Improved estimation of portfolio value‐at‐risk under copula models with mixed marginals

Portfolio value‐at‐risk (PVAR) is widely used in practice, but recent criticisms have focused on risks arising from biased PVAR estimates due to model specification errors and other problems. The PVAR estimation method proposed in this article combines generalized Pareto distribution tails with the empirical density function to model the marginal distributions for each asset in the portfolio, and a copula model is used to form a joint distribution from the fitted marginals. The copula–mixed distribution (CMX) approach converges in probability to the true marginal return distribution but is based on weaker assumptions that may be appropriate for the returns data found in practice. CMX is used to estimate the joint distribution of log returns for the Taiwan Stock Exchange (TSE) index and the associated futures contracts on SGX and TAIFEX. The PVAR estimates for various hedge portfolios are computed from the fitted CMX model, and backtesting diagnostics indicate that CMX outperforms the alternative PVAR estimators. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:997–1018, 2006     

Efficient use of commodity futures in diversified portfolios

We provide evidence on the role of commodity futures in portfolios comprised of stocks, bonds, T‐bills, and real estate. Over the period investigated (1973–1997), Markowitz optimization over a range of risk levels gives substantial weight to commodity futures, thereby enhancing the portfolios’ returns. We find dramatically different results when we use a simple ex ante measure of monetary stringency to dichotomize the sample into expansive‐versus‐restrictive monetary‐policy periods. In periods characterized by restrictive monetary policy, commodity futures are shown to have substantial weight in the efficient portfolios, with significant return enhancement at all levels of risk. In periods characterized by expansive monetary policy, commodity futures are shown to have little or no weight in the efficient portfolios, with no return enhancement at all levels of risk. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:489–506, 2000     

Forecasting equity returns: The role of commodity futures along the supply chain

This paper examines equity return predictability using the returns of commodity futures along the supply chain in China's financial market. We find that a considerable number of commodities exhibit significant in‐sample forecasting ability at the daily horizon, especially for supplier‐side equity returns. The macroeconomic risk premium effect, captured by the aggregate commodity prices, is an important source for this predictability. The out‐of‐sample results show that for most commodities, the predictability remains both statistically and economically significant, and the forecasting performance improves substantially during recessions or with economic constraints.     

Intermediary asset pricing in commodity futures returns

This paper assesses the extent to which intermediary capital (IC) risk contributes toward explaining commodity futures returns. We find that the IC effect is substantially positive and continues to grow as the financialization of commodities deepens. Positive and negative IC risks play asymmetric roles, with the effect of negative IC strengthening in recent subperiods. We further confirm the heterogeneous roles of IC across individual commodities by cross-section analyses. Overall, the effect of the positive IC risk factor varies significantly. Portfolios with low basis, low open interest, low momentum, and low liquidity earn significantly higher returns than counterparty portfolios.     

Dealing with downside risk in a multi‐commodity setting: A case for a “Texas hedge”?

This study analyzes the problem of multi‐commodity hedging from the downside risk perspective. The lower partial moments (LPM₂)‐minimizing hedge ratios for the stylized hedging problem of a typical Texas panhandle feedlot operator are calculated and compared with hedge ratios implied by the conventional minimum‐variance (MV) criterion. A kernel copula is used to model the joint distributions of cash and futures prices for commodities included in the model. The results are consistent with the findings in the single‐commodity case in that the MV approach leads to over‐hedging relative to the LPM₂‐based hedge. An interesting and somewhat unexpected result is that minimization of a downside risk criterion in a multi‐commodity setting may lead to a “Texas hedge” (i.e. speculation) being an optimal strategy for at least one commodity. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:290–304, 2010     

Panel quantile regressions for estimating and predicting the value-at-risk of commodities

Using a flexible panel quantile regression framework, we show how the future conditional quantiles of commodities returns depend on both ex post and ex ante uncertainty. Empirical analysis of the most liquid commodities covering main sectors, including energy, food, agriculture, and precious and industrial metals, reveal several important stylized facts. We document common patterns of the dependence between future quantile returns and ex post as well as ex ante volatilities. We further show that the conditional returns distribution is platykurtic. The approach can serve as a useful risk management tool for investors interested in commodity futures contracts.     

Do country risk and financial uncertainty matter for energy commodity futures?

