Analytical VaR VaR Mapping
Content
September 2008 Edition
LETTER
FROM
CRAIG HEATTER
Welcome to the latest issue of the J.P. Morgan Investment Analytics and Consulting newsletter, which aims to provide informative and thought-provoking articles on topics relating to portfolio optimization. In this issue, we analyze the historical returns and future prospects of private equity investments, explore the potential benefits and pitfalls of an active currency management strategy, and provide an overview of Value-at-Risk modeling, with a particular focus on Analytical VaR. We welcome your thoughts and suggestions, and hope that this issue provides you with useful information.
CRAIG HEATTER MANAGING DIRECTOR AND GLOBAL EXECUTIVE FOR INVESTMENT ANALYTICS AND CONSULTING J.P. MORGAN WORLDWIDE SECURITIES SERVICES [email protected]
ABOUT J.P. MORGAN INVESTMENT ANALYTICS AND CONSULTING
J.P. Morgan Investment Analytics and Consulting (IAC) helps institutional clients make more informed investment decisions and optimize their portfolios through creating customized, innovative, and forward-looking solutions that address both current and future needs. IAC services over 230 clients globally with over 7,000 institutional portfolios, representing approximately $2 trillion in assets. Its diverse client list includes corporate and public DB/DC pensions, investment managers, endowments and foundations, corporate treasuries, insurance companies, central banks, and investment authorities. Having the broadest and deepest product offering in the market, IAC offers security-level, multi-currency performance measurement (monthly and daily) using J.P. Morgan or third party accounting; analytics and attribution at the asset class, sector, country, and individual security level; ex-ante risk management (including Risk Budgeting and security-level VaR); investment manager analysis, universe comparison, and peer grouping; global consolidated reporting for multi-national plans; and consultative services in the areas of liability and plan allocation strategy, manager search, and liability-driven investments. For further information, please visit www.jpmorgan.com/visit/iac or
Americas: Mark Huamani Executive Director [email protected] 212-552-0527 Asia Pacific: Stuart Hoy Vice President [email protected] 612-9250-4733 Europe, Middle East, Africa: Romain Berry Vice President [email protected] 44-20-7325-8981 Alex Stimpson Vice President [email protected] 44-12-0234-3386
TABLE OF CONTENTS
Private Equity For Institutional Investors Can You Make Cash With Currency? Value-at-Risk: An Overview of Analytical VaR Global Capital Markets Global Market Indices 2
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7 10 12
Copyright ©2008 JPMorgan Chase & Co. All rights reserved.
PRIVATE EQUITY
PRIVATE EQUITY FOR INSTITUTIONAL INVESTORS
by Karl Mergenthaler, CFA, and Chad Moten J.P. Morgan Investment Analytics and Consulting [email protected], [email protected]
SPOTLIGHT
Pension plans and other institutional investors are pouring money into private equity at an astounding rate. At this time, the private equity industry accounts for approximately $1.5 trillion in invested capital, and private equity firms raised $300 billion in fresh capital in 2007. Undoubtedly, there will be both winners and losers in this high-stakes, modern-day gold rush.
In our view, private equity involves a complicated risk and return proposition. Private equity investors may be attracted to the potential for impressive returns that are not highly correlated with traditional equity and fixed income investments. Skeptics point to the multiple risks due to the illiquid and opaque nature of the funds. The J.P. Morgan Investment Analytics and Consulting group analyzed more than 5,500 private equity funds for vintage years from 1990 through 2005, including both U.S. and global funds and representing every major style. Our analysis indicates that there is a wide range of performance between top quartile and median funds among every major style. Moreover, the relative performance of private equity funds versus the public equity markets has been mixed. In our view, institutional investors face several hurdles to investment success in private equity. Institutional investors have to identify the funds, management teams, and deal structures that are likely to result in positive results. Moreover, once attractive funds and strong managers are identified, it is often difficult to gain access to the most attractive funds. Finally, private equity partnerships typically involve annual fees of approximately 2% and carried interest of 20% of profits. Nonetheless, investors seem willing to take their chances in this challenging asset class. According to a recent survey conducted by J.P. Morgan and Greenwich Associates, approximately 62% of current investors in private equity expect to increase their allocations in the near term. In our view, plan sponsors should only consider allocations to private equity if they believe they are able to identify, and gain access to, managers that are likely to be in the top quartile.
THE INVESTMENT CASE
In many ways, private equity holds the potential for huge gains. Clearly, high rates of return are possible, particularly among top-quartile funds. For example, top-quartile venture capital funds that were raised between 1993-1997 generated average internal rates of return of 52%. Likewise, buyout funds that were raised between 2001-2005 generated average internal rates of return of 40% for the top quartile. In good times, private equity can generate outstanding investment results. In Exhibit 1, we summarize recent results for private equity. However, the risks are daunting. First, investment in private equity is illiquid, and the money is often tied up for ten years or more. Second, the funds are often highly concentrated and involve significant company-specific risks. Third, private equity funds are not transparent, and there is frequently a lack of reliable, publicly-available information. Fourth, and perhaps most importantly, there is a wide dispersion between the top performing funds and the rest of the pack.
Exhibit 1 – Private Equity Performance (as of Dec. 31, 2007)
1 Year
U.S. Venture Capital Index U.S. Private Equity Index Global (ex-U.S.) Private Equity and Venture Capital CSFB / Tremont Hedge Fund Index Russell 2000 16.3% 20.4% 35.3% 6.7% -1.6%
3 Year
14.1% 25.1% 36.0% 10.2% 6.9%
5 Year
11.3% 24.5% 30.9% 10.8% 16.3%
10 Year
35.2% 14.1% 19.7% 8.3% 7.2%
Source: J.P. Morgan Investment Analytics & Consulting estimates, Cambridge Associates, CSFB/Tremont, Bloomberg.
Exhibit 2 – Fundraising
US Private Equity Fundraising Totals, 1993-2007 Venture Capital Other Mezzanine Capital Buyouts 300,000 250,000 (US$ Millions) 200,000 150,000 100,000 50,000 0 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Source: J.P. Morgan Investment Analytics & Consulting estimates, Dow Jones Private Equity Analyst.
Fund of Funds
SEPTEMBER 2008 EDITION — 2
PRIVATE EQUITY
The amount of capital raised in private equity funds has skyrocketed over the past five years. As shown in Exhibit 2, the total amount of capital raised in private equity funds increased to approximately $300 billion in 2007. With the huge amount of capital raised, private equity funds are searching for new markets to deploy the cash. For example, emerging markets funds raised approximately $59 billion in 2007. In our opinion, the large inflow of capital into private equity funds begs one question: Will future results be as attractive as they have been historically? performance of private equity and the public markets is mixed. Most importantly, our analysis suggests that the ultimate returns of private equity funds that are raised in years with high levels of fundraising are likely to be poor. Clearly, there is a wide dispersion between top performing funds and the median. Our analysis focuses on venture capital and buyout funds, which together account for more than 80% of assets invested in private equity. In Exhibits 3 and 4, we illustrate the top quartile and median returns for venture capital and buyout funds with vintage years between 1990 and 2005. As indicated in Exhibit 3, top quartile venture capital funds out-performed median funds by 1,750 basis points for vintage years between 1990 and 2005. Also, top quartile buyout funds (see Exhibit 4) out-performed the median by 1,230 basis points during this time period.
SPOTLIGHT
HISTORICAL RETURNS – THE EVIDENCE IS MIXED
Our analysis suggests that investment success in private equity is not a “lay-up.” First, there is a wide dispersion of returns for similar funds, and top quartile funds tend to perform much better than the median. Also, the relative
Exhibit 3 – Venture Capital
Top Quartile 70.0% 60.0% 50.0% 40.0% IRR 30.0% 20.0% 10.0% 0.0% -10.0% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Vintage Median
Exhibit 4 – Buyout Funds
Top Quartile
70.0% 60.0% 50.0% IRR 40.0% 30.0% 20.0% 10.0% 0.0%
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Median
Vintage
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Exhibit 5 – Venture Capital
Exhibit 6 – Buyout Funds
35.0 140,000
20.0
Venture Capital - Median IRR Russell 2000 (Annualized) Fundraising
80,000 70,000 Fundraising ($M) 60,000 50,000
30.0 25.0
Returns
Buyout - Median IRR Russell 2000 (Annualized) Fundraising
120,000 100,000 80,000 60,000 40,000 20,000 0
Fundraising ($M)
15.0 Returns
20.0 15.0 10.0 5.0 0.0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
10.0
40,000 30,000
5.0
20,000 10,000
0.0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 -5.0
0 -10,000 -20,000
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
SEPTEMBER 2008 EDITION — 3
PRIVATE EQUITY
Exhibit 7 – Diversification Benefits
U.S. Small Stocks
U.S. Small Stocks Lehman AGG EAFE Wilshire 5000 Venture Capital Private Equity Timber Realty Fund of Hedge Funds 1.00 -0.20 0.60 0.83 0.39 0.58 -0.06 -0.08 0.37 1.00 -0.14 -0.12 -0.17 -0.20 0.11 -0.18 -0.09 1.00 0.76 0.33 0.53 0.05 0.10 0.26 1.00 0.44 0.65 0.06 -0.03 0.40 1.00 0.60 0.11 0.08 0.39 1.00 0.26 0.23 0.39 1.00 -0.21 0.21 1.00 -0.13 1.00
SPOTLIGHT
Lehman AGG
EAFE
Wilshire 5000
Venture Capital
Private Equity
Timber
Realty
Fund of Hedge Funds
Source: J.P. Morgan Investment Analytics & Consulting estimates, Cambridge Associates, Hedge Fund Research Inc.
The performance of private equity funds versus the public equity markets has been mixed. We compared the internal rate of return for private equity funds versus the annualized time-weighted rate of return for the Russell 2000 over comparable time periods. Although comparing results between public and private equity is problematic due to the different performance measurement methodologies, we believe the comparison is directionally correct and provides some useful information. As indicated in Exhibit 5, venture capital funds that were raised in the mid-1990’s posted returns in excess of the Russell 2000. In our opinion, it is likely that many ventures that were funded in the mid-1990’s were harvested in the late-1990’s technology bubble. It is interesting to note that funds raised in 1998-2002 (i.e., the strong fundraising years) produced internal rates of return that were materially lower than the public markets. In fact, based on our analysis, the median venture capital fund has under-performed the Russell 2000 for most of the past decade. Buyout funds raised over the past decade have outperformed the Russell 2000 over the time period from 19952005 (see Exhibit 6). In recent years, fundraising for buyout funds sky-rocketed. Meanwhile, the differential between median buyout funds and the Russell 2000 has been declining in the most recent years.
