APPENDIX
Data Sources
This appendix provides details regarding data sources, followed by details regarding the empirical analyses that are used throughout the book.
| Index Name and Description | Source | Granularity |
| MSCI Total Return Net World Free USD | Bloomberg | Monthly |
| Description: The MSCI World is a stock market index of more than 6,000 global stocks. It is maintained by MSCI Inc., formerly Morgan Stanley Capital International. | ||
| JPMorgan Global Aggregate Bond—Total Return Unhedged USD | Bloomberg | Monthly |
| Description: JPM Global Aggregate Bond Index (GABI) consists of the JPM GABI US, a U.S. dollar–denominated, investment-grade index spanning asset classes from developed to emerging markets, and extends the U.S. index to also include multicurrency, investment-grade instruments. Launched in November 2008, the JPM GABI represents nine distinct asset classes: Developed Market Treasuries, Emerging Market Local Treasuries, Emerging Markets External Debt, Emerging Markets Credit, U.S. Credit, Euro Credit, U.S. Agencies, U.S. MBS, and Pfandbriefe—represented by well-established JPMorgan indices. The JPM GABI US is constructed from more than 3,200 instruments issued from over 50 countries, and collectively represents US$8.6 trillion in market value. The JPM GABI is constructed from over 5,500 instruments issued from over 60 countries and denominated in more than 25 currencies, collectively representing US$20 trillion in market value. | ||
| Barclays U.S. Corporate High Yield Total Return Index Value Unhedged USD | Bloomberg | Monthly |
| Description: The U.S. Corporate High Yield Index covers the USD-denominated, non-investment-grade, fixed-rate, taxable corporate bond market. Securities are classified as high-yield if the middle rating of Moody's, Fitch, and S&P is Ba1/BB+/BB+ or below. The index excludes emerging markets debt. The index was created in 1986, with index history backfilled to January 1, 1983. The U.S. Corporate High Yield Index is part of the U.S. Universal and Global High-Yield Indices. | ||
| Index Name and Description | Source | Granularity |
| S&P GSCI Total Return Index | Bloomberg | Monthly |
| Description: The S&P GSCI Total Return Index measures a fully collateralized commodity futures investment that is rolled forward from the 5th to the 9th business day of each month. Currently the S&P GSCI includes 24 commodity nearby futures contracts. The S&P GSCI Total Return Index is significantly different from the return from buying physical commodities. | ||
| Moody's Bond Indices Corporate AAA | Bloomberg | Monthly |
| Description: Monthly values are an average of the daily values for the corresponding month. Moody's Long-Term Corporate Bond Yield Averages are derived from pricing data on a regularly replenished population of corporate bonds in the U.S. market, each with current outstanding over $100 million. The bonds have maturities as close as possible to 30 years; they are dropped from the list if their remaining life falls below 20 years, if they are susceptible to redemption, or if their ratings change. All yields are yield to maturity calculated on a semiannual basis. Each observation is an unweighted average, with average corporate yields representing the unweighted average of the corresponding average industrial and average public utility observations. Bonds and stocks that are given this rating are regarded as of the highest class as to both security and general convertibility. Practically all such issues are dependent for their prices on the current rates for money, rather than the fluctuations in earning power. In other words, their position is such that their value is not affected, or likely to be affected (except in the cases of stocks not limited as to dividends), by any normal changes in the earning capacity of, for example, the railroad itself, either for better or for worse. | ||
| Moody's Bond Indices Corporate BAA | Bloomberg | Monthly |
| Description: Same method of calculation as Moody's Bond Indices Corporate AAA, except using BAA bonds. Obligations rated Baa are subject to moderate credit risk. They are considered medium-grade and as such may possess certain speculative characteristics. | ||
| ICE LIBOR USD 1-Month | Bloomberg | Monthly |
| Description: London Interbank Offered Rate—British Bankers' Association Fixing for U.S. Dollar. The fixing is conducted each day at 11 a.m. (London time). The rate is an average derived from the quotations provided by the banks determined by the British Bankers' Association. The top and bottom quartiles are eliminated and an average of the remaining quotations is calculated to arrive at fixing. The fixing is rounded up to five decimal places where the sixth digit is 5 or more. BBA USD LIBOR is calculated on an ACT/360 basis and for value two business days after the fixing. Please note that for the overnight rate, the value date is on the same day as the fixing date, with the maturity date falling the next business day in both centers. | ||