Using an instrumental variable quantile regression technique, this paper assesses whether country risk and financial uncertainty exert an impact on energy commodity futures prices under different commodity conditional return distributions over the period from January 1994 to July 2017. We also discuss whether the correlations change with different dimensions of country risk, that is economic, financial, and political. The results reveal that country risk and financial stress do have a significant impact on energy commodity returns of futures contracts with different maturities, but their direction, intensity, and significance differ, caused by the distinct market situations and divergent channels of country risk.     

Economic uncertainty,trading activity,and commodity futures volatility

This paper investigates the dynamics of commodity futures volatility. I derive the variance decomposition for the futures basis and show unexpected excess returns result from new information about expected future interest rates, convenience yields, and risk premia. Measures of uncertainty in economic conditions have significant predictive power for realized volatility of commodity futures returns, after controlling for lagged volatility, returns, commodity index trading, hedging pressure, and other trading activity, even during the so-called “index financialization” period. During this period, hedge fund performance predicts volatility in grain commodities, which are affected by the US ethanol mandate.     

Modeling discontinuous periodic conditional volatility: Evidence from the commodity futures market

This paper examines a wide variety of models that allow for complex and discontinuous periodic variation in conditional volatility. The value of these models (including augmented versions of existing models) is demonstrated with an application to high frequency commodity futures return data. Their use is necessary, in this context, because commodity futures returns exhibit discontinuous intraday and interday periodicities in conditional volatility. The former of these effects is well documented for various asset returns; however, the latter is unique amongst commodity futures returns, where contract delivery and climate are driving forces. Using six years of high‐frequency cocoa futures data, the results show that these characteristics of conditional return volatility are most adequately captured by a spline‐version of the periodic generalized autoregressive conditional heteroscedastic (PGARCH) model. This model also provides superior forecasts of future return volatility that are robust to variation in the loss function assumed by the user, and are shown to be beneficial to users of Value‐at‐Risk (VaR) models. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:805–834, 2004     

Revisiting the finite mixture of Gaussian distributions with application to futures markets

We present a new estimation method for Gaussian mixture modeling, namely, the kurtosis‐controlled expectation‐maximization (EM) algorithm, which overcomes the limitations of the usual estimation techniques via kurtosis control and kernel splitting. Our simulation study shows that the dynamic allocation of kernels according to the value of the total kurtosis measure makes the proposed kurtosis‐controlled EM algorithm an efficient method for Gaussian mixture density estimation. This algorithm yielded considerable improvements over the classical EM algorithm. We then used the discrete Gaussian mixture framework to account for the observed thick‐tailed distributions of futures returns and applied the kurtosis‐controlled EM algorithm to estimate the distributions of real (agricultural, metal, and energy) and financial (stock index and currency) futures returns. We proved that this framework is perfectly adapted to capturing the departures from normality of the observed return distributions. Unlike in previous studies, we found that a two‐component Gaussian mixture is too poor a model to accurately capture the distributional properties of returns. Similar results have been obtained for stocks, indexes, currencies, interest rates, and commodities. This has important implications in many financial studies using Gaussian mixtures to incorporate the thickness of the tails of the distributions in the computation of the value at risk or to infer implied risk‐neutral densities from option prices, to name but a few. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 347–376, 2001     

From carry trades to curvy trades

Traditional carry trade strategies are based on differences in short-term interest rates, neglecting any other information embedded in yield curves. We derive return distributions of currency portfolios, where the signals to buy and sell currencies are based on summary measures of the yield curve. We find that a strategy based on the relative curvature factor, the curvy trade, yields higher Sharpe ratios and a smaller return skewness than traditional carry strategies. Curvy trades build less upon the typical carry currencies and are hence less susceptible to crash risk. In line with that, standard pricing factors of traditional carry returns fail to explain curvy trade returns.     