The correlation of private equity to other asset classes is low, which does indicate that there may be some diversification benefit to participating in this asset class. However, we would note that many of the correlations for other alternative assets, such as Timber and Funds of Hedge Funds, are lower than those experienced by private equity. Also, we believe the correlations may be understated due to the infrequency of reporting for private equity and use of estimates in calculating private equity returns. Therefore, diversification should not be the sole reason to invest in private equity.
CONCLUSIONS
In our view, an allocation to private equity may make sense in the context of a large institutional portfolio. However, investors in private equity should be aware of the wide dispersion in results among funds with similar strategies. In our view, the high levels of fundraising in recent years may hinder the ability of private equity firms to generate stellar results going forward. We believe investors in private equity should take a longterm view. It may make sense to spread out capital allocations over many years to dampen the impact of fundraising cycles. We believe plan sponsors must analyze the details of any individual private equity fund, and consider how that fund is likely to perform in various market conditions. Furthermore, plan sponsors should only consider allocations to private equity if they believe they are able to identify, and gain access to, managers that are likely to be in the top quartile. In all, we believe it is worth the effort to analyze private equity funds and consider allocating a percentage of portfolio assets to this asset class.
For a copy of our complete white paper, “Private Equity for Institutional Investors”, please contact Karl Mergenthaler at [email protected].
DIVERSIFICATION
In order to assess the diversification benefits of private equity, we analyzed the 20-year track record of the Cambridge Venture Capital and Private Equity indices relative to several traditional and alternative asset classes. The results of our correlation analysis are summarized in Exhibit 7.
SEPTEMBER 2008 EDITION — 4
CURRENCY MANAGEMENT
CAN YOU MAKE CASH WITH CURRENCY?
by Paul Ha and Carlos Marenco J.P. Morgan Investment Analytics and Consulting [email protected], [email protected]
Pension plans, endowments, and foundations allocate a significant portion of their total portfolio to foreign assets in both developed and emerging markets. In a recent study of institutional investment strategies, the J.P. Morgan Investment Analytics and Consulting group found that U.S. investors, on average, have targeted a 20% allocation to international investments. This sizeable allocation, if left un-hedged, has benefited from the weakness in the U.S. Dollar over the last several years. For the most recent year, the gain on currency has helped bolster these international equity returns by an estimated 9.64% (see Exhibit 1). Even longer term, the currency gains as a proportion of the total international return has been significant.
SPOTLIGHT
Exhibit 1 - Foreign Currency Impact on Domestic Returns (as of June 30, 2008)
YTD EAFE - USD EAFE - Local Return from Currency 1 Yr 3 Yr 6.66 6.18 5 Yr 16.67 11.22 5.45 10 Yr 5.83 2.63 3.20 -10.96 -10.61 12.84 -15.70 -20.25 4.74 9.64
HEDGING STRATEGIES
Some institutional investors may choose to leave their portfolios un-hedged. In this instance, the portfolio will experience the full impact of the appreciation and depreciation of the local currency. Although the currency returns over a long time horizon should approach zero, the portfolio may experience an increase in volatility due to exchange rate fluctuations. Passive currency management is intended to reduce foreign currency exposure and risk, not necessarily to increase return. The sole purpose of a passive currency program is to eliminate, to a degree, the impact from currency fluctuations on the value of foreign investments. The degree to which the currency risk is eliminated is dictated by the level of the hedge ratio that is employed1. A hedge ratio of 50%, for example, would indicate that half of the currency exposure has been eliminated. The goal of an active currency strategy is to capture gains while reducing risk on international investments. This can be achieved by altering the hedge ratio of the currencies to be hedged. Depending on the guidelines and latitude provided by the plan sponsor, the currency manager may be able to take advantage of the movement and volatility in the foreign exchange market. For example, if the currency managers have a view that the Euro will continue to appreciate relative to the U.S. Dollar, they could under-hedge the Euro (or leave it completely unhedged) to capture the anticipated currency gain. Conversely, if the currency managers have a view that the Swiss Franc would depreciate relative to the U.S. Dollar, they could overhedge (or completely hedge) the Swiss Franc to offset the impact of the falling Franc. By partially hedging, institutional investors can enhance their portfolio returns by actively managing their currency risk.
Source: J.P. Morgan Investment Analytics & Consulting estimates.
Since the U.S. Dollar is currently near all-time lows, we are seeing an increasing number of U.S. institutional investors revising, or at a minimum, reviewing their currency strategy. In our opinion at this point in time, it is certainly possible that the U.S. Dollar will bounce back, and that a strengthening dollar could have an adverse effect on the returns of international investments. Foreign exchange rate risk and security valuation risk are the two main types of investment risk associated with foreign investments. Security valuation risk in foreign positions is driven by a number of factors such as market, sector, industry and stock specific – similar to the risk associated with domestic investments. Foreign exchange rate risk is the risk associated with the ownership of foreign securities that are traded in a foreign currency. The FX risk is due to the implicit currency exposure when holding these foreign positions. Traditionally, when dealing with currency risk, institutional investors have relied on three primary options: maintain currency exposure, passively manage foreign currency exposure, or actively manage foreign currency exposure. Recently, J.P. Morgan Investment Analytics and Consulting has seen more plan sponsors treat currency as a separate asset class in an alpha-seeking strategy. In this article, we will make a case for active currency management through a pure currency alpha strategy. The argument for an alpha-seeking currency mandate is threefold. First, currency’s low correlation to other traditional asset classes makes it an ideal candidate for diversification. Secondly, an active currency manager can capitalize on the trending nature of the currency market. Lastly, there are inefficiencies in the currency market that present opportunities to capture profit.
ALPHA-SEEKING STRATEGIES
Unlike traditional hedging programs, currency alpha strategies are not constrained by the currency exposures of the portfolio. By managing currency as a separate asset class, plan sponsors can make a pure alpha play by using forward contracts and eliminating the need for any initial funding. In this
1
It is important to note that the effectiveness of the passive currency hedge is also dependent upon the efficiency of the currency trade execution.
SEPTEMBER 2008 EDITION — 5
CURRENCY MANAGEMENT
context, the currency managers are expected to add alpha (i.e., increase the overall risk-adjusted returns of the portfolio).
DIVERSIFICATION
The asset allocation of a typical institutional investor may include domestic and foreign equity, fixed income, real estate, and commodities. In our opinion, institutional investors may be able to reduce the overall risk of the portfolio by incorporating an alpha currency program into an established asset allocation. The addition of an asset class that is lowly or negatively correlated to the other major asset classes is a way to reduce the volatility of the overall plan and thus improve its risk/return profile. In Exhibit 2, it is evident that a currency allocation can help offset some of the volatility that a “traditional” portfolio may encounter. The currency markets, as measured by the U.S. Dollar Index (DXY), have a low to negative correlation to the stock, bond, real estate and commodity markets, making it an attractive portfolio diversifier.
The currency market is the world’s largest and most liquid market, with an average daily turnover of $3.2 trillion USD3. The daily currency turnover is more than ten times that of all of the world’s equity markets combined4. The volume can be attributed to a number of factors, including the different type of market participants and the various objectives they have for currency exchange. Currency exchange is employed by central banks to implement monetary policy, by commercial banks to manage cash flow, and by institutional investors to hedge exposure and enhance return. For example, many investment managers execute foreign exchange trades for the sole purpose of making funds available in the local trading currency to execute foreign stock or bond trades. A central bank’s motivation for being players in the currency market is to stabilize their domestic currency or stave off the forces of inflation. In fact, central banks may have to buy or sell currency at inopportune times to satisfy their primary goals. Corporations can have significant currency exposure from foreign operations, trading, or debt servicing obligations. Their greater interest lies in neutralizing their currency exposure rather than maximizing profits. With any active management strategy, there should be an exploitable market inefficiency in order for the strategy to be successful. Usually, this inefficiency comes at the cost of liquidity. In the currency market, we find the rare case where both are available.
SPOTLIGHT
Exhibit 2 - Correlation of U.S. Dollar Index (DXY) with Traditional Asset Classes2
USD Index Domestic Equity Foreign Equity Fixed Income Real Estate Commodities 1.00 0.03 -0.29 -0.21 -0.07 -0.19
CONCLUSION
As institutional investors continue to increase their allocation to international investments, especially in the emerging markets, a clear currency mandate is becoming an increasingly important part of portfolio management. Based on the goals, requirements and restrictions of the plan, the plan sponsor should review the currency policy in place and determine the optimal strategy. Leaving the portfolio completely un-hedged may leave the portfolio exposed to unwanted volatility. While a passive strategy will help neutralize the currency risk associated with foreign investments, on a long-term basis, a 100% hedge can only be right 50% of the time. Given the portfolio diversification effects, the exploitable opportunities present in the currency market, and the potential to increase the risk/reward profile of the overall portfolio, institutional investors may want to consider alpha-seeking strategies in order to cash on currency.
2
Source: J.P. Morgan Investment Analytics & Consulting estimates.
OPPORTUNITIES
The argument against active currency management is that the long-term investment in a currency of a developed country is essentially a zero-sum investment. The long-term expected returns of the major currencies are zero. During times of economic prosperity, the host nation’s currency will become stronger relative to other currencies. However, when the economic tides turn, it will eventually give back the previous gains. Currencies typically will move according to the outlook of a country’s economic data, and exchange rates tend to gain directional momentum and trend. In the short term, there is an inherent volatility as with any other asset class. However, over a longer time horizon, the economic health of the host nation should keep the momentum moving in the same direction. Exchange rate trends do persist for some time, resulting in an opportunity for skilled active managers to exploit currency swings.
3 4
The correlation coefficients are based on 17.5 years of historical data ending June 2008. The following indices were used as proxies for the asset classes shown in the table. Domestic Equity - Russell 3000 Index; Foreign Equity - MSCI EAFE Index (Net Div); Fixed Income - L.B. Aggregate Bond Index; Real Estate - NCREIF Property; Commodities - Dow Jones AIG Commodities Index. Source – Bank of International Settlements. Source – Bloomberg.
SEPTEMBER 2008 EDITION — 6
RISK MANAGEMENT
VALUE-AT-RISK: AN OVERVIEW OF ANALYTICAL VAR
by Romain Berry J.P. Morgan Investment Analytics and Consulting [email protected]
SPOTLIGHT
In the last issue, we discussed the principles of a sound risk management function to efficiently manage and monitor the financial risks within an organization. To many risk managers, the heart of a robust risk management department lies in risk measurement through various complex mathematical models. But even one who is a strong believer in quantitative risk management would have to admit that a risk management function that heavily relies on these sophisticated models cannot add value beyond the limits of understanding and expertise that the managers themselves have towards these very models. Risk managers relying exclusively on models are exposing their organization to events similar to that of the sub-prime crisis, whereby some extremely complex models failed to accurately estimate the probability of default of the most senior tranches of CDOs1. Irrespective of how you put it, there is some sort of human or operational risk in every team within any given organization. Models are valuable tools but merely represent a means to manage the financial risks of an organization.
