Economics of Sovereign Wealth Funds

Chapter 12 Managing a Sovereign Wealth Fund: A View from Practitioners

Udaibir Das, Adnan Mazarei, and Han Hoorn
Published Date:
December 2010
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Sovereign wealth funds (SWFs) often have dual natures, serving both nonfinancial and financial objectives. On the one hand, they are created to achieve domestic and political aims, which can lead to strategic investments motivated by politics or by social policy. On the other hand, they are purely financial investment vehicles, created to protect and expand the capital entrusted to them. Explicitly recognizing the dual nature of a wealth fund helps to clarify its objectives and governance. The ideal—and the view followed in this chapter—is to segregate the two functions: one arm pursuing the nonfinancial goals under political governance, and a second arm with purely financial goals. Indeed, the nonfinancial goals will often be better served when the financial objectives are being met.

In this view, SWFs resemble endowment funds and can successfully learn from such funds’ investment models. Endowment funds’ investment practices have been studied and implemented by talented and successful investors for decades. Having a long-term horizon puts the investor in a unique and favorable position in the market. It drives the institution’s organization and governance, its investments, and its perception of risk, and therefore its asset management practices.

SWFs, however, differ from endowment funds in two important respects. First, although SWFs’ asset growth comes from both investment returns and contributions of new assets (as for endowment funds), new contributions to SWFs are usually linked to taxation on exports, which often follows commodity prices. Second, because of their dual nature (nonfinancial as well as financial objectives), an SWF may be called on to transfer assets to its nonfinancial arm to support political objectives. These specific features (correlation with commodity prices and the possibility of liquidity calls) modify the composition of wealth funds’ utility functions and attention must be paid to mitigating these risks.

This chapter examines a conceptual framework for advising SWFs on portfolio allocation and construction, together with application of the framework in practice.2 The first and second sections focus on the conceptual framework unique to SWFs: (1) their perceptions of asset risks and returns as long-term investors, and (2) the particular form of their utility function and how it incorporates both return expectations and cost of risks. The third section describes implementation of the conceptual framework.


Being a long-term investor means taking advantage of low redemption risk. Long-term investment does not imply focusing on return only and ignoring risk, because risk management has short- and long-term consequences for wealth creation. Neither does long-term investment imply slavishly following long-term economic forecasts, which are themselves notoriously uncertain.

There are two ways to benefit from low redemption risk. The first is to increase the asset allocation toward illiquid assets and earn the resulting higher return (the illiquidity premium). The second is to invest in liquid assets but choose a long-term risk-return metric and an allocation that maximizes long-term wealth creation with higher short-term volatility.

All SWFs exhibit redemption risks lower than the market average, but that redemption risk is not zero. Because of their dual mission to generate financial as well as social returns, their redemption risk is most probably higher than that of other long-term investors, such as endowment funds. SWFs will, therefore, benefit by maintaining liquidity and focusing on the second method of exploiting their favorable position in the market.

Long-Term Assets’ Returns

Gaining an understanding of long-term attributes requires that long periods of history be examined. Equities have historically returned more than other asset classes. In the United States since 1800, there has been no single 25-year period in which common stocks had a negative real return. For 85 percent of the periods, long-term government bonds would have returned less than common stocks (Siegel, 2007). For a shorter reference period—the last 80 years, say, to improve the macroeconomic homogeneity of the sample—the conclusion is the same (see Table 12.1). Over the long run, across many economic cycles, the market remunerates risk takers—investors who put more value at risk get higher returns.

TABLE 12.1Real Returns Across U.S. Asset Classes, 1928–2008
Asset classReal returns1Volatility2
U.S. treasury bills, 1-month0.71.8
U.S. government bonds, 10-year2.15.9
Corporate bonds, 10-year, Aaa2.75.0
Corporate bonds, 10-year, Baa3.76.0
Equities (S&P 500)5.919.4
Sources: Global Financial Data (; U.S. Federal Reserve (www.federal; Shiller (

Continuously compounded rates of real returns over the period, annualized, in percent.

Annualized standard deviations of monthly returns.

Sources: Global Financial Data (; U.S. Federal Reserve (www.federal; Shiller (

Continuously compounded rates of real returns over the period, annualized, in percent.

Annualized standard deviations of monthly returns.

Within the equity asset class, returns vary significantly, contrasting value versus growth, or large capitalization (cap) versus small cap (Table 12.2).3

TABLE 12.2Real U.S. Equity Returns by Category, 1925–2008
Equity categoryReal equity returns1
Large-cap growth5.5
Small-cap growth6.2
Large-cap value7.7
Small-cap value10.6
Source: Renaissance Investment Management.

Continuously compounded rates of real returns over the period, annualized, in percent.

