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I&WM Janfeb010 Blueline.Indd FEATURE Value at Risk An Advanced Discussion of a Tool to Assist Advisors in Measuring and Communicating Portfolio Risk By John Nersesian, CIMA®, CIS, CPWA®, CFP® osses in investment portfolios 1. Help manage client expectations later mandated disclosure of risk to over the past two years have had regarding downside potential. investors and VaR became the de facto L a sobering eff ect on investors 2. Help consultants construct appropri- measure.1 Within the past few years, as they have come to understand the ate portfolios that accurately refl ect advisors to high-net-worth individuals two-sided nature of investment deci- the risk preference of their clients. who wanted to take a more institutional sions: return and risk. With these losses 3. Position the advisor as an institu- approach to portfolio construction and top-of-mind, clients have a renewed tional-caliber consultant with an management began using VaR. interest in fully understanding their advanced skill set. portfolio risks and a renewed desire for Th e extraordinary recent market Value at Risk Defined their advisors to demonstrate how they decline has brought into focus the short- VaR quantifi es the maximum downside manage the potential for loss. comings of traditional risk management loss exposure under normal market Most investors have a good under- tools, including VaR. Proponents of risk conditions within a specifi ed period of standing of the concept of return. measures, including VaR, have cau- time, in dollar terms, with a confi dence Advisor-client conversations about risk, tioned about the importance of realizing level of occurrence (generally ranging however, can be challenging because that these measures are intended to be from 90–99 percent). often each has a diff erent perspec- quantitative tools used in concert with While many VaR models are propri- tive or defi nition of risk. Investment due diligence and quantitative judgment. etary, they all incorporate the statistical professionals often seek to quantify risk Critics highlight the importance of concepts of probability distributions, using standard deviation. Th ey see the viewing risk management as a continu- confi dence intervals,2 asset class corre- downside potential of risk as well as the ous process, not a static event. Working lation, and volatility. Th ese are the three upside, i.e., the return opportunities with their clients, advisors need to methods of calculating VaR: available for taking on a certain level of establish a target risk for the portfolio Historical models use real market risk. Th is upside is an abstract concept and measure risk on an ongoing basis. data from prior market phases, allowing to most investors, who view risk simply VaR can help investors understand the for nonnormal distribution patterns. as the potential to lose money (and, risk associated with their investment Many consultants favor this approach by extension, the potential for falling decisions as part of a process that also because it accurately refl ects the mar- short of objectives or having to reduce uses other appropriate risk measures ket’s kurtosis (the fatness of a distribu- spending, etc.) One way to quantify the including beta, capture ratio, downside tion tail).3 However, this approach is potential downside risk is Value at Risk deviation, and tracking error. dependent on historical time series and (VaR), which calculates the maximum assumes that future conditions will be expected loss over a certain time period Value at Risk’s Evolution the same as historical conditions so it and confi dence level. Clients are looking VaR has roots in the institutional world. may not always be statistically relevant. for the answer to the question, “How Its development is widely credited to Monte Carlo models use a statisti- much money can I potentially lose in a JP Morgan in the late 1980s and early cally signifi cant number of simulations given period?” In their quest to answer 1990s. At that time the risk of indi- of randomly sequenced returns to that question, some advisors have found vidual trading desks could be known, project a range of future results and the the concept of VaR to be helpful. but JP Morgan’s then-chairman, Dennis probability of achieving them. Because Th is paper discusses how VaR can be Weatherstone, was seeking a measure this model is unlimited by historical a useful tool to assess risk exposure and to understand the fi rm’s overall risk results, it provides a forward-looking to communicate with clients. Th ere are every day. Over time VaR was embraced VaR with potentially greater predic- three benefi ts to understanding, embrac- by others in the institutional world; the tive ability than linear methods. Monte ing, and employing the VaR calculation: Securities and Exchange Commission Carlo simulations do, however, have 14 Investments&Wealth MONITOR © 2010 Investment Management Consultants Association. Reprint with permission only. I&WM JanFeb010 Blueline.indd 14 1/25/10 10:05 AM FEATURE their limitations and the outcomes are not guaranteed or FIGURE 1: STANDARD DEVIATIONS IN A NORMAL assured in any respect. DISTRIBUTION Both the Historical and Monte Carlo methods use large data sets. Parametric VaR (or Delta Normal) uses the known properties of standard deviation to help determine maximum 1.65σ downside risk. It assumes a normal distribution of returns 95% and a linear relationship to the various risk factors, which 2.33σ seldom occur, making the tool simple but somewhat limited. 