Managed commodity funds

The performance of managed commodity fund investments during the years l982 through 1996 is examined, both as stand-alone investments and as assets in diversified stock and bond portfolios. Nine stylized commodity fund investments are examined: randomly-selected, single-CTAs, pool, and fund portfolios; equally weighted market portfolios (EWMPs) of CTAs, pools, and funds; and value-weighted portfolios (VWMP) of CTAs, pools, and funds. Further, two subperiods are examined: 1982–1988 and 1989–1996. Based on an analysis using Sharpe ratios as the performance criterion, several types of managed commodity funds make both good stand-alone investments and good portfolio assets; an EWMP of CTAs and a VWMP of pools receive the highest ranking among the alternative commodity fund investments. It is also shown that commodity indexes are not a substitute for a managed commodity fund investment. A number of issues warrant further study: Can investors still earn consistently attractive risk-adjusted returns on managed commodity fund investments if they do not hold diversified portfolios of CTAs and pools? Also: How can such high speculative returns be earned in efficient commodity markets? And: Are CTA and pool returns high because commodity fund managers have superior trading skill? An important issue for future research is to determine whether in fact CTAs do possess such skill. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 377–411, 1999     

Predictive abilities of speculators in energy markets

Using nonparametric methodology, I find that speculators are successful in taking profitable positions in energy futures markets, although the magnitude of this effect is lower than that found previously for agricultural markets. A plausible explanation for this difference is that price forecasting is more difficult for energy commodities. Moreover, I find that the energy speculators’ returns are due to the existence of the risk premiums rather than to speculators’ forecasting abilities. Futures risk premium is highly time-variant; notably, energy investors’ profits have been very limited in the GFC and post-GFC period, which coincided with the financialization of commodity markets.     

Long memory models for daily and high frequency commodity futures returns

The volatility of daily futures returns for six important commodities are found to be well described as FIGARCH, fractionally integrated processes, whereas the mean returns exhibit very small departures from the martingale difference property. Several years of high frequency intraday commodity futures returns are also found to have very similar long memory in volatility features as the daily returns. Semiparametric local Whittle estimation of the long memory parameter in absolute returns also finds very significant long memory features. Estimating the long memory parameter across many different data sampling frequencies provides consistent estimates of the long memory parameter, suggesting that the series are self‐similar. The results have important implications for empirical work using commodity futures price data. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:643–668, 2007     

Publicly traded venture capital funds: implications for institutional “fund of funds” investors

Institutional investors supply the bulk of the funds which are used by venture capital investment firms in financing emerging growth companies. These investors typically place their funds in a number of venture capital firms, thus achieving diversification across a range of investment philosophy, geography, management, industry, investment life cycle stage and type of security. Essentially, each institutional investor manages a “fund of funds,” attempting through the principles of portfolio theory to reduce the risk of participating in the venture capital business while retaining the up-side potential which was the original source of attraction to the business. Because most venture capital investment firms are privately held limited partnerships, it is very difficult to measure risk adjusted rates of return on these funds on a continuous basis.In this paper, we use the set of twelve publicly traded venture capital firms as a proxy to develop insight regarding the risk reduction effect of investment in a portfolio of venture capital funds, i.e., a fund of funds. Measurements of weekly total returns for the shares of these funds are compared with similar returns on a set of comparably sized “maximum capital gain” mutual funds and the daily return of the S&P 500 Index. A comparison of returns on an individual fund basis, as well as a correlation of daily returns of these individual funds, were made. In order to adjust for any systematic bias resulting from the “thin market” characteristic of the securities of the firms being observed, the Scholes-Williams beta estimation technique was used to reduce the effects of nonsynchronous trading.The results indicate that superior returns are realized on such portfolios when compared with portfolios of growth-oriented mutual funds and with the S&P 500 Index. This is the case whether the portfolios are equally weighted (i.e., “naive”) or constructed to be mean-variant efficient, ex ante, according to the capital asset pricing model. When compared individually, more of the venture funds dominated the S&P Market Index than did the mutual funds and by much larger margins. When combined in portfolios, the venture capital funds demonstrated very low beta coefficients and very low covariance of returns among portfolio components when compared with portfolios of mutual funds. To aid in interpreting these results, we analyzed the discounts and premia from net asset value on the funds involved and compared them to Thompson's findings regarding the contribution of such differences to abnormal returns. We found that observed excess returns greatly exceed the level which would be explained by these differences.The implications of these results for the practitioner are significant. They essentially tell us that, while investment in individual venture capital deals is considered to have high risk relative to potential return, combinations of deals (i.e., venture capital portfolios) were shown to produce superior risk adjusted returns in the market place. Further, these results show that further combining these portfolios into larger portfolios (i.e., “funds of funds”) provides even greater excess returns over the market index, thus plausibly explaining the “fund of funds” approach to venture capital investment taken by many institutional investors.While the funds studied are relatively small and are either small business investment companies or business development companies, they serve as a useful proxy for the organized venture capital industry, despite the fact that the bulk of the funds in the industry are institutionally funded, private, closely held limited partnerships which do not trade continuously in an open market. These results demonstrate to investors the magnitude of the differences in risk adjusted total return between publicly traded venture capital funds and growth oriented mutual funds on an individual fund basis. They also demonstrate to investors the power of the “fund of funds” approach to institutional involvement in the venture capital business. Because such an approach produces better risk adjusted investment results for the institutional investor, it seems to justify a greater flow of capital into the business from more risk averse institutional investment sources. This may mean greater access to institutional funds for those seeking to form new venture capital funds. For entrepreneurs seeking venture capital funds for their young companies, it may also mean a lower potential cost of capital for the financing of business venturing. From the viewpoint of public policy makers interested in facilitating the funding of business venturing, it may provide insight regarding regulatory issues surrounding taxation and the barriers and incentives which affect venture capital investment.     