| NCREIF Timberland Index | NCREIF.org | Quarterly |
| Description: The NCREIF Timberland Index is a quarterly time series composite return measure of investment performance of a large pool of individual timber properties acquired in the private market for investment purposes only. All properties in the Timberland Index have been acquired, at least in part, on behalf of tax-exempt institutional investors, the great majority being pension funds. As such, all properties are held in a fiduciary environment. | ||
| Index Name and Description | Source | Granularity |
| NCREIF Farmland Returns | NCREIF.org | Quarterly |
| Description: The NCREIF Farmland Index is a quarterly time series composite return measure of investment performance of a large pool of individual agricultural properties acquired in the private market for investment purposes only. All properties in the Farmland Index have been acquired, at least in part, on behalf of tax-exempt institutional investors, the great majority being pension funds. As such, all properties are held in a fiduciary environment. | ||
| FTSE NAREIT Mortgage REITs Total Return Index | Bloomberg | Quarterly |
| Description: Mortgage REITs include all tax-qualified REITs with more than 50 percent of total assets invested in mortgage loans or mortgage-backed securities secured by interests in real property. | ||
| FTSE NAREIT Equity REITs Total Return Index | Bloomberg | Quarterly |
| Description: This investment sector includes all Equity REITs not designated as Timber REITs. | ||
| HFRI Macro (Total) Index | Bloomberg | Monthly |
| Description: Macro investment managers trade a broad range of strategies in which the investment process is predicated on movements in underlying economic variables and the impact these have on equity, fixed income, hard currency, and commodity markets. Managers employ a variety of techniques, both discretionary and systematic analysis, combinations of top-down and bottom-up theses, quantitative and fundamental approaches, and long- and short-term holding periods. Although some strategies employ relative value (RV) techniques, macro strategies are distinct from RV strategies in that the primary investment thesis is predicated on predicted or future movements in the underlying instruments, rather than realization of a valuation discrepancy between securities. In a similar way, while both macro and equity hedge (EH) managers may hold equity securities, the overriding investment thesis is predicated on the impact movements in underlying macroeconomic variables may have on security prices, as opposed to EH, in which the fundamental characteristics of the company are the most significant and are integral to the investment thesis. | ||
| Credit Suisse Global Macro Index | Bloomberg | Monthly |
| Description: The Credit Suisse Global Macro Hedge Fund Index is a subset of the Credit Suisse Hedge Fund Index that measures the aggregate performance of global macro funds. Global macro funds typically focus on identifying extreme price valuations, and leverage is often applied on the anticipated price movements in equity, currency, interest rate, and commodity markets. Managers typically employ a top-down global approach to concentrate on forecasting how political trends and global macroeconomic events affect the valuation of financial instruments. Profits can be made by correctly anticipating price movements in global markets and having the flexibility to use a broad investment mandate, with the ability to hold positions in practically any market with any instrument. These approaches may be systematic trend-following models or discretionary. | ||
| Index Name and Description | Source | Granularity |
| HFRI Macro: Systematic Diversified Index | Bloomberg | Monthly |
| Description: Systematic diversified strategies have investment processes typically as function of mathematical, algorithmic, and technical models, with little or no influence of individuals over the portfolio positioning. The strategies employ an investment process designed to identify opportunities in markets exhibiting trending or momentum characteristics across individual instruments or asset classes. The strategies typically employ quantitative processes that focus on statistically robust or technical patterns in the return series of the asset, and typically focus on highly liquid instruments and maintain shorter holding periods than either discretionary or mean-reverting strategies. Although some strategies seek to employ countertrend models, strategies benefit most from an environment characterized by persistent, discernible trending behavior. Systematic diversified strategies typically would expect to have no greater than 35% of portfolio in either dedicated currency or commodity exposures over a given market cycle. | ||
| HFRI Event Driven (Total) Index | Bloomberg | Monthly |