Source: Renaissance Investment Management.

Continuously compounded rates of real returns over the period, annualized, in percent.

Equities have returned more on average than bonds and are expected to continue to do so. The higher average return makes a substantial difference over time and should attract SWFs’ attention. Based on history, a fund invested in the Standard & Poor’s 500 index (S&P 500) would, after 20 years, be worth three times more than a fund invested in treasury bills, on average.

Private equities have recently been popular with endowment funds. Private equities can produce even higher returns than listed equities, but with a larger dispersion of returns and medium-term liquidity constraints. SWFs must analyze the risk of redemption in recessions when nonfinancial objectives might take the lead. The probability is high that a product with a medium-term lock-up—for instance, more than seven years—will cross an economic downturn during its lifetime. The distribution of the length of economic cycles in the United States since 1900 exhibits a 4-year median duration and a 2.6-year standard deviation.

Long-Term versus Short-Term Risk-Return Trade-Offs

Although equities provide higher average returns than any other asset class over the long run, they also exhibit higher volatility and value-at-risk (VaR), which means they are riskier than other asset classes. Its long-term horizon, however, means an SWF will assess the trade-off between risk and return differently from a short-term investor. Therefore, the question is whether a long-term investor will suffer from higher risk when investing in assets with higher volatility and VaR.

Risk is a slippery concept, but as a working definition, risk is captured by the distribution of profits and losses (P&L), as shown in panel a of Figure 12.1. Generally speaking, a distribution that is less spread out will be less risky and, provided it has the same mean as a distribution that is more spread out, will be preferred by investors; panel b of Figure 12.1 shows a more risky versus less risky distribution. Other popular summary risk measures, in addition to volatility, are VaR, expected shortfall, and expected drawdown. None of these risk measures will change the conclusion that equities are riskier than bonds over the short run.

Figure 12.1Distribution of Returns

Source: Authors’ compilation.

Note: P&L = profit and loss.

In the real world, assets are difficult to rank by riskiness. The real world is more like panel c of Figure 12.1, with lower volatility associated with lower mean return. In such a case there is no unique ranking of riskiness and investors’ risk preferences will matter.

Most risk measures focus on short periods for which the mean return is not critical. Because many SWFs target long-term wealth creation, they have to look at risk in a different manner. Over the long term, the mean return becomes important and the relative ranking of assets’ riskiness can change, simply because the mean return grows relative to the volatility. Figure 12.2 shows diagrammatically what will happen for low-volatility bonds and high-volatility equities over a short period and a long period. For the shorter period, the means are close enough that the distributions overlap substantially and an investor is more likely to suffer losses from equities. Equities will be risky relative to bonds.

Figure 12.2Diagrammatic Representation of VaR for Higher-Volatility Equities Shifting Below VaR for Lower-Volatility Bonds

Source: Authors’ compilation.

For the longer period, however, the mean of the returns on equity shifts the distribution up enough that the distributions overlap less. Extreme losses are still more likely for stocks but so are large gains, while moderate losses are much more likely for bonds. The investor’s preferences for gains versus losses will determine the exact trade-off between stocks and bonds, but it should be clear that the tradeoff differs when considering a long period versus a short period.

Figure 12.3 demonstrates the effect from a slightly different perspective. The figure shows the empirical frequency of losses worse than specific levels for the period 1907–2008. Panel a shows that the probability of large losses (more than 10, 20, or 30 percent) is higher for equities than for bonds for a one-year holding period. Panel b shows that for a seven-year holding period, the situation reverses, with the probability of large losses being lower for equities than for bonds. This is a result of the higher average return for equities offsetting the higher volatility for the longer period.

Figure 12.3Empirical Distribution of Losses Based on Historical Returns, 1907–2008

Sources: Global Financial Data (; authors’ calculations.

The end result is that a short-term investor will consider an investment in U.S. government bonds to be a safer strategy than an investment in equities, while a long-term investor could have the opposite view.

Single Asset Class Strategies Are Not Appropriate for SWFs

Equity Risk over the Economic Cycle

Although equities generally outperform bonds and ensure better capital protection over the long term, exceptions occur (Bernstein, 1996). Returns will vary over time and can do so in a consistent manner over the economic cycle. Investors may experience significant shifts in the risk-return relationship if, for example, they invest at the early stage of a recession phase or the early stage of an expansion phase (Table 12.3). In an early expansion phase, the more capital an investor puts at risk, the higher the return that might be expected over time. If the investment is made in an early recession phase, the correlation between risk and return turns negative and the more capital an investor puts at risk, the higher the loss that might be suffered.