This article aims at giving an overview of one of the most widespread models in use in most of risk management departments across the financial industry: Value-at-Risk (or VaR)2. VaR calculates the worst expected loss over a given horizon at a given confidence level under normal market conditions. VaR estimates can be calculated for various types of risk: market, credit, operational, etc. We will only focus on market risk in this article. Market risk arises from mismatched positions in a portfolio that is marked-to-market periodically (generally daily) based on uncertain movements in prices, rates, volatilities and other relevant market parameters. In such a context, VaR provides a single number summarizing the organization’s exposure to market risk and the likelihood of an unfavorable move. There are mainly three designated methodologies to compute VaR: Analytical (also called Parametric), Historical Simulations, and Monte Carlo Simulations. For now, we will focus only on the Analytical form of VaR. The two other methodologies will be treated separately in the upcoming issues of this newsletter. Part 1 of this article defines what VaR is and what it is not, and describes the main parameters. Then, in Part 2, we mathematically express VaR, work through a few examples and play with varying the parameters. Part 3 and 4 briefly touch upon two critical but complex steps to computing VaR: mapping positions to risk factors and selecting the volatility model of a portfolio. Finally, in Part 5, we discuss the pros and cons of Analytical VaR. that should always be kept in mind when handling VaR. VaR involves two arbitrarily chosen parameters: the holding period and the confidence level. The holding period corresponds to the horizon of the risk analysis. In other words, when computing a daily VaR, we are interested in estimating the worst expected loss that may occur by the end of the next trading day at a certain confidence level under normal market conditions. The usual holding periods are one day or one month. The holding period can depend on the fund’s investment and/or reporting horizons, and/or on the local regulatory requirements. The confidence level is intuitively a reliability measure that expresses the accuracy of the result. The higher the confidence level, the more likely we expect VaR to approach its true value or to be within a pre-specified interval. It is therefore no surprise that most regulators require a 95% or 99% confidence interval to compute VaR.
PART 2: FORMALIZATION AND APPLICATIONS
Analytical VaR is also called Parametric VaR because one of its fundamental assumptions is that the return distribution belongs to a family of parametric distributions such as the normal or the lognormal distributions. Analytical VaR can simply be expressed as: (1) where α • VaRα is the estimated VaR at the confidence level 100 × (1 – α)%. • xα is the left-tail α percentile of a normal distribution is described in the expression where R is the expected return. In order for VaR to be meaningful, we generally choose a confidence level of 95% or 99%. xα is generally negative. • P is the marked-to-market value of the portfolio. The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance. But even if we have a large enough sample of historical returns, is it realistic to assume that the returns of any given fund follow a normal distribution? Thus, we need to associate the return distribution to a standard normal distribution which has a zero mean and a standard deviation of
1
PART 1: DEFINITION OF ANALYTICAL VAR
VaR is a predictive (ex-ante) tool used to prevent portfolio managers from exceeding risk tolerances that have been developed in the portfolio policies. It can be measured at the portfolio, sector, asset class, and security level. Multiple VaR methodologies are available and each has its own benefits and drawbacks. To illustrate, suppose a $100 million portfolio has a monthly VaR of $8.3 million with a 99% confidence level. VaR simply means that there is a 1% chance for losses greater than $8.3 million in any given month of a defined holding period under normal market conditions. It is worth noting that VaR is an estimate, not a uniquely defined value. Moreover, the trading positions under review are fixed for the period in question. Finally, VaR does not address the distribution of potential losses on those rare occasions when the VaR estimate is exceeded. We should also bear in mind these constraints when using VaR. The ease of using VaR is also its pitfall. VaR summarizes within one number the risk exposure of a portfolio. But it is valid only under a set of assumptions
2
CDO stands for Collaterized Debt Obligation. These instruments repackage a portfolio of average- or poor-quality debt into high-quality debt (generally rated AAA) by splitting a portfolio of corporate bonds or bank loans into four classes of securities, called tranches. Pronounced V’ah’R.
SEPTEMBER 2008 EDITION — 7
RISK MANAGEMENT
one. Using a standard normal distribution enables us to replace xα by zα through the following permutation: (2) which yields: (3) zα is the left-tail α percentile of a standard normal distribution. Consequently, we can re-write (1) as: (4) replace in (4) the mean of the asset by the weighted mean of the portfolio, μp and the standard deviation (or volatility) of the asset by the volatility of the portfolio, σ p. The volatility of a portfolio composed of two assets is given by: (6) where • w1 is the weighting of the first asset • w2 is the weighting of the second asset • σ1 is the standard deviation or volatility of the first asset • σ2 is the standard deviation or volatility of the second asset • ρ1,2 is the correlation coefficient between the two assets And (4) can be re-written as: (7) Let us assume that we want to calculate Analytical VaR at a 95% confidence level over a one-day horizon on a portfolio composed of two assets with the following assumptions: • P = $100 million • w1 = w2 = 50%6 • μ1 = 0.3% • σ1 = 3% • μ2 = 0.5% • σ2 = 5% • ρ1,2 = 30%
SPOTLIGHT
EXAMPLE 1 – ANALYTICAL VAR OF A SINGLE ASSET
Suppose we want to calculate the Analytical VaR at a 95% confidence level and over a holding period of 1 day for an asset in which we have invested $1 million. We have estimated3 μ (mean) and σ (standard deviation) to be 0.3% and 3% respectively. The Analytical VaR of that asset would be:
This means that there is a 5% chance that this asset may lose at least $46,347 at the end of the next trading day under normal market conditions.
EXAMPLE 2 – CONVERSION OF THE CONFIDENCE
LEVEL4
Assume now that we are interested in a 99% Analytical VaR of the same asset over the same one-day holding period. The corresponding VaR would simply be:
(8) There is a 1% chance that this asset may experience a loss of at least $66,789 at the end of the next trading day. As you can see, the higher the confidence level, the higher the VaR as we travel downwards along the tail of the distribution (further left on the x-axis).
EXAMPLE 5 – ANALYTICAL VAR OF A PORTFOLIO
COMPOSED OF N ASSETS
From the previous example, we can generalize these calculations to a portfolio composed of n assets. In order to keep the mathematical formulation handy, we use matrix notation and can re-write the volatility of the portfolio as:
EXAMPLE 3 – CONVERSION OF THE HOLDING
PERIOD
If we want to calculate a one-month (21 trading days on average) VaR of that asset using the same inputs, we can simply apply the square root of the time5: (5) Applying this rule to our examples above yields the following VaR for the two confidence levels:
(9) where • w is the vector of the weights of the n assets • w’ is the transpose vector of w • Σ is the covariance matrix of the n assets Practically, we could design a spreadsheet in Excel (Exhibit 1) to calculate Analytical VaR on the portfolio in Example 4.
EXAMPLE 4 – ANALYTICAL VAR OF A PORTFOLIO
OF TWO ASSETS
Let us assume now that we have a portfolio worth $100 million that is equally invested in two distinct assets. One of the main reasons to invest in two different assets would be to diversify the risk of the portfolio. Therefore, the main underlying question here is how one asset would behave if the other asset were to move against us. In other words, how will the correlation between these two assets affect the VaR of the portfolio? As we aggregate one level up the calculation of Analytical VaR, we
3
4 5
6
Note that these parameters have to be estimated. They are not the historical parameters derived from the series. Note that zα is to be read in the statistical table of a standard normal distribution. This rule stems from the fact that the sum of n consecutive one-day log returns is the nday log return and the standard deviation of n-day returns is √n × standard deviation of one-day returns. These weights correspond to the weights of the two assets at the end of the holding period. Because of market movements, there is little likelihood that they will be the same as the weights at the beginning of the holding period.
SEPTEMBER 2008 EDITION — 8
RISK MANAGEMENT
Exhibit 1 – Excel Spreadsheet to calculate Analytical VaR for a portfolio of two assets
Analytical VaR
Expected parameters p w1 w2
SPOTLIGHT
PART 4: VOLATILITY MODELS
We can guess from the various expressions of Analytical VaR we have used that its main driver is the expected volatility (of the asset or the portfolio) since we multiply it by a constant factor greater than 1 (1.6449 for a 95% VaR, for instance) – as opposed to the expected mean, which is simply added to the expected volatility. Hence, if we have used historical data to derive the expected volatility, we could consider how today’s volatility is positively correlated with yesterday’s volatility. In that case, we may try to estimate the conditional volatility of the asset or the portfolio. The two most common volatility models used to compute VaR are the Exponential Weighted Moving Average (EWMA) and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH). Again, in order to be exhaustive on this very important part in computing VaR, we will discuss these models in a future article.
100,000,000 50% 50% 0.3% 3% 0.5% 5% 30% 0.40% 3.28% Exposures Covariance Matrix Standard Deviation Correlation Matrix
Asset 1 0.03
Asset 2 0.05
μ1 σ1 μ2 σ2
p1,2
1 0.3
0.3 1
Σ
μp σp
Confidence level 95% -1.6449
0.00090 0.00045
0.00045 0.00250
PART 5: ADVANTAGES AND DISADVANTAGES OF ANALYTICAL VAR
Analytical VaR is the simplest methodology to compute VaR and is rather easy to implement for a fund. The input data is rather limited, and since there are no simulations involved, the computation time is minimal. Its simplicity is also its main drawback. First, Analytical VaR assumes not only that the historical returns follow a normal distribution, but also that the changes in price of the assets included in the portfolio follow a normal distribution. And this very rarely survives the test of reality. Second, Analytical VaR does not cope very well with securities that have a non-linear payoff distribution like options or mortgage-backed securities. Finally, if our historical series exhibits heavy tails, then computing Analytical VaR using a normal distribution will underestimate VaR at high confidence levels and overestimate VaR at low confidence levels.
w1
0.5 0.00068 0.00148 0.00108 0.03279 4,993,012
0.5
Σw
σ 2=w’Σw σ
VaR
Grey = input cells Source: J.P. Morgan Investment Analytics & Consulting.
