most from involving themselves into this new business due to the additional negative incremental VaR (or small positive incremental VaR) as they expand their portfolios? There are just too many questions remaining to be researched on, tested against, discussed about and thought over. As the industry progress at an astronomical pace within the foreseeable future, many bankers, academics and systems specialists would certainly remain their gainful employment by making contribution to the further understanding of this exciting new world of risk management business. VII. Future Directions 17 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  18. 18. ARMS At the moment, many would agree that what we have seen so far is only the beginning of a new industry, i. e. the financial risk management industry. The awareness of VaR is revolutionary and it certainly will transform the way finance professionals do business in the near future. With the availability of the more advanced systems technology, many of the theories people could only talk about a few years ago are becoming more and more like realities. The concept of VaR derivatives sound novel to many financial market participants of today. It would not be totally without possibility that the first ever VaR derivatives trade will be done within the next two to three years. After all, for many of the early birds among today’s financial institutions, once they have got through the hurdle of understanding, calculating and implementing VaR in their respective institution, what they should be doing with this new found information is the next big question. VaR, by itself, is nothing more than another measure of risks, an integrated version of risks, unlike the isolated risks such as FX, interest rate, etc. If these people are thinking of somehow they should try to reduce the VaR, try to alter it or to use some way to temporarily offset it without totally eliminating it, then without knowing it, they have already been preparing themselves to become tomorrow’s vast group of the VaR derivatives consumers. By: Ralph Yiehmin Liu Founder and Managing Director Advanced Risk Management Solutions Pte Ltd (Singapore) Co-Chairman, Singapore Dinner Committee, International Association of Financial Engineers Ralph Yiehmin Liu, MChE, MSE, Ph.D. Cand., MBA (Wharton Business School), is the founder and the Managing Director of Advanced Risk Management Solutions Pte Ltd, a 18 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G
  19. 19. ARMS Singapore-based consultancy specializing in the area of treasury, equity investment, commodity, capital markets, derivatives trading and risk management. ARMS is the first and so far the largest operation of such leading-edge financial engineering consultancy in the Asia Pacific region. Ralph is primarily responsible for introducing the market risk management concept of Value-at-Risk to the Asian markets by conducting extensive training seminars, both public and in-house on VaR through ARMS Financial Series programs. ARMS currently provides advisory services for major central banks, futures and options exchanges, investment fund managers, commercial banks, state and local banks, industrial corporations, and other financial institutions in the Asia Pacific region on the state-of-the-art financial risk management concepts. Previously he served as the Managing Director of Chase Manhattan Asia Limited in Hong Kong, where he set up an FX, interest rate and commodity structured derivatives business for its Asian operations. He also built a structured FX options and derivatives business in Asia for the Union Bank of Switzerland headquartered in Singapore. Prior to moving back to Asia, Ralph had many years of experience running FX options and the interest rate swaps & equity derivatives business with major investment (Morgan Stanley) and money center (Chemical) banks on Wall Street. Ralph also had an extensive experience as a user of interest rate and FX derivatives when he managed derivatives trading at AT&T and Equitable Life in New York. Ralph has been an active writer/contributor for many well-known finance journals & publications. Ralph has been appointed as the Co- Chairman of the Singapore Dinner Committee of the International Association of Financial Engineers headquartered in New York. 19 AD V AN C E D R I S K M AN AG E M E N T S O L U T I O N S P T E L T D T E L : ( 6 5 ) 7 3 4 - 9 8 0 3 , 7 3 4 - 9 8 0 4 F AX :( 6 5 ) 7 3 4 - 0 3 9 2 AR M S P L @ S I N G N E T . C O M . S G