TABLE 12.3U.S. Assets’ Returns in Early Recession and Expansion Phases, 1928–2008
Asset classReal return, early

recession phase (%)
Real return, early

expansion phase (%)
U.S. treasury bills, 1-month2.7–0.1
U.S. government bonds, 10-year2.2–0.6
Corporate bonds, 10-year, Aaa1.13.9
Corporate bonds, 10-year, Baa–2.06.4
Equities (S&P 500)–22.911.0
Sources: U.S. Federal Reserve (; Global Financial Data (
Sources: U.S. Federal Reserve (; Global Financial Data (

Precise timing with respect to the economic cycle is not possible, but at any point an investor can know with some confidence which phase the economy is not in. When performing portfolio simulations and allocations, such phases can be excluded from the analysis and allocations chosen based on the reduced choice set.

The conclusion is that investing in equities only for the long run cannot protect an SWF from significant wealth destruction in the short run, particularly in recession phases. A large loss, even if only temporary, may not be bearable by the SWF.

Long-Term Drawdown Risk for Single Asset Class Investment Strategies

Maximum drawdown is a summary risk measure particularly suited to SWFs’ long horizons. A drawdown is the peak-to-trough loss that an investor would suffer if the investor invests at a maximum of the market and sells at the minimum, before the recovery. It captures the maximum loss that an investor could have experienced over the period. Over 80 years’ history for the United States, Table 12.4 shows that all asset classes have suffered extremely high drawdowns in real terms.

TABLE 12.4Drawdowns by Asset Class, 1928–2008
Asset classMaximum


drawdown (%)



U.S. treasury bills, 1-month4905/3311/5104/97
U.S. government bonds, 10-year6011/4009/8107/89
Corporate bonds, 10-year, Aaa5111/4009/8102/86
Corporate bonds, 10-year, Baa3709/7709/8109/84
Equities (S&P 500)7908/2906/3202/45
Sources: Renaissance Investment Management; Global Financial Data (
Sources: Renaissance Investment Management; Global Financial Data (

An investment in treasury bills, for instance, would have barely protected the capital over the whole period and would have incurred significant purchasing-power losses, almost 50 percent at a maximum. It took 45 years to recover the loss from the trough. The SWF investment model should search for alternatives that avoid large and prolonged purchasing-power losses. This chapter argues that this objective can be met by combining assets (multi-asset-class strategies) in such a way that the risk is reduced and the probability of large drawdowns is reduced, using either static allocation or dynamic allocation.


SWFs differ from other long-term investors for two important reasons—their dual nature (they serve both strategic and financial objectives) and, in most cases, their potential exposure to commodity price fluctuations. These specific features affect their financial objectives and constraints, and are most concisely incorporated by carefully defining the utility function. Precisely defining a fund’s utility function is an extremely valuable exercise because it helps decision makers set up structures, assign clear mandates, and establish benchmarking processes to measure performance.

Utility Function

Distinction Between Strategic Utility and Financial Utility

An SWF pursues financial objectives that may translate into strategic objectives, either planned and mandated, such as the funding of pension schemes, or on a one-time basis, such as during an economic downturn. Strategic objectives may include equity investment in strategic sectors (politically mandated investment in sectors considered important for political reasons, such as energy or high technology), but they may also include a wealth transfer to the government budget to support social policies.

Strategic objectives may be pursued at the expense of financial objectives. To avoid potential conflicts, SWFs can split their activities, teams, and legal bodies to separate strategic from financial objectives. This separation can be facilitated and highlighted by the exercise of defining the utility function. The conceptual distinction between the two sets of objectives in the utility function aids in translating the distinction into practical structures and mandates.

One study (Bernstein, Lerner, and Schoar, 2009) examines the relationship between funds’ organizational structures and their private equity investments. The conclusion is that mixing strategic objectives with financial objectives leads to a higher likelihood of investing at home and to conflicts between financial targets and strategic objectives: “SWFs with external managers tend to invest in lower P/E industries, which see an increase in the P/E ratios in the year after the investment. By way of contrast, funds with politicians involved invest in higher P/E industries, which have a negative valuation change in the year after the investment” (Bernstein, Lerner, and Schoar, 2009, p. 28). The results of this study argue for a clear separation of the strategic and the financial parts of the SWF’s utility function.

Figure 12.4 shows a pro forma utility function for an SWF, separating the utility into strategic and financial components. Figure 12.5 concentrates on the financial component.

Figure 12.4SWF Utility Function Components

Source: Authors’ compilation.

Figure 12.5Financial Utility Function for an SWF

Source: Authors’ compilation.