.77
CONCLUSION
As we have demonstrated, Analytical VaR is easy to implement as long as we follow these steps. First, we need to collect historical data on each security in the portfolio (we advise using at least one year of historical data – except if one security has experienced high volatility, which would suggest a shorter period of time). Second, if the portfolio has a large number of underlying positions, then we would need to map them against a more manageable set of risk factors. Third, we need to calculate the historical parameters (mean, standard deviation, etc.) and need to estimate the expected prices, volatilities and correlations. Finally we apply (7) to find the Analytical VaR estimate of the portfolio. As always when building a model, it is important to make sure that it has been reviewed, fully tested and approved, that a User Guide (including any potential code) has been documented and will be updated if necessary, that a training has been designed and delivered to the members of the risk management team and to the recipients of the outputs of the risk management function, and finally that a capable person has been allocated the oversight of the model, its current use, and regular refinement.
It is easy from there to expand the calculation to a portfolio of n assets. But be aware that you will soon reach the limits of Excel as we will have to calculate n(n-1)/2 terms for your covariance matrix.
PART 3: RISK MAPPING
In order to cope with an increasing covariance matrix each time you diversify your portfolio further, we can map each security of the portfolio to common fundamental risk factors and base our calculations of Analytical VaR on these risk factors. This process is called reverse engineering and aims at reducing the size of the covariance matrix and speeding up the computational time of transposing and multiplying matrices. We generally consider four main risk factors: Spot FX, Equity, Zero-Coupon Bonds and Futures/Forward. The complexity of this process goes beyond the scope of this overview of Analytical VaR and will need to be treated separately in a future article.
Opinions and estimates offered in this Investment Analytics and Consulting newsletter constitute our judgment and are subject to change without notice, as are statements of financial market trends, which are based on current market conditions. We believe the information provided here is reliable, but do not warrant its accuracy or completeness. References to specific asset classes, financial markets, and investment strategies are for information purposes only and are not intended to be, and should not be interpreted as, recommendations or a substitute for obtaining your own investment advice. This document contains information that is the property of JPMorgan Chase & Co. It may not be copied, published, or used in whole or in part for any purposes other than expressly authorized by JPMorgan Chase & Co. www.jpmorgan.com/visit/iac
SEPTEMBER 2008 EDITION — 9
GLOBAL CAPITAL MARKETS
U.S. CURRENCY
by Manpreet Hochadel, CFA J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF AUGUST 2008
1.60 1.50 US Dollar vs. EURO 1.40 1.30 1.20 1.10 1.00 0.90 0.80 Dec-98 Dec-99 Dec-00
US Dollar vs. EURO and Japanese Yen
0.0110
0.0100 US Dollar vs. JPY
JPY Right Scale
0.0090
0.0080
EURO Left Scale
Dec-01
Dec-02
Dec-03
Dec-04
Dec-05
Dec-06
Dec-07
0.0070 Dec-08
Source: J.P. Morgan Investment Analytics and Consulting
• The U.S. Dollar recovered some of the losses of the past few years against both the Euro and Yen, as the Euro-zone and Japanese economies showed signs of weakening and the U.S. Federal Reserve hinted at monetary tightening in the future.
U.S. FIXED INCOME
by Manpreet Hochadel, CFA J.P. Morgan Investment Analytics and Consulting [email protected]
AS OF AUGUST 2008
5.00%
US Treasury Yield Curve
4.00% December 31, 2007 August 31, 2008 3.00% June 30, 2008
2.00%
1.00% 2 5 10 20 30 Yr.
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
• The U.S. Treasury yield curve steepened as rates continued to fall across the entire yield curve.
SEPTEMBER 2008 EDITION — 10
GLOBAL CAPITAL MARKETS
EUROPEAN
AND
CORNER
ASIAN CURRENCIES
AS OF JULY 2008
Swiss Franc vs GBP, EUR & USD
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4
by Simreet Gill J.P. Morgan Investment Analytics and Consulting [email protected]
Pound Sterling vs USD and EUR
2.2 2 1.8 1.6 1.4 1.2 1 2001 2002 2003 2004 GBP/USD 2005 2006 GBP/EUR 2007 2008
0.3 2001
2002
2003
2004
2005 CHF/EUR
2006
2007 CHF/USD
2008
CHF/GBP
Norwegian Krone vs EUR, USD & GBP
0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 2001 2002 2003 NOK/EUR 2004 2005 NOK/USD 2006 2007 NOK/GBP 2008
• The uptrend in EUR/GBP over the past six months through July reflected the risk of an independent implosion in the UK economy. The economy is certainly buckling under the post-credit crisis strain but so too is the Euro area, a story which is much more recent. (Morgan Markets)
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Japanese Yen vs GBP, EUR, USD & AUD
0.018 0.015
Australian Dollar vs GBP, EUR & USD
1
0.8 0.012 0.009 0.006 0.4 0.003 0.000 2001 2002 JPY/GBP 2003 2004 JPY/EUR 2005 2006 JPY/USD 2007 2008 JPY/AUD 0.2 2001 0.6
2002
2003
2004
2005 AUD/EUR
2006
2007 AUD/USD
2008
AUD/GBP
Chinese Yuan vs EUR, USD & JPY
17 16 15 14 CNY/JPY 13 12 11 10 9 8 2001 0.06 2002 2003 CNY/EUR 2004 2005 2006 2007 2008 CNY/USD CNY/JPY 0.08 0.12 0.1 0.14 CNY/ USD & EUR 0.16
• There has been a growing divergence between the falling equity markets and the lagged response of Asian FX lately. The key concern is whether Asian currencies will catch up with falling equities. At a superficial level, this equity:FX correlation is being driven by international portfolio equity flows. However, the ultimate drivers for these flows are expectations for the global growth cycle and how these may impact export and corporate earnings in the future. (Morgan Markets)
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
SEPTEMBER 2008 EDITION — 11
GLOBAL MARKET INDICES
ASSET CLASS RETURN COMPARISON (INCLUDING U.S.)
by William Pometto J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF AUGUST 2008
Index
L.B. AGGREGATE BOND INDEX M.L. HIGH YIELD INDEX MSCI EMERGING MARKETS FREE MSCI-Eafe (Net) RUSSELL 1000 GROWTH (Gross) RUSSELL 2000 VALUE (Gross) RUSSELL 3000 INDEX (Gross) S & P 500 - CAP. WEIGHTED
Monthly Return
0.95 0.32 (7.95) (4.05) 1.08 4.75 1.55 1.45
Trailing 3 Months
0.79 (3.91) (20.18) (14.73) (7.99) (0.44) (7.57) (7.89)
Year To Date
2.00 (2.62) (21.67) (17.31) (9.83) (0.71) (10.39) (11.39)
1 Year
5.86 (1.42) (9.83) (14.41) (6.77) (7.52) (10.22) (11.14)
2 Year
5.56 2.48 13.96 0.80 4.76 (0.69) 1.58 1.15
3 Year
4.26 3.42 19.38 8.08 4.39 3.59 3.92 3.67
5 Year
4.61 6.87 23.89 13.86 6.10 10.25 7.57 6.93
10 Year
5.58 4.23 17.72 6.34 2.59 11.28 5.52 3.11
30 25 20 15 10 5 0 -5 -10 -15 -20 -25 Current Month 3 Months Return MSCI EMERGING MARKETS FREE MSCI-Eafe (Net) Year to Date 1 Year 2 Year 3 Year 5 Year 10 Year
M.L. HIGH YIELD INDEX L.B. AGGREGATE BOND INDEX
RUSS-Russell 1000 Growth (Gross) S & P 500 - CAP. WEIGHTED
RUSS-Russell 3000 (Gross) RUSS-Russell 2000 Value (Gross)
U.S. EQUITY • U.S. Stock Markets avoided a third straight down month, posting modest gains in August. • Much of the upward momentum was driven by declining oil prices. • Value stocks experienced the biggest lift with the Russell 2000 Value Index posting a 4.75 percent gain for the month. • The S&P 500 and NASDAQ Composite added 1.45 percent and 1.92 percent respectively. INTERNATIONAL EQUITY • International Markets performed poorly in August. • Investor concern continues over the slumping United States economy and how it will affect international markets. • The strengthening U.S. dollar has also negatively impacted international market returns. • The Emerging Markets were hit the hardest, as evidenced by the 7.95 percent loss for the MSCI Emerging Markets Free Index in August.
FIXED INCOME • Fixed Income Markets were a safe bet for August. • Government bonds continued to post respectable gains. • The L.B. Government Long Term Index posted a 2.32 percent return for the month, putting it up 3.75 percent year to date. REAL ESTATE • Real Estate Markets haven't improved as mortgage concerns still exist. • Home sales continued to slow.
SEPTEMBER 2008 EDITION — 12
GLOBAL MARKET INDICES
GLOBAL EQUITIES (EXCLUDING U.S.)
by Simreet Gill J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF JULY 2008
Europe
12,000 10,000 8,000 6,000 4,000 2,000 0 2000 2001 2002 FTSE 100 2003 CAC 2004 DAX 2005 Swiss Markets 2006 MSCI Europe 2007 2008 180 160 140 120 100 80 60 40 20 0
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
• The financial markets have remained highly unstable in July, owing in part to the troubles at GSEs such as Freddie Mac. Equities have been slowly grinding through the cyclical slowdown triggered by a housing bust, credit crunch, and commodity price pressures. • In July, equities saw a month of two halves with sharp falls in the first half and a rebound of equal magnitude and intensity in the second half. The downshift in global growth indicators
earlier in the month triggered further declines in global equity markets. In particular, the abrupt weakening in European and Japanese growth into midyear, combined with signs that global industrial activity is now contracting, marked a sharper downshift in momentum than the consensus anticipated. Later in the month, sharply lower oil prices and short covering in financials helped equity markets to more than retrace their losses seen in the first two weeks of July. (Morgan Markets)
Australia, Hong Kong, Singapore
5,000 4,000 3,000 2,000 1,000 0 2000 2001 2002 2003 2004 2005 2006 2007 2008
Australia (AS51) Hong Kong (Hang Seng) Singapore (Straits Times)
Japan (Nikkei 225)
250 200 150 100 50 0 2000 2001 2002 2003 2004 2005 2006 2007 2008
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Korean (KOSPI)
1.8 1.5 1.2 0.9 0.6 0.3 0 2000
• Resource-consuming emerging markets such as India and China, which had been sharply sold off owing to growing inflationary concerns on rising commodity prices, picked up. The Japanese market had the second largest fall among major developed nations after England. However, while the Japanese market has tended to be as highly volatile as emerging markets recently, we think movement in the Japanese market in July was only slight compared with the sharp movement in emerging markets. (Morgan Markets)
2003 2004 2005 2006 2007 2008
2001
2002
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
SEPTEMBER 2008 EDITION — 13
LETTER
FROM
CRAIG HEATTER
Welcome to the latest issue of the J.P. Morgan Investment Analytics and Consulting newsletter, which aims to provide informative and thought-provoking articles on topics relating to portfolio optimization. In this issue, we analyze the historical returns and future prospects of private equity investments, explore the potential benefits and pitfalls of an active currency management strategy, and provide an overview of Value-at-Risk modeling, with a particular focus on Analytical VaR. We welcome your thoughts and suggestions, and hope that this issue provides you with useful information.
