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Abstract:
In this paper we develop and demonstrate the workings of a copula-based technique that allows the derivation of dynamic trading strategies, which generate returns with statistical properties similar to hedge funds. We show that this technique is not only capable of replicating fund of funds returns, but is equally well suited for the replication of individual hedge fund returns. Since replication is accomplished by trading futures on traditional assets only, it avoids the usual drawbacks surrounding hedge fund investments, including the need for extensive due diligence, liquidity, capacity, transparency and style drift problems, as well as excessive management fees. As such, our synthetic hedge fund returns are clearly to be preferred over real hedge fund returns.

hedge fund, replication, copula, dynamic trading

Abstract:
By dynamically trading futures in very much the same way as investment banks hedge their OTC option positions it is possible to generate returns that are statistically very similar to the returns generated by hedge funds but without any of the usual drawbacks surrounding alternative investments, i.e. without liquidity, capacity, transparency or style drift problems and without paying over-the-top management fees. Hedge fund returns may be different, but they are certainly not unique.

hedge fund, replication

Abstract:
The monthly return distributions of many hedge fund indices exhibit highly unusual skewness and kurtosis properties as well as first-order serial correlation. This has important consequences for investors. We demonstrate that although hedge fund indices are highly attractive in mean-variance terms, this is much less the case when skewness, kurtosis and autocorrelation are taken into account. Sharpe Ratios will substantially overestimate the true risk-return performance of (portfolios containing) hedge funds. Similarly, mean-variance portfolio analysis will over-allocate to hedge funds and overestimate the attainable benefits from including hedge funds in an investment portfolio. We also find substantial differences between indices that aim to cover the same type of strategy. Investors' perceptions of hedge fund performance and value added will therefore strongly depend on the indices used.

hedge fund, hedge fund index, Sharpe Ratio, Mean-Variance analysis, skewness, kurtosis

Abstract:
In this paper we investigate the claim that hedge funds offer investors a superior risk-return trade-off. We do so using a continuous time version of Dybvig's (1988a, 1988b) payoff distribution pricing model. The evaluation model, which does not require any assumptions with regard to the return distribution of the funds in question, is applied to the monthly returns of 77 hedge funds and 13 hedge fund indices over the period May 1990-April 2000. The results show that as a stand-alone investment hedge funds do not offer a superior risk-return profile. We find 12 indices and 72 individual funds to be inefficient, with the average efficiency loss amounting to 2.76% per annum for indices and 6.42% for individual funds. Part of the inefficiency cost of individual funds can be diversified away. Funds of funds, however, are not the preferred vehicle for this as their performance appears to suffer badly from their double fee structure. Looking at hedge funds in a portfolio context results in a marked improvement in the evaluation outcomes. Seven of the 12 hedge fund indices and 58 of the 72 individual funds classified as inefficient on a stand-alone basis are capable of producing an efficient payoff profile when mixed with the S&P 500. The best results are obtained when 10-20% of the portfolio value is invested in hedge funds

Abstract:
With average hedge fund performance steadily deteriorating and equity markets picking up again, interest in hedge fund return replication as a cheaper means of obtaining hedge fund-like returns is growing steadily. Currently, there are various products on offer. Compared to real hedge funds (of funds), all of them offer improved liquidity, transparency, capacity, etc. and thereby solve a range of problems surrounding hedge fund investment. There are, however, substantial differences in terms of their attraction as portfolio diversifiers. The multi-strategy replication products offered by Merrill Lynch (Factor Index), Goldman Sachs (ART Index), and Partners Group (ABS fund) exhibit a strong correlation with the stock market. This severely limits these products' attraction as portfolio diversifiers. FundCreator does not necessarily replicate any specific fund or index, but allows investors to design their own diversifier from scratch. This gives investors a unique opportunity to create new tailor-made diversifiers with characteristics that are optimal given their existing portfolios. Clearly, this makes FundCreator-based synthetic funds much more attractive than the various multi-strategy hedge fund replication and alternative beta products currently on offer

Hedge fund, synthetic fund, replication, asset management

Abstract:
In this paper we study the univariate return properties of a large variety of commodity futures. Our analysis shows that the volatility of commodity futures is comparable to that of US large cap stocks. Yet, with the exception of energy, a consistently positive risk premium is lacking in commodity futures. We also find that for many commodities, futures returns and volatility can vary considerably over different phases of the business cycle, under different monetary conditions as well as with the shape of the futures curve. Skewness in commodity futures returns is largely insignificant, whereas kurtosis is significantly positive and comparable to that of US large cap stocks. In almost all commodities we find significant degrees of autocorrelation, which affects the properties of longer horizon returns.