Mathematical Translation of the Financial Utility Function

The mathematical definition of a financial utility function requires a comprehensive understanding of both purchasing-power expectations and the cost of risk. The standard approach to portfolio optimization (mean-variance optimization) assumes utility depends on only the mean or expected return and the volatility of that return, as measured by its variance. This simple utility function is appropriate when either the distribution of returns is normal (in that case, the mean and variance completely describe the distribution) or investors actually care only about expected return and volatility.

For SWFs, such a utility function is generally too simplistic. The wealth component of utility must specify a target for purchasing power in the denominated currency. The cost or risk component of utility must be expanded; risk as a linear function of volatility may not be appropriate. First, risk measures such as VaR, expected shortfall, or drawdown risk may be included in addition to volatility. A normal distribution need not include VaR or expected shortfall because these measures will be simple functions (multiples) of volatility. In practice, distributions of returns have fat tails and VaR or expected shortfall will help measure the loss the fund can suffer without being forced to modify its investment philosophy. Second, liquidity measures may be included. These will depend on the amounts the fund could be requested to transfer to the strategic arm in the short term. Third, the unique funding position of SWFs—often from commodity revenues—means that correlations with particular asset classes may be specifically included.

The different components are blended into one utility function, written as

This utility function can be used by portfolio managers to monitor asset allocation and risk parameters. The expected return function is based on assets’ yields and valuation models. The cost of risk function depends on the SWF’s risk metric and takes into account assets’ idiosyncratic risks, asset dependencies, and the SWF’s risk preferences.

Cost of Risk

Assets’ Idiosyncratic Risks

The P&L distribution of an asset incorporates all aspects of idiosyncratic risk, but it is generally convenient to concentrate on one or another risk measure that summarizes the variability of the distribution. Volatility (measured by standard deviation) is useful for its simplicity. In practice, there are additional risk measures that are as or more suitable:

  • The tail of the P&L distribution, which is essentially a VaR measure but accounts for long periods and incorporates mean growth.
  • Drawdown risk, which captures the possibility of serial correlation of losses leading to cumulated and prolonged diminution of wealth.
  • Risk and return conditional on the economic and financial environment.

The traditional VaR measures the lower tail of the distribution. It is a loss threshold, with a certain probability of losing more than that threshold amount at the end of a period. The period is usually short and the VaR is usually calculated as a deviation from the mean or median. As argued above (see also Figure 12.2), the growth in the mean can be important for long-term investment and it is thus important to consider the distribution and the lower tail, including the mean growth.

Financial transactions exchange utilities between market participants, that is, expected trade-offs between return and risk as well as risk appetite. The interconnection between market participants creates positive feedback mechanisms that can lead to self-fulfilling prophesies, particularly for the demand for cash or its counterpart, the so-called market risk appetite. Such feedback mechanisms can create extended periods of good or bad results and produce, for low returns, persistent underperformance. The drawdown risk measure is intended to capture persistency, that is, to be sensitive to persistence and serial correlation in losses.

Figure 12.6 shows drawdown and evidence of persistence in returns for the S&P index. The horizontal axis represents drawdown in year t + 1, that is, the maximum peak-to-valley percentage return during the year t + 1. The vertical axis represents the frequency (probability) of that drawdown. Each of the four lines represents a specified level of drawdown in year t (for example, drawdown worse than 10 percent or drawdown worse than 20 percent). From Figure 12.6, we can see that the curves for higher drawdowns in year t are above the curves for lower drawdowns. This represents persistence: the probability of a severe drawdown in year t + 1 increases after a large drawdown in year t.

Figure 12.6Drawdown Risk as a Function of Past Drawdown

Current drawdown from highest price in the past year

Sources: Shiller (; authors’ calculations.

Note: S&P 500 return data 1900–2009. Drawup means that the current price is the highest one for one year.

Asset Dependencies


Diversification is a well-known way to reduce risk and is the foundation of all modern portfolio theory. The risk of two assets held together will generally be lower than the sum of the risks of the assets held individually. Volatility is an example of a risk measure that exhibits this diversification effect. The linear correlation coefficient, which ranges between —1 and +1, is a measure of the degree of comovement between two assets: when the correlation is less than +1, the volatility of a portfolio will be less than the sum of the volatilities of the individual assets. This holds for most commonly used risk measures, including volatility or standard deviation. However, it does not necessarily hold for VaR, unless losses are linear combinations of underlying elliptically distributed risk factors.

Table 12.5 shows the correlations between major asset classes for the United States.

TABLE 12.5Return Correlation Matrix, Real U.S. Assets, 1945–2008
Asset classU.S.









10-year, Aaa



10-year, Baa

(S&P 500)
U.S. treasury bills, 1-month1
U.S. government bonds, 10-year0.351
Corporate bonds, 10-year, Aaa0.430.851
Corporate bonds, 10-year, Baa0.460.740.901
Equities (S&P 500)
Source: Renaissance Investment Management.
Source: Renaissance Investment Management.