CRAIG HEATTER MANAGING DIRECTOR AND GLOBAL EXECUTIVE FOR INVESTMENT ANALYTICS AND CONSULTING J.P. MORGAN WORLDWIDE SECURITIES SERVICES [email protected]
ABOUT J.P. MORGAN INVESTMENT ANALYTICS AND CONSULTING
J.P. Morgan Investment Analytics and Consulting (IAC) helps institutional clients make more informed investment decisions and optimize their portfolios through creating customized, innovative, and forward-looking solutions that address both current and future needs. IAC services over 230 clients globally with over 7,000 institutional portfolios, representing approximately $2 trillion in assets. Its diverse client list includes corporate and public DB/DC pensions, investment managers, endowments and foundations, corporate treasuries, insurance companies, central banks, and investment authorities. Having the broadest and deepest product offering in the market, IAC offers security-level, multi-currency performance measurement (monthly and daily) using J.P. Morgan or third party accounting; analytics and attribution at the asset class, sector, country, and individual security level; ex-ante risk management (including Risk Budgeting and security-level VaR); investment manager analysis, universe comparison, and peer grouping; global consolidated reporting for multi-national plans; and consultative services in the areas of liability and plan allocation strategy, manager search, and liability-driven investments. For further information, please visit www.jpmorgan.com/visit/iac or
Americas: Mark Huamani Executive Director [email protected] 212-552-0527 Asia Pacific: Stuart Hoy Vice President [email protected] 612-9250-4733 Europe, Middle East, Africa: Romain Berry Vice President [email protected] 44-20-7325-8981 Alex Stimpson Vice President [email protected] 44-12-0234-3386
TABLE OF CONTENTS
Private Equity For Institutional Investors Can You Make Cash With Currency? Value-at-Risk: An Overview of Analytical VaR Global Capital Markets Global Market Indices 2
5
7 10 12
Copyright ©2008 JPMorgan Chase & Co. All rights reserved.
PRIVATE EQUITY
PRIVATE EQUITY FOR INSTITUTIONAL INVESTORS
by Karl Mergenthaler, CFA, and Chad Moten J.P. Morgan Investment Analytics and Consulting [email protected], [email protected]
SPOTLIGHT
Pension plans and other institutional investors are pouring money into private equity at an astounding rate. At this time, the private equity industry accounts for approximately $1.5 trillion in invested capital, and private equity firms raised $300 billion in fresh capital in 2007. Undoubtedly, there will be both winners and losers in this high-stakes, modern-day gold rush.
In our view, private equity involves a complicated risk and return proposition. Private equity investors may be attracted to the potential for impressive returns that are not highly correlated with traditional equity and fixed income investments. Skeptics point to the multiple risks due to the illiquid and opaque nature of the funds. The J.P. Morgan Investment Analytics and Consulting group analyzed more than 5,500 private equity funds for vintage years from 1990 through 2005, including both U.S. and global funds and representing every major style. Our analysis indicates that there is a wide range of performance between top quartile and median funds among every major style. Moreover, the relative performance of private equity funds versus the public equity markets has been mixed. In our view, institutional investors face several hurdles to investment success in private equity. Institutional investors have to identify the funds, management teams, and deal structures that are likely to result in positive results. Moreover, once attractive funds and strong managers are identified, it is often difficult to gain access to the most attractive funds. Finally, private equity partnerships typically involve annual fees of approximately 2% and carried interest of 20% of profits. Nonetheless, investors seem willing to take their chances in this challenging asset class. According to a recent survey conducted by J.P. Morgan and Greenwich Associates, approximately 62% of current investors in private equity expect to increase their allocations in the near term. In our view, plan sponsors should only consider allocations to private equity if they believe they are able to identify, and gain access to, managers that are likely to be in the top quartile.
THE INVESTMENT CASE
In many ways, private equity holds the potential for huge gains. Clearly, high rates of return are possible, particularly among top-quartile funds. For example, top-quartile venture capital funds that were raised between 1993-1997 generated average internal rates of return of 52%. Likewise, buyout funds that were raised between 2001-2005 generated average internal rates of return of 40% for the top quartile. In good times, private equity can generate outstanding investment results. In Exhibit 1, we summarize recent results for private equity. However, the risks are daunting. First, investment in private equity is illiquid, and the money is often tied up for ten years or more. Second, the funds are often highly concentrated and involve significant company-specific risks. Third, private equity funds are not transparent, and there is frequently a lack of reliable, publicly-available information. Fourth, and perhaps most importantly, there is a wide dispersion between the top performing funds and the rest of the pack.
Exhibit 1 – Private Equity Performance (as of Dec. 31, 2007)
1 Year
U.S. Venture Capital Index U.S. Private Equity Index Global (ex-U.S.) Private Equity and Venture Capital CSFB / Tremont Hedge Fund Index Russell 2000 16.3% 20.4% 35.3% 6.7% -1.6%
3 Year
14.1% 25.1% 36.0% 10.2% 6.9%
5 Year
11.3% 24.5% 30.9% 10.8% 16.3%
10 Year
35.2% 14.1% 19.7% 8.3% 7.2%
Source: J.P. Morgan Investment Analytics & Consulting estimates, Cambridge Associates, CSFB/Tremont, Bloomberg.
Exhibit 2 – Fundraising
US Private Equity Fundraising Totals, 1993-2007 Venture Capital Other Mezzanine Capital Buyouts 300,000 250,000 (US$ Millions) 200,000 150,000 100,000 50,000 0 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Source: J.P. Morgan Investment Analytics & Consulting estimates, Dow Jones Private Equity Analyst.
Fund of Funds
SEPTEMBER 2008 EDITION — 2
PRIVATE EQUITY
The amount of capital raised in private equity funds has skyrocketed over the past five years. As shown in Exhibit 2, the total amount of capital raised in private equity funds increased to approximately $300 billion in 2007. With the huge amount of capital raised, private equity funds are searching for new markets to deploy the cash. For example, emerging markets funds raised approximately $59 billion in 2007. In our opinion, the large inflow of capital into private equity funds begs one question: Will future results be as attractive as they have been historically? performance of private equity and the public markets is mixed. Most importantly, our analysis suggests that the ultimate returns of private equity funds that are raised in years with high levels of fundraising are likely to be poor. Clearly, there is a wide dispersion between top performing funds and the median. Our analysis focuses on venture capital and buyout funds, which together account for more than 80% of assets invested in private equity. In Exhibits 3 and 4, we illustrate the top quartile and median returns for venture capital and buyout funds with vintage years between 1990 and 2005. As indicated in Exhibit 3, top quartile venture capital funds out-performed median funds by 1,750 basis points for vintage years between 1990 and 2005. Also, top quartile buyout funds (see Exhibit 4) out-performed the median by 1,230 basis points during this time period.
SPOTLIGHT
HISTORICAL RETURNS – THE EVIDENCE IS MIXED
Our analysis suggests that investment success in private equity is not a “lay-up.” First, there is a wide dispersion of returns for similar funds, and top quartile funds tend to perform much better than the median. Also, the relative
Exhibit 3 – Venture Capital
Top Quartile 70.0% 60.0% 50.0% 40.0% IRR 30.0% 20.0% 10.0% 0.0% -10.0% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Vintage Median
Exhibit 4 – Buyout Funds
Top Quartile
70.0% 60.0% 50.0% IRR 40.0% 30.0% 20.0% 10.0% 0.0%
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Median
Vintage
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Exhibit 5 – Venture Capital
Exhibit 6 – Buyout Funds
35.0 140,000
20.0
Venture Capital - Median IRR Russell 2000 (Annualized) Fundraising
80,000 70,000 Fundraising ($M) 60,000 50,000
30.0 25.0
Returns
Buyout - Median IRR Russell 2000 (Annualized) Fundraising
120,000 100,000 80,000 60,000 40,000 20,000 0
Fundraising ($M)
15.0 Returns
20.0 15.0 10.0 5.0 0.0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
10.0
40,000 30,000
5.0
20,000 10,000
0.0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 -5.0
0 -10,000 -20,000
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
Source: J.P. Morgan Investment Analytics & Consulting estimates, Private Equity Intelligence.
SEPTEMBER 2008 EDITION — 3
PRIVATE EQUITY
Exhibit 7 – Diversification Benefits
U.S. Small Stocks
U.S. Small Stocks Lehman AGG EAFE Wilshire 5000 Venture Capital Private Equity Timber Realty Fund of Hedge Funds 1.00 -0.20 0.60 0.83 0.39 0.58 -0.06 -0.08 0.37 1.00 -0.14 -0.12 -0.17 -0.20 0.11 -0.18 -0.09 1.00 0.76 0.33 0.53 0.05 0.10 0.26 1.00 0.44 0.65 0.06 -0.03 0.40 1.00 0.60 0.11 0.08 0.39 1.00 0.26 0.23 0.39 1.00 -0.21 0.21 1.00 -0.13 1.00
SPOTLIGHT
Lehman AGG
EAFE
Wilshire 5000
Venture Capital
Private Equity
Timber
Realty
Fund of Hedge Funds
Source: J.P. Morgan Investment Analytics & Consulting estimates, Cambridge Associates, Hedge Fund Research Inc.
The performance of private equity funds versus the public equity markets has been mixed. We compared the internal rate of return for private equity funds versus the annualized time-weighted rate of return for the Russell 2000 over comparable time periods. Although comparing results between public and private equity is problematic due to the different performance measurement methodologies, we believe the comparison is directionally correct and provides some useful information. As indicated in Exhibit 5, venture capital funds that were raised in the mid-1990’s posted returns in excess of the Russell 2000. In our opinion, it is likely that many ventures that were funded in the mid-1990’s were harvested in the late-1990’s technology bubble. It is interesting to note that funds raised in 1998-2002 (i.e., the strong fundraising years) produced internal rates of return that were materially lower than the public markets. In fact, based on our analysis, the median venture capital fund has under-performed the Russell 2000 for most of the past decade. Buyout funds raised over the past decade have outperformed the Russell 2000 over the time period from 19952005 (see Exhibit 6). In recent years, fundraising for buyout funds sky-rocketed. Meanwhile, the differential between median buyout funds and the Russell 2000 has been declining in the most recent years.