Arbitrage risk and the cross-section of stock returns: Evidence from China

We demonstrate that arbitrage risk, constructed using three measures — noise trader risk, trading cost and information uncertainty — can predict the return of stocks cross-sectionally in China. The findings are broadly consistent even when out-of-sample tests are conducted using the Fama-MacBeth cross-sectional regression approach. We also construct hypothetical portfolios using the information arising from arbitrage risk and find the existence of abnormal returns which is robust to the use of various portfolios constructed by re-sampling the observations through multiple approaches (e.g., by market capitalization and by book-to-market ratio). Lastly, we reconstruct our portfolios by considering the unique nature of the Chinese stock market (e.g., the dominance of individual investors). Our trading strategies again successfully obtain abnormal returns, suggesting that arbitrage risk can be useful to construct effective investment portfolios in China.     

Risk and ex ante cost of equity estimates of emerging market firms

We examine the empirical relationship between estimates of ex ante cost of equity and risk for a sample of individual emerging market equities for the period 1990–2000. The ex ante cost of equity estimates are obtained using the residual income valuation model. As in studies that use mean realized returns on emerging market indexes, a measure of total risk (return volatility) is the most significant risk factor in explaining ex ante expected return estimates. For emerging market equities with substantial investability to global investors, global beta adds some explanatory power.     

Risk Management in Agricultural Markets: A Review

This article surveys and evaluates the current state of knowledge about producers' marketing strategies to manage price and revenue risk for farm commodities. The review highlights gaps between concepts and their implementation. Many well‐developed models of price behavior exist, but appropriate characterization and estimation of the probability distributions of commodity prices remain elusive. Hence, the preferred measure of price risk is ambiguous. Numerous models of optimal marketing portfolios for farmers have been specified, but their behavior appears to be inconsistent with most, if not all, of these models. In addition, some research suggests that farmers can earn speculative profits, which is inconsistent with notions of efficient markets. The conclusions discuss what academic research can and cannot accomplish in relation to assisting producers with risk‐management decisions. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:953–985, 2001     

Managing the retail format portfolio: An application of modern portfolio theory

We apply modern financial portfolio theory (MPT) to managing portfolios of retail formats. The objective of MPT is to maximize overall portfolio return for a given level of portfolio risk. We applied MPT to three prominent hotel firms to determine the ideal mix of formats in their hotel brand portfolios, using revenue per available room (RevPAR) as a proxy for return on investment. We found that all three firms could improve their returns and reduce their risk by reallocating the number of hotel rooms (i.e., scarce resources) across their different retail formats.     

Book Reviews

In a world of limited resources, marketing managers tasked to deliver shareholder value face decisions about how to maximise the returns on their marketing portfolio. Risk is less often considered. In finance the picture is very different; financial portfolio management is concerned with both risk and returns. The central innovation in this paper is the application of modern portfolio theory (MPT) to the management of marketing portfolios in food retailing and in drinks manufacturing. The authors develop a model that calculates an efficient frontier of marketing portfolios that maximise overall return within certain risk constraints, first for a simple two-segment marketing world and then for a more realistic multi-segment portfolio. However, marketing portfolios differ from financial ones in the sense that the allocation of marketing spend affects the returns from the portfolio. Therefore, a second innovation, an extension of MPT to take account of marketing spend allocation decisions, has been developed. Using this model, marketers can determine the risk and the returns of marketing investments, helping them select an optimal portfolio. This would go some way to ensuring that marketing contributes to shareholder value creation, currently one of its major challenges.