99% Th is is the method used in this paper. Each method relies on historical results. Past performance σ ⊗ σ⊗ σ σ σ σ -3 -2 -1 mean +1 +2 +3 Return is no guarantee of future results. VaR does not measure all 84% of returns 97.5% of returns forms of risk. 99.5% of returns Hypothetical example does not refl ect the performance of an actual investment; for Levels of Value at Risk illustrative purposes only. Th e fl exibility of the VaR measure is another reason it has be- come an important tool for many practitioners. In addition to being able to specify risk for various horizons and confi dence Figure 1 illustrates standard deviations in a normal intervals, it also can be expressed in both absolute and rela- distribution. In a normal distribution, 50 percent of returns tive terms. Th ere are three related VaR measures outside the will be greater than the mean and 50 percent will be less traditional absolute measure. than the mean. For the purposes of VaR, which measures the Relative VaR measures the risk of underperformance potential for loss, the 95-percent confi dence level is at 1.65 relative to a pre-determined index. Most institutional inves- standard deviations to the left of the mean and the 99-percent tors use this measure because their performance is frequently confi dence level is at 2.33 standard deviations to the left of evaluated against a target benchmark. the mean.4 Marginal VaR measures how much risk a position or manager adds to the portfolio. Moreover, this metric mea- A Hypothetical Example—Portfolio Scenario sures how much overall portfolio VaR would change by elimi- Th is hypothetical example does not refl ect the performance nating the position completely from the portfolio. Marginal of an actual investment; it is for illustrative purposes only. VaR is useful for measuring which position or manager is the largest contributor to portfolio risk. Investment A Investment B Incremental VaR measures how a small percentage change Allocation $5 million $5 million in an individual position weight aff ects the overall portfolio. Average Return (X) 0.15 0.09 It is closely related to marginal VaR because both metrics measure the change in overall VaR caused by changing the Weight (Wt) 0.50 0.50 construct of the portfolio. Incremental VaR, however, is useful Variance (␴2) 0.04 0.02 for identifying positions for gradual risk reduction over time. Covariance (COV) 0.05 0.05 of AB Calculating Value at Risk Th e formula for a parametric VaR calculation (using 95-per- cent and 99-percent probability) can be expressed as: Calculating Value at Risk Assuming One-Year Time Period VaR @ 95% = PV$ X – 1.65σ To determine the client’s maximum exposure to loss in any ͌N one-year holding period (with a 95-percent confi dence level), we use the following calculation (results of Step 2 are rounded VaR @ 99% = PV$ X – 2.33σ to two decimal places): ͌N (1) Compute the mean weighted return of the portfolio: PV$ = Portfolio value in dollars ʳ ʳ ERp = WA X + WB X σ = Standard deviation of the portfolio ϫ ϫ — = (0.50 0.15) + (0.50 0.09) = 0.12 X = Mean return of the portfolio for holding period N = Number of years in projected holding period January/February 2010 15 © 2010 Investment Management Consultants Association. Reprint with permission only. I&WM JanFeb010 Blueline.indd 15 1/25/10 10:05 AM FEATURE (2) Compute the variance of the portfolio: is especially true if the portfolio or manager measured has 2 σ2 2 σ2 high turnover. Also note the assumed level of risk and return Vp = W A A + W B B + 2WAWBCOVAB = (0.502 0.04) + (0.502 0.02) + (2 0.50 0.50 0.05) remain constant over varying time horizons. Th is assumption may lead to an unreliable VaR outcome over very short or very = 0.0100 + 0.005 + 0.0250 = 0.04 long time horizons. To measure the potential for loss over a (3) Compute the standard deviation of the portfolio: six-month horizon or a fi ve-year horizon the calculations are: σ ͌ = Vp 0.12 – (1.65 ϫ 0.20) VaR = $10,000,000 ϫ = –$2,969,848 = ͌ 6mo ͌ 0.04 = 0.20 0.50 0.12 – (1.65 ϫ 0.20) (4) Compute the VaR of the portfolio: VaR5yr = $10,000,000 = –$939,149 5.0 VaR @ 95% = PV$ X – 1.65σ ͌N Calculation Summary = $10,000,000 (0.120 – 1.65 (0.20)) Th e VaR calculation depends largely on two variables: the probability level and the time period.
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