| Description: Event-driven investment managers maintain positions in companies currently or prospectively involved in corporate transactions of a wide variety, including but not limited to mergers, restructurings, financial distress, tender offers, shareholder buybacks, debt exchanges, security issuance, or other capital structure adjustments. Security types can range from most senior in the capital structure to most junior or subordinated, and frequently involve additional derivative securities. Event-driven exposure includes a combination of sensitivities to equity markets, credit markets, and idiosyncratic, company-specific developments. Investment theses are typically predicated on fundamental characteristics (as opposed to quantitative), with the realization of the thesis predicated on a specific development exogenous to the existing capital structure. | ||
| HFRI Event Driven: Merger Arbitrage Index | Bloomberg | Monthly |
| Description: Merger arbitrage strategies employ an investment process primarily focused on opportunities in equity and equity-related instruments of companies that are currently engaged in a corporate transaction. Merger arbitrage involves primarily announced transactions, typically with limited or no exposure to situations that predate or postdate, or situations in which no formal announcement is expected to occur. Opportunities are frequently presented in cross-border, collared, and international transactions that incorporate multiple geographic regulatory institutions, and typically involve minimal exposure to corporate credits. Merger arbitrage strategies typically have over 75% of positions in announced transactions over a given market cycle. | ||
| HFRI Event Driven: Distressed/Restructuring Index | Bloomberg | Monthly |
| Description: Distressed/restructuring strategies employ an investment process focused on corporate fixed-income instruments, primarily on corporate credit instruments of companies trading at significant discounts to their value at issuance or obliged (par value) at maturity as a result of either formal bankruptcy proceeding or financial market perception of near-term proceeding. Managers are typically actively involved with the management of these companies, frequently involved on creditors' committees in negotiating the exchange of securities for alternative obligations, either swaps of debt, equity, or hybrid securities. Managers employ fundamental credit processes focused on valuation and asset coverage of securities of distressed firms; in most cases portfolio exposures are concentrated in instruments that are publicly traded, in some cases actively and in others under reduced liquidity but in general for which a reasonable public market exists. In contrast to special situations, distressed strategies employ primarily debt (greater than 60%) but also may maintain related equity exposure. | ||
| Index Name and Description | Source | Granularity |
| HFRX Event Driven: Activist | Bloomberg | Monthly |
| Description: Activist strategies may obtain or attempt to obtain representation on the company's board of directors in an effort to impact the firm's policies or strategic direction, and in some cases may advocate activities such as division or asset sales, partial or complete corporate divestiture, dividend or share buybacks, and changes in management. Strategies employ an investment process primarily focused on opportunities in equity and equity-related instruments of companies that are currently or prospectively engaged in a corporate transaction, security issuance/repurchase, asset sales, division spin-off, or other catalyst-oriented situation. These involve both announced transactions as well as situations that predate or postdate, or situations in which no formal announcement is expected to occur. Activist strategies are distinguished from other event-driven strategies in that, over a given market cycle, activist strategies would expect to have greater than 50% of the portfolio in activist positions, as described. | ||
| Credit Suisse Event Driven: Multi-Strategy | Bloomberg | Monthly |
| Description: The Credit Suisse Event Driven Multi-Strategy Hedge Fund Index is a subset of the Credit Suisse Hedge Fund Index that measures the aggregate performance of multistrategy event-driven funds. Multistrategy event-driven managers typically invest in a combination of event-driven equities and credit. Within the equity space, sub-strategies may include risk arbitrage, holding company arbitrage, equity special situations, and value equities with a hard or soft catalyst. Within the credit-oriented portion, sub-strategies may include long/short high-yield credit (sub-investment-grade corporate bonds), leveraged loans (bank debt, mezzanine, or self-originated loans), capital structure arbitrage (debt vs. debt or debt vs. equity), and distressed debt (workout situations or bankruptcies), including post-reorganization equity. Multistrategy event-driven managers typically have the flexibility to pursue event investing across different asset classes and take advantage of shifts in economic cycles. | ||
| HFRI Relative Value (Total) Index | Bloomberg | Monthly |