Compared with volatility and risk of assets considered individually, however, asset dependencies or correlations are difficult to estimate. The number of correlations grows quadratically with the number of assets, so that the number of parameters quickly grows large relative to the number of observations. Furthermore, joint normality may not be a good description of return data and an appropriate description of dependence across assets may well require more than a single correlation per asset pair. This again increases the number of parameters relative to observations and further aggravates the estimation problem. These problems are particularly acute for the tails of the distribution, exactly where dependencies are most critical.

There are two common approaches to handling correlation and asset dependence for the tail of the portfolio distribution:

  • The bottom-up approach attempts to estimate the conditional dependence of assets in rare events only (but generally still relying on joint normality). Portfolio managers using such an approach might modify the correlation matrix to account for assets’ joint behavior in stressed periods. Such an approach is situation-dependent, given that local or conditional correlations can be very unstable.
  • The top-down approach is based on the idea that fitting a single asset’s distribution gives a high degree of statistical robustness. The return of the overall portfolio is calculated and the distribution fitted as a single synthetic asset. Elements of the conditional correlation between assets will be embedded in the distribution, together with the idiosyncratic behavior of each asset. The distribution fit could then be extrapolated to estimate in a more robust manner rare events that have never occurred.

One reason most statistical models failed to anticipate the proper level of risk during the global financial crisis of 2007—09 is because of the structural lack of statistical information on asset dependencies.

Conditional Dependence of Assets

Risk is time dependent. Asset dependencies that might be unreliable in the short term can exhibit structures at longer terms. Figure 12.7 shows the correlation of various asset classes with inflation over increasingly longer periods. The figure illustrates that the strength of the correlation increases as the time scale increases. A long-term investor will consider asset dependencies over the long run and try to bypass the inherent instability of asset dependencies using other top-down risk indicators as well as by measuring conditional risks.

Figure 12.7Correlation of Asset Classes with Inflation, 1900–2009

Sources: Shiller (; Global Financial Data (; authors’ calculations.

Risk is also dependent on economic growth. Risk and return vary across the business cycle and market phases, and analysts attempt to capture differences in risk and correlation structures conditional on specific market phases. Figure 12.8 shows the return/risk ratio, also called the information ratio, for U.S. equities and government bonds as a function of the economic phase. Over the long term, equities and bonds exhibit a low but positive correlation. However, information ratios are desynchronized, leading to increased diversification power of government bonds in early recession phases. This is why government bonds can be seen as a protection against financial accidents.

Figure 12.8Return-to-Risk Ratio Across the Economic Cycle, Equities (S&P 500) and Debt (U.S. Treasury Bond, 10-Year), Annualized Real Returns and Volatilities, 1900–2009

Sources: Shiller (; Global Financial Data (; authors’ calculations.


This section describes how this chapter’s authors, as wealth fund managers, have put the framework discussed above into practice, combining quantitative research and long-term asset management experience.

Static Allocation versus Dynamic Allocation

Static Allocation

Static allocation means an allocation of assets that is not based on the present economic environment. Developing a static allocation involves analyzing asset risk and dependencies over a long period (over many business cycles)—including times of high and low inflation, high and low equity risk premiums, and various economic growth situations—and calculating the optimal allocation on the long-term efficient frontier.

The standard portfolio allocation process of modern portfolio theory involves the efficient frontier, plotting returns as a function of volatility, and choosing the best possible asset allocation over a period. The process can be extended to incorporate a measure of real drawdowns. We use genetic algorithm techniques that create random populations of portfolios and mutate them to mimic a Darwinian selection process. The utility function, or “fitness,” of any portfolio includes the portfolio return together with a cost of risk, counted negatively, for instance, the maximum drawdown multiplied by a scaling parameter.

The algorithm randomly generates a large number of candidate solutions (portfolios). Each portfolio is defined by its genes, that is, its allocations to the underlying assets. The best candidates survive; the worst ones are eliminated and replaced by a new population of survivors or “children” (resulting from a recombination of “parents’ genes” and from random mutations of genes). The process is repeated many times to converge toward an optimal or near-optimal set of solutions.

Genetic algorithms are nothing but optimization tools but with two major qualities:

  • The fitness function can include a variety of risk components, such as moments, drawdowns, correlation to various indices, and so forth. This flexibility is particularly important for monitoring complex utility functions, as described in the section above titled Mathematical Translation of the Financial Utility Function.
  • Genetic algorithms can explore a vast universe of solutions relatively quickly.