Commodities, commodity futures, risk premium, volatility, skewness, kurtosis, autocorrelation

Abstract:
Recently, Kat and Palaro (2005) showed how dynamic trading technology can be used to create dynamic futures trading strategies (or 'synthetic funds' as we call them), which generate returns with predefined statistical properties. In this paper we put their approach to the test. In a set of four out-of-sample tests over the period March 1995-April 2006 we show that the Kat and Palaro (2005) strategies are indeed capable of accurately generating returns with a variety of properties, including negative correlation with stocks and bonds and high positive skewness. Under difficult conditions, the synthetic funds also produce impressive average excess returns. Combined with their liquid and transparent nature, this confirms that synthetic funds are an attractive alternative to direct investment in popular alternative asset classes such as (funds of) hedge funds, commodities, etc.

synthetic fund, dynamic trading, correlation, skewness, asset allocation

Abstract:
In this paper we use the hedge fund return replication technique recently introduced in Kat and Palaro (2005) to evaluate the net-of-fee performance of 485 funds of hedge funds. The results indicate that the majority of funds of funds have not provided their investors with returns, which they could not have generated themselves by trading S&P 500, T-bond and Eurodollar futures. Purely in terms of returns therefore, most funds of hedge funds have failed to add value.

Hedge funds, fund of funds, return replication, performance evaluation, copula, alpha

Abstract:
This paper incorporates investor preferences for return distributions' higher moments into a Polynomial Goal Programming (PGP) optimisation model. This allows us to solve for multiple competing hedge fund allocation objectives within a mean -variance - skewness - kurtosis framework. Our empirical analysis underlines the existence of significant differences in the return behaviour of different hedge fund strategies. Irrespective of investor preferences, the PGP optimal portfolios contain hardly any allocation to long/short equity, distressed securities, and emerging markets funds. Equity market neutral and global macro funds on the other hand tend to receive very high allocations, primarily due to their low co-variance, high co-skewness and low co-kurtosis properties. More specifically, equity market neutral funds act as volatility and kurtosis reducers, while global macro funds act as portfolio skewness enhancers. In PGP optimal portfolios of stocks, bonds, and hedge funds, where equity exposure tends to be traded off for hedge fund exposure, we observe a similar preference for equity market neutral and global macro funds.

Hedge funds, asset allocation, diversification, skewness, kurtosis, optimisation

Abstract:
In this paper we study the multivariate return properties of a large variety of commodity futures. We find that between commodity groupings (such as metals, energy, etc.) correlations are very low and mostly insignificant whereas within groups they tend to be much stronger. In addition, commodity futures are roughly uncorrelated with stocks and bonds. Still, correlations may vary somewhat over the different phases of the business cycle, suggesting that not all commodities make equally good diversifiers at all times. Copula-based tests do not indicate any deviant behaviour in the tails of the joint return distribution of commodity futures and stocks or bonds. Contrary to equities and bonds, we show that commodity futures returns are positively correlated with unexpected inflation (i.e. 25% on average with CPI inflation as opposed to -30% for equities and -50% for bonds). There are significant differences between the various commodities, however, with energy, metals, cattle, and sugar offering the best hedging potential. Altogether, assuming that the observed regularities will persist, our results confirm that a well-balanced commodity futures portfolio could offer a worthwhile diversification service to the typical traditional investment portfolio.