| Description: Investment managers who maintain positions in which the investment thesis is predicated on realization of a valuation discrepancy in the relationship between multiple securities. Managers employ a variety of fundamental and quantitative techniques to establish investment theses, and security types range broadly across equity, fixed income, derivative, or other security types. Fixed-income strategies are typically quantitatively driven to measure the existing relationship between instruments and, in some cases, identify attractive positions in which the risk-adjusted spread between these instruments represents an attractive opportunity for the investment manager. Relative value (RV) positions may be involved in corporate transactions also, but, as opposed to event-driven (ED) exposures, the investment thesis is predicated on realization of a pricing discrepancy between related securities, as opposed to the outcome of the corporate transaction. | ||
| HFRI Relative Value: Fixed Income–Convertible Arbitrage Index | Bloomberg | Monthly |
| Description: Fixed Income: Convertible Arbitrage includes strategies in which the investment thesis is predicated on realization of a spread between related instruments in which one or multiple components of the spread are convertible fixed-income instruments. Strategies employ an investment process designed to isolate attractive opportunities between the price of a convertible security and the price of a nonconvertible security, typically of the same issuer. Convertible arbitrage positions maintain characteristic sensitivities to credit quality of the issuer, implied and realized volatility of the underlying instruments, levels of interest rates, and the valuation of the issuer's equity, among other more general market and idiosyncratic sensitivities. | ||
| Index Name and Description | Source | Granularity |
| HFRI Relative Value: Fixed Income–Corporate Index | Bloomberg | Monthly |
| Description: Fixed Income: Corporate includes strategies in which the investment thesis is predicated on realization of a spread between related instruments in which one or multiple components of the spread are corporate fixed-income instruments. Strategies employ an investment process designed to isolate attractive opportunities between a variety of fixed-income instruments, typically realizing an attractive spread between multiple corporate bonds or between a corporate bond and a risk-free government bond. Fixed Income: Corporate strategies differ from Event-Driven: Credit Arbitrage in that the former more typically involve more general market hedges that may vary in the degree to which they limit fixed-income market exposure, while the latter typically involve arbitrage positions with little or no net credit market exposure, but are predicated on specific, anticipated idiosyncratic developments. | ||
| HFRX Relative Value: Multi-Strategy | Bloomberg | Monthly |
| Description: RV: Multi-Strategy managers employ an investment thesis that is predicated on realization of a spread between related yield instruments in which one or multiple components of the spread contain a fixed-income, derivative, equity, real estate, master limited partnership (MLP), or combination of these or other instruments. Strategies are typically quantitatively driven to measure the existing relationship between instruments and, in some cases, identify attractive positions in which the risk-adjusted spread between these instruments represents an attractive opportunity for the investment manager. In many cases these strategies may exist as distinct strategies across which a vehicle allocates directly, or may exist as related strategies over which a single individual or decision-making process manages. Multistrategy is not intended to provide broadest-based appeal for mass market investors, but is most frequently distinguished from other arbitrage strategies in that managers expect to maintain >30% of portfolio exposure in two or more strategies meaningfully distinct from each other that are expected to respond to diverse market influences. | ||
| HFRX Relative Value: Volatility Index | Bloomberg | Monthly |
| Description: Volatility strategies trade volatility as an asset class, employing arbitrage, directional, market-neutral, or a mix of types of strategies, and include exposures that can be long, short, neutral, or variable to the direction of implied volatility and can include both listed and unlisted instruments. Directional volatility strategies maintain exposure to the direction of implied volatility of a particular asset or, more generally, to the trend of implied volatility in broader asset classes. Arbitrage strategies employ an investment process designed to isolate opportunities between the prices of multiple options or instruments containing implicit optionality. Volatility arbitrage positions typically maintain characteristic sensitivities to levels of implied and realized volatility, levels of interest rates, and the valuation of the issuer's equity, among other more general market and idiosyncratic sensitivities. | ||