Static allocation is simple to implement and is a first step toward risk mitigation. The strategy does not, however, address the issue of model uncertainty and data (particularly correlation) instability. It can be quite rigid, particularly in times of crisis when asset correlations increase in tandem with market volatilities.

Among the most significant issues is that static allocation assumes that asset dependencies will be relatively stable, when in fact they can change for prolonged periods. Consider, as an example, the informal currency arrangements that have held during the decade since 2000: several countries have effectively fixed their currencies relative to the U.S. dollar (at undervalued levels according to many commentators) and funded the U.S. current account deficit. The behavior of all asset classes relative to the U.S. dollar has been distorted by this arrangement, altering dependencies relative to earlier periods. Another example is that in the decade to come, the increased risk of commodity shortages could alter the historical pattern of commodity dependencies versus traditional asset classes. For these and other reasons, dynamic allocation, considered next, is viewed as an essential alternative.

Dynamic Allocation

Dynamic allocation among various asset classes is a way to both extract value from asset price behavior in various economic regimes and to control risk exposures. It is the most sophisticated and controlled process for monitoring drawdown risks. Dynamic allocation is based on the observation that there are long-term regularities in asset returns based on the phase of the economic cycle. Figure 12.9, for example, shows that commodity prices tend to follow the economic cycle; that is, prices accelerate with the expansion phase and decelerate with the recession phase, while stock markets and bond markets tend to anticipate the economic cycle.

Figure 12.9Returns to Asset Classes over the Economic Cycle, 1900–2009

Sources: Shiller (; Global Financial Data (; authors’ calculations.

Diversification and dynamic rebalancing provide a first layer of protection against risk, both readily identifiable day-to-day risk, and tail-end risks that are largely unknown and unpredictable.

Three Investment Principles

Principle I: Top-Down Macroeconomic Analysis

Top-down macroeconomic analysis acts as a filter to the investment universe. The objective is not to forecast the market but to try to avoid regional and global macro risks that can translate into sudden monetary outflows and the regional collapse of debt, equity, and currency markets. Regional imbalances can be gauged by measuring features such as external balances, debt levels and the currency denomination of the debt liquidity profile, and currency regime (e.g., fixed versus floating). Investing in economies with sound macroeconomic fundamentals is a first layer of protection against the erratic behavior of so-called hot money.

The second objective of macro research is to estimate the current position of the economic cycle. Economies exhibit a succession of booms and busts. Asset returns are particularly sensitive to two factors: price levels and economic cycles. Figure 12.10 shows the dispersion of S&P equity returns in four different market phases as a function of price levels, measured as the P/E ratio at the entry into the market phase. The figure shows that equities provide higher returns when P/Es are low in any market phase. Figure 12.10 also shows that equity rebounds usually happen during the late recession phase, well in advance of the economy as a whole.

Figure 12.10Returns to S&P 500 in Various Market Phases as a Function of P/E Ratio

Sources: Shiller (; authors’ calculations.

Measuring the precise position of the economic cycle can be a difficult and uncertain exercise. However, a few conclusions can be drawn with a high degree of confidence. At any moment, an investor knows which one of the four phases the economy is not in. For example, at the time of this writing in early 2009, the U.S. economy may be in early recession or late recession, but it most certainly is not in a late expansion phase. When performing portfolio simulations, such historical phases can be excluded from the data set. The investor can also make reasonable assumptions about the relative likelihood of the remaining three phases. In the absence of satisfactory information, the investor can assign equal weight to the likelihood of each phase and stress test the portfolio in the three cases.

Principle II: Value Investing

Value investing across asset classes is a principle that improves the safety and mitigates the risk of a portfolio. Asset prices tend to oscillate around their fair values. A “cheap asset” has two advantages for a long-term investor: First, it offers higher yield, meaning the probability that it will deliver real value over time is high. Second, if the market moves adversely, a cheap asset is less likely than an expensive asset to be priced dramatically downward by the market, a situation that a long-term investor does not want to face.

The valuations of assets can be assessed with mathematical models. Although these models are imperfect, they are more robust for value investment than are market forecasts.

Figure 12.11 shows that investors usually overpay for the hope of growth. The earnings for equities classified as value investments turn out to be close to those predicted by analysts (actual is close to expected) and higher than in the prior period. In contrast, the earnings for equities classified as growth investments turn out to be lower than both predicted earnings and prior-period earnings. This shows that for growth companies analysts’ expectations for earnings seem to be based on priors, as if expectations were reverse engineered to match market price, and actual earnings disappoint relative to prior and expectations. For value companies the reverse is true, with the actual outcome close to expectations and higher than the prior.

Figure 12.11Annualized Earnings Growth in the United States, 1985–2007

Source: SocGen Research (

Value concepts at the company level aggregate at the country or sector index levels and provide investment guidelines to enhance yield expectations across market phases.