The correlation of private equity to other asset classes is low, which does indicate that there may be some diversification benefit to participating in this asset class. However, we would note that many of the correlations for other alternative assets, such as Timber and Funds of Hedge Funds, are lower than those experienced by private equity. Also, we believe the correlations may be understated due to the infrequency of reporting for private equity and use of estimates in calculating private equity returns. Therefore, diversification should not be the sole reason to invest in private equity.
CONCLUSIONS
In our view, an allocation to private equity may make sense in the context of a large institutional portfolio. However, investors in private equity should be aware of the wide dispersion in results among funds with similar strategies. In our view, the high levels of fundraising in recent years may hinder the ability of private equity firms to generate stellar results going forward. We believe investors in private equity should take a longterm view. It may make sense to spread out capital allocations over many years to dampen the impact of fundraising cycles. We believe plan sponsors must analyze the details of any individual private equity fund, and consider how that fund is likely to perform in various market conditions. Furthermore, plan sponsors should only consider allocations to private equity if they believe they are able to identify, and gain access to, managers that are likely to be in the top quartile. In all, we believe it is worth the effort to analyze private equity funds and consider allocating a percentage of portfolio assets to this asset class.
For a copy of our complete white paper, “Private Equity for Institutional Investors”, please contact Karl Mergenthaler at [email protected].
DIVERSIFICATION
In order to assess the diversification benefits of private equity, we analyzed the 20-year track record of the Cambridge Venture Capital and Private Equity indices relative to several traditional and alternative asset classes. The results of our correlation analysis are summarized in Exhibit 7.
SEPTEMBER 2008 EDITION — 4
CURRENCY MANAGEMENT
CAN YOU MAKE CASH WITH CURRENCY?
by Paul Ha and Carlos Marenco J.P. Morgan Investment Analytics and Consulting [email protected], [email protected]
Pension plans, endowments, and foundations allocate a significant portion of their total portfolio to foreign assets in both developed and emerging markets. In a recent study of institutional investment strategies, the J.P. Morgan Investment Analytics and Consulting group found that U.S. investors, on average, have targeted a 20% allocation to international investments. This sizeable allocation, if left un-hedged, has benefited from the weakness in the U.S. Dollar over the last several years. For the most recent year, the gain on currency has helped bolster these international equity returns by an estimated 9.64% (see Exhibit 1). Even longer term, the currency gains as a proportion of the total international return has been significant.
SPOTLIGHT
Exhibit 1 - Foreign Currency Impact on Domestic Returns (as of June 30, 2008)
YTD EAFE - USD EAFE - Local Return from Currency 1 Yr 3 Yr 6.66 6.18 5 Yr 16.67 11.22 5.45 10 Yr 5.83 2.63 3.20 -10.96 -10.61 12.84 -15.70 -20.25 4.74 9.64
HEDGING STRATEGIES
Some institutional investors may choose to leave their portfolios un-hedged. In this instance, the portfolio will experience the full impact of the appreciation and depreciation of the local currency. Although the currency returns over a long time horizon should approach zero, the portfolio may experience an increase in volatility due to exchange rate fluctuations. Passive currency management is intended to reduce foreign currency exposure and risk, not necessarily to increase return. The sole purpose of a passive currency program is to eliminate, to a degree, the impact from currency fluctuations on the value of foreign investments. The degree to which the currency risk is eliminated is dictated by the level of the hedge ratio that is employed1. A hedge ratio of 50%, for example, would indicate that half of the currency exposure has been eliminated. The goal of an active currency strategy is to capture gains while reducing risk on international investments. This can be achieved by altering the hedge ratio of the currencies to be hedged. Depending on the guidelines and latitude provided by the plan sponsor, the currency manager may be able to take advantage of the movement and volatility in the foreign exchange market. For example, if the currency managers have a view that the Euro will continue to appreciate relative to the U.S. Dollar, they could under-hedge the Euro (or leave it completely unhedged) to capture the anticipated currency gain. Conversely, if the currency managers have a view that the Swiss Franc would depreciate relative to the U.S. Dollar, they could overhedge (or completely hedge) the Swiss Franc to offset the impact of the falling Franc. By partially hedging, institutional investors can enhance their portfolio returns by actively managing their currency risk.
Source: J.P. Morgan Investment Analytics & Consulting estimates.
Since the U.S. Dollar is currently near all-time lows, we are seeing an increasing number of U.S. institutional investors revising, or at a minimum, reviewing their currency strategy. In our opinion at this point in time, it is certainly possible that the U.S. Dollar will bounce back, and that a strengthening dollar could have an adverse effect on the returns of international investments. Foreign exchange rate risk and security valuation risk are the two main types of investment risk associated with foreign investments. Security valuation risk in foreign positions is driven by a number of factors such as market, sector, industry and stock specific – similar to the risk associated with domestic investments. Foreign exchange rate risk is the risk associated with the ownership of foreign securities that are traded in a foreign currency. The FX risk is due to the implicit currency exposure when holding these foreign positions. Traditionally, when dealing with currency risk, institutional investors have relied on three primary options: maintain currency exposure, passively manage foreign currency exposure, or actively manage foreign currency exposure. Recently, J.P. Morgan Investment Analytics and Consulting has seen more plan sponsors treat currency as a separate asset class in an alpha-seeking strategy. In this article, we will make a case for active currency management through a pure currency alpha strategy. The argument for an alpha-seeking currency mandate is threefold. First, currency’s low correlation to other traditional asset classes makes it an ideal candidate for diversification. Secondly, an active currency manager can capitalize on the trending nature of the currency market. Lastly, there are inefficiencies in the currency market that present opportunities to capture profit.
ALPHA-SEEKING STRATEGIES
Unlike traditional hedging programs, currency alpha strategies are not constrained by the currency exposures of the portfolio. By managing currency as a separate asset class, plan sponsors can make a pure alpha play by using forward contracts and eliminating the need for any initial funding. In this
1
It is important to note that the effectiveness of the passive currency hedge is also dependent upon the efficiency of the currency trade execution.
SEPTEMBER 2008 EDITION — 5
CURRENCY MANAGEMENT
context, the currency managers are expected to add alpha (i.e., increase the overall risk-adjusted returns of the portfolio).
DIVERSIFICATION
The asset allocation of a typical institutional investor may include domestic and foreign equity, fixed income, real estate, and commodities. In our opinion, institutional investors may be able to reduce the overall risk of the portfolio by incorporating an alpha currency program into an established asset allocation. The addition of an asset class that is lowly or negatively correlated to the other major asset classes is a way to reduce the volatility of the overall plan and thus improve its risk/return profile. In Exhibit 2, it is evident that a currency allocation can help offset some of the volatility that a “traditional” portfolio may encounter. The currency markets, as measured by the U.S. Dollar Index (DXY), have a low to negative correlation to the stock, bond, real estate and commodity markets, making it an attractive portfolio diversifier.
The currency market is the world’s largest and most liquid market, with an average daily turnover of $3.2 trillion USD3. The daily currency turnover is more than ten times that of all of the world’s equity markets combined4. The volume can be attributed to a number of factors, including the different type of market participants and the various objectives they have for currency exchange. Currency exchange is employed by central banks to implement monetary policy, by commercial banks to manage cash flow, and by institutional investors to hedge exposure and enhance return. For example, many investment managers execute foreign exchange trades for the sole purpose of making funds available in the local trading currency to execute foreign stock or bond trades. A central bank’s motivation for being players in the currency market is to stabilize their domestic currency or stave off the forces of inflation. In fact, central banks may have to buy or sell currency at inopportune times to satisfy their primary goals. Corporations can have significant currency exposure from foreign operations, trading, or debt servicing obligations. Their greater interest lies in neutralizing their currency exposure rather than maximizing profits. With any active management strategy, there should be an exploitable market inefficiency in order for the strategy to be successful. Usually, this inefficiency comes at the cost of liquidity. In the currency market, we find the rare case where both are available.
SPOTLIGHT
Exhibit 2 - Correlation of U.S. Dollar Index (DXY) with Traditional Asset Classes2
USD Index Domestic Equity Foreign Equity Fixed Income Real Estate Commodities 1.00 0.03 -0.29 -0.21 -0.07 -0.19
CONCLUSION
As institutional investors continue to increase their allocation to international investments, especially in the emerging markets, a clear currency mandate is becoming an increasingly important part of portfolio management. Based on the goals, requirements and restrictions of the plan, the plan sponsor should review the currency policy in place and determine the optimal strategy. Leaving the portfolio completely un-hedged may leave the portfolio exposed to unwanted volatility. While a passive strategy will help neutralize the currency risk associated with foreign investments, on a long-term basis, a 100% hedge can only be right 50% of the time. Given the portfolio diversification effects, the exploitable opportunities present in the currency market, and the potential to increase the risk/reward profile of the overall portfolio, institutional investors may want to consider alpha-seeking strategies in order to cash on currency.
2
Source: J.P. Morgan Investment Analytics & Consulting estimates.
OPPORTUNITIES
The argument against active currency management is that the long-term investment in a currency of a developed country is essentially a zero-sum investment. The long-term expected returns of the major currencies are zero. During times of economic prosperity, the host nation’s currency will become stronger relative to other currencies. However, when the economic tides turn, it will eventually give back the previous gains. Currencies typically will move according to the outlook of a country’s economic data, and exchange rates tend to gain directional momentum and trend. In the short term, there is an inherent volatility as with any other asset class. However, over a longer time horizon, the economic health of the host nation should keep the momentum moving in the same direction. Exchange rate trends do persist for some time, resulting in an opportunity for skilled active managers to exploit currency swings.
3 4
The correlation coefficients are based on 17.5 years of historical data ending June 2008. The following indices were used as proxies for the asset classes shown in the table. Domestic Equity - Russell 3000 Index; Foreign Equity - MSCI EAFE Index (Net Div); Fixed Income - L.B. Aggregate Bond Index; Real Estate - NCREIF Property; Commodities - Dow Jones AIG Commodities Index. Source – Bank of International Settlements. Source – Bloomberg.
SEPTEMBER 2008 EDITION — 6
RISK MANAGEMENT
VALUE-AT-RISK: AN OVERVIEW OF ANALYTICAL VAR
by Romain Berry J.P. Morgan Investment Analytics and Consulting [email protected]
SPOTLIGHT
In the last issue, we discussed the principles of a sound risk management function to efficiently manage and monitor the financial risks within an organization. To many risk managers, the heart of a robust risk management department lies in risk measurement through various complex mathematical models. But even one who is a strong believer in quantitative risk management would have to admit that a risk management function that heavily relies on these sophisticated models cannot add value beyond the limits of understanding and expertise that the managers themselves have towards these very models. Risk managers relying exclusively on models are exposing their organization to events similar to that of the sub-prime crisis, whereby some extremely complex models failed to accurately estimate the probability of default of the most senior tranches of CDOs1. Irrespective of how you put it, there is some sort of human or operational risk in every team within any given organization. Models are valuable tools but merely represent a means to manage the financial risks of an organization.