| HFRI Equity Hedge (Total) Index | Bloomberg | Monthly |
| Description: Equity hedge (EH) investment managers maintain positions both long and short in primarily equity and equity derivative securities. A wide variety of investment processes can be employed to arrive at an investment decision, including both quantitative and fundamental techniques; strategies can be broadly diversified or narrowly focused on specific sectors and can range broadly in terms of levels of net exposure, leverage employed, holding period, concentrations of market capitalizations, and valuation ranges of typical portfolios. EH managers would typically maintain at least 50% exposure to, and may in some cases be entirely invested in, equities, both long and short. | ||
| Index Name and Description | Source | Granularity |
| HFRI Equity Hedge: Equity Market Neutral Index | Bloomberg | Monthly |
| Description: Equity market-neutral strategies employ sophisticated quantitative techniques of analyzing price data to ascertain information about future price movement and relationships between securities, to select securities for purchase and sale. These can include both factor-based and statistical arbitrage/trading strategies. Factor-based investment strategies include strategies in which the investment thesis is predicated on the systematic analysis of common relationships between securities. In many but not all cases, portfolios are constructed to be neutral to one or multiple variables, such as broader equity markets in dollar or beta terms, and leverage is frequently employed to enhance the return profile of the positions identified. Statistical arbitrage/trading strategies consist of strategies in which the investment thesis is predicated on exploiting pricing anomalies that may occur as a function of expected mean reversion inherent in security prices; high-frequency techniques may be employed, and trading strategies may also be employed on the basis of technical analysis or opportunistically to exploit new information the investment manager believes has not been fully, completely, or accurately discounted into current security prices. Equity market-neutral strategies typically maintain characteristic net equity market exposure no greater than 10% long or short. | ||
| HFRI Equity Hedge: Short Bias Index | Bloomberg | Monthly |
| Description: Short-bias strategies employ analytical techniques in which the investment thesis is predicated on assessment of the valuation characteristics on the underlying companies with the goal of identifying overvalued companies. Short-bias strategies may vary the investment level or the level of short exposure over market cycles, but the primary distinguishing characteristic is that the manager maintains consistent short exposure and expects to outperform traditional equity managers in declining equity markets. Investment theses may be fundamental or technical in nature, and the manager has a particular focus, above that of a market generalist, on identification of overvalued companies and would expect to maintain a net short equity position over various market cycles. | ||
| HFRI Fund of Funds: Composite Index | Bloomberg | Monthly |
| Description: Funds of funds invest with multiple managers through funds or managed accounts. The strategy designs a diversified portfolio of managers with the objective of significantly lowering the risk (volatility) of investing with an individual manager. The fund of funds manager has discretion in choosing which strategies to invest in for the portfolio. A manager may allocate funds to numerous managers within a single strategy, or to numerous managers in multiple strategies. The minimum investment in a fund of funds may be lower than an investment in an individual hedge fund or managed account. The investor has the advantage of diversification among managers and styles with significantly less capital than investing with separate managers. Note: The HFRI Fund of Funds Index is not included in the HFRI Fund Weighted Composite Index. | ||
| HFRI Fund of Funds: Conservative Index | Bloomberg | Monthly |
| Description: FoFs classified as conservative exhibit one or more of the following characteristics: seeks consistent returns by primarily investing in funds that generally engage in more conservative strategies such as equity market-neutral, fixed-income arbitrage, and convertible arbitrage; exhibits a lower historical annual standard deviation than the HFRI Fund of Funds Composite Index. A fund in the HFRI FoF Conservative Index shows generally consistent performance regardless of market conditions. | ||
| Index Name and Description | Source | Granularity |
| HFRI Fund of Funds: Diversified Index | Bloomberg | Monthly |