For example, Table 12.6 shows the total return to the S&P 500 in different inflationary environments, and also for low versus high P/Es. Total returns are higher in low-inflation environments, but regardless of the circumstances, investing in equities when P/Es are low provides higher returns than when P/Es are high. Dynamic reallocation across asset classes based on value concepts is a process used for extracting value.

TABLE 12.6Total Returns to Equities, S&P 500, 1901–2009


accelerating (%)


decelerating (%)


accelerating (%)


decelerating (%)
Annualized return0.
Annualized return when P/E ≤ 172.511.415.725.7
Annualized return when P/E ≥ 17–5.5–0.3–2.66.7
Source: Shiller ( Accelerating means a year-over-year consumer price index (CPI) above its six-month average, decelerating means a year-over-year CPI below its six-month average.

High inflation: U.S. year-over-year CPI > 3 percent.

Low inflation: U.S. year-over-year CPI ≤ 3 percent.

Source: Shiller ( Accelerating means a year-over-year consumer price index (CPI) above its six-month average, decelerating means a year-over-year CPI below its six-month average.

High inflation: U.S. year-over-year CPI > 3 percent.

Low inflation: U.S. year-over-year CPI ≤ 3 percent.

Although value investing focuses on yield, and therefore on expected returns, risk should not be ignored. Any market participant’s utility function combines expected return and risk. If asset prices tend to oscillate around their equilibrium value, so does the global appetite for risk, or its counterpart, the demand for cash.

The market’s risk appetite for a given asset or asset class can be measured in various ways, including by trend-following models using a medium-term time frame. The more favorable situation for a long-term investor occurs when risky assets are assigned a low price for embedded value while the market appetite for risk is growing. In 2009, analysts witnessed an example of this situation, in line with the historical behavior of equities and corporate bonds at the end of a recession phase and the beginning of an expansion phase.

Inclusion of the risk component in the asset-valuation process can also protect the portfolio from secular shifts in assets’ offer and demand equilibrium, which cannot be predicted using historical data. This issue is especially relevant for commodities, which do not bear interest and therefore cannot be easily integrated into a simple value-investing approach.

Principle III: Risk-Management Discipline

Risk-management discipline is an additional, critical layer of protection against tail-end risk. Asset managers make assumptions based on valuation methods and economic analysis, and those assumptions can turn out to be wrong. A crucial element of the investment process is to measure the consequences of being wrong and to ensure that such consequences would be bearable by the SWF owner.

Defining an SWF utility function is the process managers use to clarify the mandate entrusted to them. Risk-management discipline requires that the cost-of-risk function be monitored to ensure that the portfolio remains within its risk parameters.

Global Portfolio Construction


Global portfolio construction starts with mapping the investment universe and filtering that universe using top-down macroeconomic considerations. This first step leads to investment restrictions and constraints (i.e., particular geographic regions or asset classes to include or exclude) that are used during the portfolio optimization process.

The second step involves assessing individual asset valuations. Considerations of risk and return presented in the previous sections are implemented at this stage. In general, an asset’s value in a portfolio results from the trade-off between expected return and risk, as well as its correlation with other assets. The valuation and filtering process at this stage selects suitable assets, so that each investment, taken individually, provides a favorable expected risk-return trade-off. Prefiltering to choose suitable assets reduces the universe of assets considered in the third stage by the optimization routine, and enhances the robustness of the optimization process, which otherwise can be overly sensitive to the assumptions made in the correlation structure.

The third stage involves the fund’s utility function, which is used to optimize allocations to various assets under several constraints, such as liquidity requirements, macro restrictions on asset exposures, maximum tolerable volatility, or cost of transactions.


Portfolio construction is a combination of science and art. The process requires the discretionary views of experienced managers in addition to computerized models to support the calculation process. It is not possible to look back in time and assume what discretionary decisions would have been made in the past. However, it is possible to build simplified models to simulate the actual process, and apply these models to past history. This exercise gives a reasonable semblance of the dynamics of the portfolio reallocation process and its potential strengths or weaknesses, at different time scales or under different economic regimes.

Such back-testing is essential, especially for measuring the potential consequences of being wrong. Managers and economists make mistakes all the time, and this is an intrinsic element of the investment process. The impact of making such mistakes can be examined by stress testing. For example, investing in equities in a late recession phase as opposed to in an early expansion phase has little consequence as measured by returns but significant costs in volatility. The control of the portfolio risk provided by a dynamic reallocation process offers some element of comfort with regard to economic uncertainties.