This article aims at giving an overview of one of the most widespread models in use in most of risk management departments across the financial industry: Value-at-Risk (or VaR)2. VaR calculates the worst expected loss over a given horizon at a given confidence level under normal market conditions. VaR estimates can be calculated for various types of risk: market, credit, operational, etc. We will only focus on market risk in this article. Market risk arises from mismatched positions in a portfolio that is marked-to-market periodically (generally daily) based on uncertain movements in prices, rates, volatilities and other relevant market parameters. In such a context, VaR provides a single number summarizing the organization’s exposure to market risk and the likelihood of an unfavorable move. There are mainly three designated methodologies to compute VaR: Analytical (also called Parametric), Historical Simulations, and Monte Carlo Simulations. For now, we will focus only on the Analytical form of VaR. The two other methodologies will be treated separately in the upcoming issues of this newsletter. Part 1 of this article defines what VaR is and what it is not, and describes the main parameters. Then, in Part 2, we mathematically express VaR, work through a few examples and play with varying the parameters. Part 3 and 4 briefly touch upon two critical but complex steps to computing VaR: mapping positions to risk factors and selecting the volatility model of a portfolio. Finally, in Part 5, we discuss the pros and cons of Analytical VaR. that should always be kept in mind when handling VaR. VaR involves two arbitrarily chosen parameters: the holding period and the confidence level. The holding period corresponds to the horizon of the risk analysis. In other words, when computing a daily VaR, we are interested in estimating the worst expected loss that may occur by the end of the next trading day at a certain confidence level under normal market conditions. The usual holding periods are one day or one month. The holding period can depend on the fund’s investment and/or reporting horizons, and/or on the local regulatory requirements. The confidence level is intuitively a reliability measure that expresses the accuracy of the result. The higher the confidence level, the more likely we expect VaR to approach its true value or to be within a pre-specified interval. It is therefore no surprise that most regulators require a 95% or 99% confidence interval to compute VaR.
PART 2: FORMALIZATION AND APPLICATIONS
Analytical VaR is also called Parametric VaR because one of its fundamental assumptions is that the return distribution belongs to a family of parametric distributions such as the normal or the lognormal distributions. Analytical VaR can simply be expressed as: (1) where α • VaRα is the estimated VaR at the confidence level 100 × (1 – α)%. • xα is the left-tail α percentile of a normal distribution is described in the expression where R is the expected return. In order for VaR to be meaningful, we generally choose a confidence level of 95% or 99%. xα is generally negative. • P is the marked-to-market value of the portfolio. The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance. But even if we have a large enough sample of historical returns, is it realistic to assume that the returns of any given fund follow a normal distribution? Thus, we need to associate the return distribution to a standard normal distribution which has a zero mean and a standard deviation of
1
PART 1: DEFINITION OF ANALYTICAL VAR
VaR is a predictive (ex-ante) tool used to prevent portfolio managers from exceeding risk tolerances that have been developed in the portfolio policies. It can be measured at the portfolio, sector, asset class, and security level. Multiple VaR methodologies are available and each has its own benefits and drawbacks. To illustrate, suppose a $100 million portfolio has a monthly VaR of $8.3 million with a 99% confidence level. VaR simply means that there is a 1% chance for losses greater than $8.3 million in any given month of a defined holding period under normal market conditions. It is worth noting that VaR is an estimate, not a uniquely defined value. Moreover, the trading positions under review are fixed for the period in question. Finally, VaR does not address the distribution of potential losses on those rare occasions when the VaR estimate is exceeded. We should also bear in mind these constraints when using VaR. The ease of using VaR is also its pitfall. VaR summarizes within one number the risk exposure of a portfolio. But it is valid only under a set of assumptions
2
CDO stands for Collaterized Debt Obligation. These instruments repackage a portfolio of average- or poor-quality debt into high-quality debt (generally rated AAA) by splitting a portfolio of corporate bonds or bank loans into four classes of securities, called tranches. Pronounced V’ah’R.
SEPTEMBER 2008 EDITION — 7
RISK MANAGEMENT
one. Using a standard normal distribution enables us to replace xα by zα through the following permutation: (2) which yields: (3) zα is the left-tail α percentile of a standard normal distribution. Consequently, we can re-write (1) as: (4) replace in (4) the mean of the asset by the weighted mean of the portfolio, μp and the standard deviation (or volatility) of the asset by the volatility of the portfolio, σ p. The volatility of a portfolio composed of two assets is given by: (6) where • w1 is the weighting of the first asset • w2 is the weighting of the second asset • σ1 is the standard deviation or volatility of the first asset • σ2 is the standard deviation or volatility of the second asset • ρ1,2 is the correlation coefficient between the two assets And (4) can be re-written as: (7) Let us assume that we want to calculate Analytical VaR at a 95% confidence level over a one-day horizon on a portfolio composed of two assets with the following assumptions: • P = $100 million • w1 = w2 = 50%6 • μ1 = 0.3% • σ1 = 3% • μ2 = 0.5% • σ2 = 5% • ρ1,2 = 30%
SPOTLIGHT
EXAMPLE 1 – ANALYTICAL VAR OF A SINGLE ASSET
Suppose we want to calculate the Analytical VaR at a 95% confidence level and over a holding period of 1 day for an asset in which we have invested $1 million. We have estimated3 μ (mean) and σ (standard deviation) to be 0.3% and 3% respectively. The Analytical VaR of that asset would be:
This means that there is a 5% chance that this asset may lose at least $46,347 at the end of the next trading day under normal market conditions.
EXAMPLE 2 – CONVERSION OF THE CONFIDENCE
LEVEL4
Assume now that we are interested in a 99% Analytical VaR of the same asset over the same one-day holding period. The corresponding VaR would simply be:
(8) There is a 1% chance that this asset may experience a loss of at least $66,789 at the end of the next trading day. As you can see, the higher the confidence level, the higher the VaR as we travel downwards along the tail of the distribution (further left on the x-axis).
EXAMPLE 5 – ANALYTICAL VAR OF A PORTFOLIO
COMPOSED OF N ASSETS
From the previous example, we can generalize these calculations to a portfolio composed of n assets. In order to keep the mathematical formulation handy, we use matrix notation and can re-write the volatility of the portfolio as:
EXAMPLE 3 – CONVERSION OF THE HOLDING
PERIOD
If we want to calculate a one-month (21 trading days on average) VaR of that asset using the same inputs, we can simply apply the square root of the time5: (5) Applying this rule to our examples above yields the following VaR for the two confidence levels:
(9) where • w is the vector of the weights of the n assets • w’ is the transpose vector of w • Σ is the covariance matrix of the n assets Practically, we could design a spreadsheet in Excel (Exhibit 1) to calculate Analytical VaR on the portfolio in Example 4.
EXAMPLE 4 – ANALYTICAL VAR OF A PORTFOLIO
OF TWO ASSETS
Let us assume now that we have a portfolio worth $100 million that is equally invested in two distinct assets. One of the main reasons to invest in two different assets would be to diversify the risk of the portfolio. Therefore, the main underlying question here is how one asset would behave if the other asset were to move against us. In other words, how will the correlation between these two assets affect the VaR of the portfolio? As we aggregate one level up the calculation of Analytical VaR, we
3
4 5
6
Note that these parameters have to be estimated. They are not the historical parameters derived from the series. Note that zα is to be read in the statistical table of a standard normal distribution. This rule stems from the fact that the sum of n consecutive one-day log returns is the nday log return and the standard deviation of n-day returns is √n × standard deviation of one-day returns. These weights correspond to the weights of the two assets at the end of the holding period. Because of market movements, there is little likelihood that they will be the same as the weights at the beginning of the holding period.
SEPTEMBER 2008 EDITION — 8
RISK MANAGEMENT
Exhibit 1 – Excel Spreadsheet to calculate Analytical VaR for a portfolio of two assets
Analytical VaR
Expected parameters p w1 w2
SPOTLIGHT
PART 4: VOLATILITY MODELS
We can guess from the various expressions of Analytical VaR we have used that its main driver is the expected volatility (of the asset or the portfolio) since we multiply it by a constant factor greater than 1 (1.6449 for a 95% VaR, for instance) – as opposed to the expected mean, which is simply added to the expected volatility. Hence, if we have used historical data to derive the expected volatility, we could consider how today’s volatility is positively correlated with yesterday’s volatility. In that case, we may try to estimate the conditional volatility of the asset or the portfolio. The two most common volatility models used to compute VaR are the Exponential Weighted Moving Average (EWMA) and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH). Again, in order to be exhaustive on this very important part in computing VaR, we will discuss these models in a future article.
100,000,000 50% 50% 0.3% 3% 0.5% 5% 30% 0.40% 3.28% Exposures Covariance Matrix Standard Deviation Correlation Matrix
Asset 1 0.03
Asset 2 0.05
μ1 σ1 μ2 σ2
p1,2
1 0.3
0.3 1
Σ
μp σp
Confidence level 95% -1.6449
0.00090 0.00045
0.00045 0.00250
PART 5: ADVANTAGES AND DISADVANTAGES OF ANALYTICAL VAR
Analytical VaR is the simplest methodology to compute VaR and is rather easy to implement for a fund. The input data is rather limited, and since there are no simulations involved, the computation time is minimal. Its simplicity is also its main drawback. First, Analytical VaR assumes not only that the historical returns follow a normal distribution, but also that the changes in price of the assets included in the portfolio follow a normal distribution. And this very rarely survives the test of reality. Second, Analytical VaR does not cope very well with securities that have a non-linear payoff distribution like options or mortgage-backed securities. Finally, if our historical series exhibits heavy tails, then computing Analytical VaR using a normal distribution will underestimate VaR at high confidence levels and overestimate VaR at low confidence levels.
w1
0.5 0.00068 0.00148 0.00108 0.03279 4,993,012
0.5
Σw
σ 2=w’Σw σ
VaR
Grey = input cells Source: J.P. Morgan Investment Analytics & Consulting.