| Description: FoFs classified as diversified exhibit one or more of the following characteristics: invests in a variety of strategies among multiple managers; has a historical annual return and/or a standard deviation generally similar to the HFRI Fund of Fund Composite Index; demonstrates generally close performance and returns distribution correlation to the HFRI Fund of Fund Composite Index. A fund in the HFRI FoF Diversified Index tends to show minimal loss in down markets while achieving superior returns in up markets. | ||
| HFRI Fund of Funds: Market Defensive Index | Bloomberg | Monthly |
| Description: FoFs classified as market defensive exhibit one or more of the following characteristics: invests in funds that generally engage in short-bias strategies such as short selling and managed futures; shows a negative correlation to the general market benchmarks (S&P). A fund in the FoF Market Defensive Index exhibits higher returns during down markets than during up markets. | ||
| HFRI Fund of Funds: Strategic Index | Bloomberg | Monthly |
| Description: FoFs classified as strategic exhibit one or more of the following characteristics: seeks superior returns by primarily investing in funds that generally engage in more opportunistic strategies such as emerging markets, sector-specific, and equity hedge; exhibits a greater dispersion of returns and higher volatility compared to the HFRI Fund of Funds Composite Index. A fund in the HFRI FoF Strategic Index tends to outperform the HFRI Fund of Funds Composite Index in up markets and underperform the index in down markets. | ||
| Cambridge Associates LLC U.S. Private Equity Index | Cambridge Associates | Quarterly |
| Description: The Cambridge Associates LLC U.S. Private Equity Index is an end-to-end calculation based on data compiled from 887 U.S. private equity funds (buyout, growth equity, private equity energy, and mezzanine funds), including fully liquidated partnerships, formed between 1986 and 2010. | ||
| Cambridge Associates LLC U.S. Venture Capital Index | Cambridge Associates | Quarterly |
| Description: The Cambridge Associates LLC U.S. Venture Capital Index is an end-to-end calculation based on data compiled from 1,308 U.S. venture capital funds (867 early stage, 170 late and expansion stage, 268 multistage, and 3 venture debt funds), including fully liquidated partnerships, formed between 1981 and 2010. | ||
| Credit Suisse Long/Short Equity Hedge Index | Bloomberg | Monthly |
| Description: The Credit Suisse Long/Short Equity Hedge Index is a subset of the Credit Suisse Hedge Fund Index that measures the aggregate performance of long/short equity funds. Long/short equity funds typically invest in both long and short sides of equity markets, generally focusing on diversifying or hedging across particular sectors, regions, or market capitalizations. Managers typically have the flexibility to shift from value to growth, from small- to medium- to large-capitalization stocks, and from net long to net short. Managers can also trade equity futures and options as well as equity-related securities and debt or build portfolios that are more concentrated than traditional long-only equity funds. | ||
| Index Name and Description | Source | Granularity |
| CAIA Alternative Index | CAIA | Quarterly |
| Description: The CAIA Alternative Index is a weighted average of monthly returns of alternative asset classes. The weights are partly based on Russell Investments' survey of alternative investments. The asset classes and their corresponding weights are: HFRI Fund Weighted Composite Index (30%), NAREIT All REITs (35%), S&P GSCI Total Return (10%), and Cambridge Associates Private Equity Index (25%). | ||
| Credit Suisse Convertible Arbitrage Hedge Fund Index | Bloomberg | Monthly |
| Description: The Credit Suisse Convertible Arbitrage Hedge Fund Index is a subset of the Credit Suisse Hedge Fund Index that measures the aggregate performance of convertible arbitrage funds. Convertible arbitrage funds typically aim to profit from the purchase of convertible securities and the subsequent shorting of the corresponding stock when there is a pricing error made in the conversion factor of the security. Managers of convertible arbitrage funds typically build long positions of convertible and other equity hybrid securities and then hedge the equity component of the long securities positions by shorting the underlying stock or options. The number of shares sold short usually reflects a delta-neutral or market-neutral ratio. As a result, under normal market conditions, the arbitrageur generally expects the combined position to be insensitive to fluctuations in the price of the underlying stock. | ||
Sources for Descriptions
- Bloomberg.com
- hedgeindex.com
- Cambridge Associates
- JP Morgan
- NAREIT.com
- Hedge Fund Research, Inc at www.hedgefundresearch.com
Computations and Explanations
This section discusses the computations used in the standardized empirical exhibits that are displayed throughout the book. To illustrate the computations, the following exhibits use a broad index of alternative investments to show the risks and returns of a broadly diversified portfolio of alternatives.