Managing Tail Event Risk

Measuring Tail-End Risks

Financial returns are not normally distributed, as is well documented. Tails are fat relative to normal, in that rare events—large losses or gains—occur more frequently than for a normal distribution. Ignoring fat tails leads to substantial underestimation of the likelihood of large losses.

A couple of approaches can be used to remedy this problem. The first, extreme value theory, focuses specifically on the tail events. A functional form for the distribution of the tail events can then be used that is more appropriate than the normal distribution. (The distribution only applies to the upper or lower tail, not the complete distribution.) One distribution (which arises naturally as the limiting distribution for maxima or threshold exceedances) is the generalized Pareto distribution. Another functional form is the stretched exponential.4

A second, simple, and practical approach is to model the complete return distribution using a distribution with tails fatter than the tails of a normal distribution. This approach has the advantage of handling both day-to-day risk (volatility) and extreme risk within the same model. Two candidate distributions are Student’s t-distribution with a small number of degrees of freedom (three to six), and a discrete mixture of normals.

Regardless of the approach chosen, a long-term investor should use risk models that can model the fat tails of return distributions. Risk mitigation, however, should not be sensitive to the exact measures of tails for two reasons: (1) tail events, by definition, are rare, and therefore can only be measured with a low confidence level; and (2) extreme events are usually triggered by a series of minor causes cascading throughout the system that are self-reinforcing and almost impossible to identify, even after the fact. Risk mitigation mainly comes from recognizing the reality of fat tails, and the dynamic of the investment process.

Price-to-Book as an Indirect Measure of Systemic Risk

The tangible value of a company is represented by its book value, that is, equity injections and accumulated earnings (less dividends), which usually are invested in productive capacity. The intangible value that results in the market price consists of two parts: (1) the ability of the organization and its employees to turn the productive capacity into an increasing flow of earnings, and (2) the favorable environmental factors that support the creation of wealth, that is, the systemic value of the economic system, which is redistributed to its members. The price given to the intangible value must turn into tangible earnings in the medium term or the price will eventually fall.

At the end of the 1990s, price-to-book in the United States jumped to 5, as it did in Japan in 1989 before Japan’s financial crash. A price-to-book of 5 means that market participants attribute 80 percent of the value of a company to its intangible assets, mostly to the systemic value of the integrated economic system and its ability to moderate macroeconomic fluctuations:

When the market, which fears increased volatility or disappointing future flows of tangible earnings, starts to question systemic and intangible values, prices of all equities fall together and correlation across risky assets increases dramatically because those risky assets are all highly sensitive to the same factor.

Therefore, expensive equity markets, as measured by the price-to-book ratio, are not only likely to underperform in the long run but also to eventually suffer from systemic repricing.

Mitigating Tail-End Risks

The investment process for SWFs laid out in the previous sections provides structural protection against systemic risks for three reasons:

  • The implementation of value-investing concepts is likely to drive the fund out of self-fulfilling asset bubbles ahead of a crash. Extreme events tend to happen when assets are very expensive and the appetite for risk turns negative, two factors integral to the valuation method.
  • The utility function guideline induces the fund to reduce its risky exposures when market volatilities and correlations increase significantly.
  • Risk monitoring is driven by investment principles and not by economic forecasts.


SWFs are favorably positioned in the market. First, they are not in a competitive situation. Therefore, they can better resist the temptation to follow the consensus, particularly in times of asset bubbles, thus increasing their margin of safety. Second, as long-term investors, they can benefit from the scaling effect of risk-return relationships and get higher returns than a short-term investor would for a given level of risk. Fulfillment of this objective requires the assignment of clear mandates to the investment management team, supported by the definition of the fund’s utility function.

Creating a governance process that encourages long-term, independent investing is an enormous challenge, especially for SWFs just starting up, when the temptation is to invest with a low-risk profile simply to meet short-term objectives of capital protection in nominal terms.


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    BernsteinShaiJoshLerner and AntoinetteSchoar2009“The Investment Strategies of Sovereign Wealth Funds,”NBER Working Paper No. 14861 (CambridgeMassachusetts: National Bureau of Economic Research).

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    MalevergneYannickVladilenPisarenko and DidierSornette2006“On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Log-Returns,”Applied Financial EconomicsVol. 16No. 3 pp. 27189.

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The authors wish to acknowledge stimulating discussions with Heiner P. T. Hartwich and to thank him for his contribution.


Organizational issues are not discussed in this chapter because they are covered elsewhere in this volume.


The S&P index is heavily weighted toward large cap growth stocks, so naturally the return on the S&P index is close to the return on the large cap growth index.


For more information on extreme value theory and generalized Pareto distributions, see Chapter 7 of McNeil, Frey, and Embrechts, 2007; and Malevergne, Pisarenko, and Sornette, 2005, 2006.

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