.77
CONCLUSION
As we have demonstrated, Analytical VaR is easy to implement as long as we follow these steps. First, we need to collect historical data on each security in the portfolio (we advise using at least one year of historical data – except if one security has experienced high volatility, which would suggest a shorter period of time). Second, if the portfolio has a large number of underlying positions, then we would need to map them against a more manageable set of risk factors. Third, we need to calculate the historical parameters (mean, standard deviation, etc.) and need to estimate the expected prices, volatilities and correlations. Finally we apply (7) to find the Analytical VaR estimate of the portfolio. As always when building a model, it is important to make sure that it has been reviewed, fully tested and approved, that a User Guide (including any potential code) has been documented and will be updated if necessary, that a training has been designed and delivered to the members of the risk management team and to the recipients of the outputs of the risk management function, and finally that a capable person has been allocated the oversight of the model, its current use, and regular refinement.
It is easy from there to expand the calculation to a portfolio of n assets. But be aware that you will soon reach the limits of Excel as we will have to calculate n(n-1)/2 terms for your covariance matrix.
PART 3: RISK MAPPING
In order to cope with an increasing covariance matrix each time you diversify your portfolio further, we can map each security of the portfolio to common fundamental risk factors and base our calculations of Analytical VaR on these risk factors. This process is called reverse engineering and aims at reducing the size of the covariance matrix and speeding up the computational time of transposing and multiplying matrices. We generally consider four main risk factors: Spot FX, Equity, Zero-Coupon Bonds and Futures/Forward. The complexity of this process goes beyond the scope of this overview of Analytical VaR and will need to be treated separately in a future article.
Opinions and estimates offered in this Investment Analytics and Consulting newsletter constitute our judgment and are subject to change without notice, as are statements of financial market trends, which are based on current market conditions. We believe the information provided here is reliable, but do not warrant its accuracy or completeness. References to specific asset classes, financial markets, and investment strategies are for information purposes only and are not intended to be, and should not be interpreted as, recommendations or a substitute for obtaining your own investment advice. This document contains information that is the property of JPMorgan Chase & Co. It may not be copied, published, or used in whole or in part for any purposes other than expressly authorized by JPMorgan Chase & Co. www.jpmorgan.com/visit/iac
SEPTEMBER 2008 EDITION — 9
GLOBAL CAPITAL MARKETS
U.S. CURRENCY
by Manpreet Hochadel, CFA J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF AUGUST 2008
1.60 1.50 US Dollar vs. EURO 1.40 1.30 1.20 1.10 1.00 0.90 0.80 Dec-98 Dec-99 Dec-00
US Dollar vs. EURO and Japanese Yen
0.0110
0.0100 US Dollar vs. JPY
JPY Right Scale
0.0090
0.0080
EURO Left Scale
Dec-01
Dec-02
Dec-03
Dec-04
Dec-05
Dec-06
Dec-07
0.0070 Dec-08
Source: J.P. Morgan Investment Analytics and Consulting
• The U.S. Dollar recovered some of the losses of the past few years against both the Euro and Yen, as the Euro-zone and Japanese economies showed signs of weakening and the U.S. Federal Reserve hinted at monetary tightening in the future.
U.S. FIXED INCOME
by Manpreet Hochadel, CFA J.P. Morgan Investment Analytics and Consulting [email protected]
AS OF AUGUST 2008
5.00%
US Treasury Yield Curve
4.00% December 31, 2007 August 31, 2008 3.00% June 30, 2008
2.00%
1.00% 2 5 10 20 30 Yr.
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
• The U.S. Treasury yield curve steepened as rates continued to fall across the entire yield curve.
SEPTEMBER 2008 EDITION — 10
GLOBAL CAPITAL MARKETS
EUROPEAN
AND
CORNER
ASIAN CURRENCIES
AS OF JULY 2008
Swiss Franc vs GBP, EUR & USD
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4
by Simreet Gill J.P. Morgan Investment Analytics and Consulting [email protected]
Pound Sterling vs USD and EUR
2.2 2 1.8 1.6 1.4 1.2 1 2001 2002 2003 2004 GBP/USD 2005 2006 GBP/EUR 2007 2008
0.3 2001
2002
2003
2004
2005 CHF/EUR
2006
2007 CHF/USD
2008
CHF/GBP
Norwegian Krone vs EUR, USD & GBP
0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 2001 2002 2003 NOK/EUR 2004 2005 NOK/USD 2006 2007 NOK/GBP 2008
• The uptrend in EUR/GBP over the past six months through July reflected the risk of an independent implosion in the UK economy. The economy is certainly buckling under the post-credit crisis strain but so too is the Euro area, a story which is much more recent. (Morgan Markets)
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Japanese Yen vs GBP, EUR, USD & AUD
0.018 0.015
Australian Dollar vs GBP, EUR & USD
1
0.8 0.012 0.009 0.006 0.4 0.003 0.000 2001 2002 JPY/GBP 2003 2004 JPY/EUR 2005 2006 JPY/USD 2007 2008 JPY/AUD 0.2 2001 0.6
2002
2003
2004
2005 AUD/EUR
2006
2007 AUD/USD
2008
AUD/GBP
Chinese Yuan vs EUR, USD & JPY
17 16 15 14 CNY/JPY 13 12 11 10 9 8 2001 0.06 2002 2003 CNY/EUR 2004 2005 2006 2007 2008 CNY/USD CNY/JPY 0.08 0.12 0.1 0.14 CNY/ USD & EUR 0.16
• There has been a growing divergence between the falling equity markets and the lagged response of Asian FX lately. The key concern is whether Asian currencies will catch up with falling equities. At a superficial level, this equity:FX correlation is being driven by international portfolio equity flows. However, the ultimate drivers for these flows are expectations for the global growth cycle and how these may impact export and corporate earnings in the future. (Morgan Markets)
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
SEPTEMBER 2008 EDITION — 11
GLOBAL MARKET INDICES
ASSET CLASS RETURN COMPARISON (INCLUDING U.S.)
by William Pometto J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF AUGUST 2008
Index
L.B. AGGREGATE BOND INDEX M.L. HIGH YIELD INDEX MSCI EMERGING MARKETS FREE MSCI-Eafe (Net) RUSSELL 1000 GROWTH (Gross) RUSSELL 2000 VALUE (Gross) RUSSELL 3000 INDEX (Gross) S & P 500 - CAP. WEIGHTED
Monthly Return
0.95 0.32 (7.95) (4.05) 1.08 4.75 1.55 1.45
Trailing 3 Months
0.79 (3.91) (20.18) (14.73) (7.99) (0.44) (7.57) (7.89)
Year To Date
2.00 (2.62) (21.67) (17.31) (9.83) (0.71) (10.39) (11.39)
1 Year
5.86 (1.42) (9.83) (14.41) (6.77) (7.52) (10.22) (11.14)
2 Year
5.56 2.48 13.96 0.80 4.76 (0.69) 1.58 1.15
3 Year
4.26 3.42 19.38 8.08 4.39 3.59 3.92 3.67
5 Year
4.61 6.87 23.89 13.86 6.10 10.25 7.57 6.93
10 Year
5.58 4.23 17.72 6.34 2.59 11.28 5.52 3.11
30 25 20 15 10 5 0 -5 -10 -15 -20 -25 Current Month 3 Months Return MSCI EMERGING MARKETS FREE MSCI-Eafe (Net) Year to Date 1 Year 2 Year 3 Year 5 Year 10 Year
M.L. HIGH YIELD INDEX L.B. AGGREGATE BOND INDEX
RUSS-Russell 1000 Growth (Gross) S & P 500 - CAP. WEIGHTED
RUSS-Russell 3000 (Gross) RUSS-Russell 2000 Value (Gross)
U.S. EQUITY • U.S. Stock Markets avoided a third straight down month, posting modest gains in August. • Much of the upward momentum was driven by declining oil prices. • Value stocks experienced the biggest lift with the Russell 2000 Value Index posting a 4.75 percent gain for the month. • The S&P 500 and NASDAQ Composite added 1.45 percent and 1.92 percent respectively. INTERNATIONAL EQUITY • International Markets performed poorly in August. • Investor concern continues over the slumping United States economy and how it will affect international markets. • The strengthening U.S. dollar has also negatively impacted international market returns. • The Emerging Markets were hit the hardest, as evidenced by the 7.95 percent loss for the MSCI Emerging Markets Free Index in August.
FIXED INCOME • Fixed Income Markets were a safe bet for August. • Government bonds continued to post respectable gains. • The L.B. Government Long Term Index posted a 2.32 percent return for the month, putting it up 3.75 percent year to date. REAL ESTATE • Real Estate Markets haven't improved as mortgage concerns still exist. • Home sales continued to slow.
SEPTEMBER 2008 EDITION — 12
GLOBAL MARKET INDICES
GLOBAL EQUITIES (EXCLUDING U.S.)
by Simreet Gill J.P. Morgan Investment Analytics and Consulting [email protected]
CORNER
AS OF JULY 2008
Europe
12,000 10,000 8,000 6,000 4,000 2,000 0 2000 2001 2002 FTSE 100 2003 CAC 2004 DAX 2005 Swiss Markets 2006 MSCI Europe 2007 2008 180 160 140 120 100 80 60 40 20 0
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
• The financial markets have remained highly unstable in July, owing in part to the troubles at GSEs such as Freddie Mac. Equities have been slowly grinding through the cyclical slowdown triggered by a housing bust, credit crunch, and commodity price pressures. • In July, equities saw a month of two halves with sharp falls in the first half and a rebound of equal magnitude and intensity in the second half. The downshift in global growth indicators
earlier in the month triggered further declines in global equity markets. In particular, the abrupt weakening in European and Japanese growth into midyear, combined with signs that global industrial activity is now contracting, marked a sharper downshift in momentum than the consensus anticipated. Later in the month, sharply lower oil prices and short covering in financials helped equity markets to more than retrace their losses seen in the first two weeks of July. (Morgan Markets)
Australia, Hong Kong, Singapore
5,000 4,000 3,000 2,000 1,000 0 2000 2001 2002 2003 2004 2005 2006 2007 2008
Australia (AS51) Hong Kong (Hang Seng) Singapore (Straits Times)
Japan (Nikkei 225)
250 200 150 100 50 0 2000 2001 2002 2003 2004 2005 2006 2007 2008
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
Korean (KOSPI)
1.8 1.5 1.2 0.9 0.6 0.3 0 2000
• Resource-consuming emerging markets such as India and China, which had been sharply sold off owing to growing inflationary concerns on rising commodity prices, picked up. The Japanese market had the second largest fall among major developed nations after England. However, while the Japanese market has tended to be as highly volatile as emerging markets recently, we think movement in the Japanese market in July was only slight compared with the sharp movement in emerging markets. (Morgan Markets)
2003 2004 2005 2006 2007 2008
2001
2002
Source: J.P. Morgan Investment Analytics and Consulting, Bloomberg
SEPTEMBER 2008 EDITION — 13