Common Indices
In Panel A, “World Equities” refers to the MSCI Total Return Net World Free USD. “Global Bonds” refers to the JPMorgan Global Aggregate Bond—Total Return Unhedged USD. “U.S. High-Yield” refers to the Barclays U.S. Corporate High Yield Total Return Index Value Unhedged USD. “Commodities” refers to the S&P GSCI Total Return Index.
Panel A: Returns Tables
| CAIA | |||||
| Alternative | World | Global | U.S. High- | ||
| Index (Jan. 2000–Dec. 2014) | Index | Equities | Bonds | Yield | Commodities |
| Annualized Arithmetic Mean | 8.1%** | 4.7%** | 5.7%** | 7.9%** | 4.8%** |
| Annualized Standard Deviation | 11.1% | 17.9% | 6.0% | 11.0% | 26.0% |
| Annualized Semistandard Deviation | 9.9% | 13.4% | 2.6% | 8.1% | 20.6% |
| Skewness | –1.4** | –0.4 | 0.5 | 0.1 | –0.9** |
| Kurtosis | 4.6** | 0.2 | –0.5 | 5.1** | 2.3** |
| Sharpe Ratio | 0.53 | 0.14 | 0.58 | 0.52 | 0.10 |
| Sortino Ratio | 0.82 | 0.35 | 2.18 | 0.97 | 0.23 |
| Annualized Geometric Mean | 7.5% | 3.1% | 5.5% | 7.3% | 1.4% |
| Annualized Standard Deviation (Autocorrelation Adjusted) | 13.9 | 20.3% | 5.5% | 14.1% | 28.2% |
| Maximum | 13.2% | 20.7% | 9.0% | 23.1% | 28.7% |
| Minimum | –21.6% | –21.8% | –3.4% | –17.9% | –47.0% |
| Autocorrelation | 30.3%** | 17.1%* | –12.3% | 34.1%** | 11.0% |
| Max Drawdown | –36.4% | –49.0% | –6.3% | –27.1% | –69.4% |
* = Significant at 90% confidence.
** = Significant at 95% confidence.
Formulas
Note: Rt = periodic return at time t, q = number of return periods within a one-year period, n = total number of return observations, q = 12 for monthly returns, and q = 4 for quarterly returns. When available, Microsoft Excel's formulas are provided.
The arithmetic mean is an estimate of the mean of the distribution. If one assumes that monthly returns are randomly drawn from the same distribution, then this figure is the best forecast of future monthly rates of return. These estimates are tested to determine if they are significantly different from zero.
The standard deviation is a measure of the dispersion of the probability distribution of monthly returns. The monthly standard deviation is annualized by multiplying it by 
. This assumes that monthly returns are randomly drawn from the same distribution.
Skewness measures the degree to which the distribution is symmetric around its mean. A negative skewness means that the tail on the left side of the probability density function is longer than on the right side, and the bulk of the values (possibly including the median) lie to the right of the mean. A positive skewness means that the tail on the right side of the probability density function is longer than on the left side, and the bulk of the values (possibly including the median) lie to the left of the mean. A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically implying a symmetric distribution.
Kurtosis is a measure of how heavy the tails of the probability distribution of a random variable are. Higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations.
The Sharpe ratio is a measure of the risk-adjusted performance of a portfolio. It is typically applied to diversified portfolios, and one of its underlying assumptions is that returns are normally distributed.
The annualized geometric mean is an estimate of expected rate of return over a given period with the compounding effect taken into account. The geometric mean is at most equal to the arithmetic mean and will be lower if monthly returns display any volatility.
Autocorrelation is an estimate of dependence in per-period returns. If returns are truly random, then autocorrelation will be zero.
Setting q = ACR:
When monthly returns are used to estimate annualized standard deviation, the common approach is to multiply the monthly standard deviation by 
, because there are 12 months in each year. This procedure is correct if one assumes that monthly returns are completely random and independent from each other. If monthly returns are autocorrelated, this assumption is violated. This typically means that the true annualized standard deviation is higher than monthly standard deviation multiplied by 
. This reason is that in the presence of autocorrelations, monthly returns will be smooth and thus annualized standard deviation will be underestimated. The scaling factor n(q) shows how to annualize the monthly standard deviation in the presence of autocorrelated returns. Notice that if ACR = 0, then n(q) = 
.
NAVt is the net asset value of the investment at time t. Notice that Dt is the percentage drawdown at time t and it will be 0 when the current NAV is at its highest value. Otherwise, Dt will be negative. Maximum drawdown is commonly used as measure of risk for actively managed strategies.
These standard errors are used to test the significance of the estimated values of skewness and kurtosis.
Significance Testing
For testing the “Annualized Arithmetic Mean,” a z-score was calculated and used in the MS Excel NORMSDIST function to determine significance.
For testing the significance of skewness, kurtosis, multivariate betas, univariate betas, and correlations, a t-score was calculated and converted to a p-value using the MS Excel TDIST formula using n – 2 degrees of freedom, with two tails. The t-score was calculated by:
For testing the “Autocorrelation,” the test statistic was calculated using the formula:
Panel B: Cumulative Wealth
Under the null hypothesis that the Autocorrelation is zero, the z-transform will be normally distributed with mean zero and standard deviation of 1. The z-transform is then placed into the MS Excel NORMSDIST function to evaluate the significance level.
Panel B was calculated using a cumulative growth calculation, starting in December 1999 at 100 USD.
Betas were calculated using the MS Excel INDEX and LINEST functions. A linear multivariate regression was calculated in the form of:
Panel C: Betas and Correlations
| Multivariate | World | Global | U.S. | Annualized | ||
| Betas | Equities | Bonds | High-Yield | Commodities | Estimated α | R2 |
| CAIA Alternative Index | 0.43** | –0.01 | 0.16* | 0.08** | 3.81%** | 0.79** |
| World | Global | U.S. | %Δ Credit | %Δ | ||
| Univariate Betas | Equities | Bonds | High-Yield | Commodities | Spread | VIX |
| CAIA Alternative Index | 0.54** | 0.03 | 0.74** | 0.21** | –0.15** | –0.09** |
| World | Global | U.S. | %Δ Credit | %Δ | ||
| Correlations | Equities | Bonds | High-Yield | Commodities | Spread | VIX |
| CAIA Alternative Index | 0.87** | 0.02 | 0.73** | 0.50** | –0.62** | –0.56** |
* = Significant at 90% confidence.
** = Significant at 95% confidence.
Here, the regression coefficient for the explanatory variable xi is given by βi coefficient to the corresponding xi, and the annualized estimated alpha is given by α = a × q.
The formula for the univariate beta, given two sets of monthly returns x and y, is:
and:
Here, xt is the observed value at time t, and pt is the predicted value of xt, for t = 1, 2, …, n.
Correlations were also calculated in MS Excel:
The multivariate betas are obtained by regressing the excess return on the CAIA Alternative Index against excess returns on the five asset classes. It is important to use returns in excess of the risk-free rate because we wish to take into account the effect of potential leverage in the investment product. Further, by using excess returns one does not have to impose the constraint that the coefficients should add to one. In this example, a portfolio consisting of 43% in world equity, –1% in global bonds, 16% in U.S. high-yield, 8% in commodities, and the rest in risk-free assets provides a benchmark for the CAIA Alternative Index. We can see the CAIA Alternative Index has historically outperformed this benchmark by 3.81% per year. Finally, we can see that 79.42% of the total volatility of the CAIA Alternative Index can be explained by this portfolio. This procedure for identifying a benchmark and calculating the alpha can be performed as long as the explanatory variables that appear on the right-hand side of the regression are investable assets.
The univariate betas are estimated using simple regression. Each coefficient represents the exposure of CAIA Alternative Index to a given factor. For example, we can see that the CAIA Alternative Index has a 54% exposure to world equities and an exposure of –15% to percentage change in credit spread.
Panel D visually shows the dispersion of returns by plotting world equities against the CAIA Alternatives index.
Panel D: Scatter Plot of Returns
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.