Commodities, commodity futures, correlation, tail-dependence, SJC copula, inflation

Abstract:
Using monthly return data on 455 hedge funds over the period 1994-2001 we study the diversification effects from introducing hedge funds into a traditional portfolio of stocks and bonds. Our results indicate that although the inclusion of hedge funds may significantly improve a portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds includes a definite trade-off between profit and loss potential and suggests that, contrary to popular belief, hedge funds might be more suitable for institutional than for private investors. Our results also emphasize the fact that to have at least some impact on the overall portfolio, one has to make an allocation to hedge funds which exceeds the typical 1-3% that many institutions are currently considering.

Hedge funds, diversification, skewness, kurtosis, portfolio

Abstract:
Using monthly return data over the period June 1994 - May 2001 we investigate the performance of randomly selected baskets of hedge funds ranging in size from 1 to 20 funds. The analysis shows that increasing the number of funds can be expected to lead not only to a lower standard deviation but also, and less attractive, to lower skewness and increased correlation with the stock market. Most of the change occurs for relatively small portfolios. Holding more than 15 funds changes little. The population average appears to be a good approximation for the average basket of 15 or more funds. With 15 funds, however, there is still a substantial degree of variation in performance between baskets, which dissolves only slowly when the number of funds is increased. Survivorship bias is largely independent of portfolio size and thus cannot be diversified away. Finally, our efficiency test indicates that one only needs to combine a small number of funds to obtain a substantially more efficient risk-return profile than that offered by the average individual hedge fund.

Hedge fund, portfolio, diversification, survivorship bias, efficiency

Abstract:
In this paper we use the hedge fund return replication technique recently introduced by Kat and Palaro (2005) to evaluate the net-of-fee performance of 1917 individual hedge funds. Comparing fund returns with the returns on dynamic futures trading strategies with the same risk and dependence characteristics, we find that no more than 17.7% of the hedge funds in our sample beat the benchmark. In other words, the majority of hedge funds have not provided their investors with returns, which they could not have generated themselves by mechanically trading S&P 500, T-bond and Eurodollar futures. Over time, we observe a substantial deterioration in overall hedge fund performance. In addition, we find a tendency for the performance of successful funds to deteriorate over time, which supports the hypothesis that increasing assets under management endanger future performance.

Hedge funds, performance evaluation, return replication

Abstract:
Hedge funds exhibit a high rate of attrition that has increased substantially over time. Using data over the period 1994-2001, we show that lack of size, lack of performance and an increasingly aggressive attitude of old and new fund managers alike are the main factors behind this. Although attrition is high, survivorship bias in hedge fund data is quite modest, which reflects the relatively small difference in performance between surviving and defunct funds. Concentrating on survivors only will overestimate the average hedge fund return by around 2% per annum. For small, young, and leveraged funds, however, the bias can be as high as 4-6%. We also find significant survivorship bias in estimates of the standard deviation, skewness and kurtosis of individual hedge fund returns. When not corrected for, this will lead investors to seriously overestimate the benefits of hedge funds. We find fund of funds attrition to be much lower than for hedge funds. Combined with a small difference in performance between surviving and defunct funds of funds, this yields relatively low survivorship bias estimates for funds of funds.

Hedge fund, attrition, survivorship bias

Abstract:
This paper provides an overview of the most important statistical properties of individual hedge fund returns. We find that the net-of-fees monthly returns of the average individual hedge fund exhibit significant degrees of negative skewness, excess kurtosis, as well as positive first-order serial correlation. The correlations between hedge funds in the same strategy group are of the same order of magnitude as the correlations between funds in different strategy groups and relatively low. Only 10-20% of the variation in the average individual hedge fund's returns can be explained by what happens in the US equity and bond markets. Compared to individual funds, portfolios of hedge funds tend to exhibit lower skewness, higher serial correlation and higher correlation with stocks and bonds. Movements in the US equity and bond markets still only explain 20-40% of the variation in hedge fund portfolios returns though. Finally, an equally-weighted portfolio of all funds in our sample offers a 2.76% higher mean return than the average fund of funds. This strongly suggests that the timing and fund picking activities of the average fund of funds are not rewarded by a higher return.

Abstract:
We study the diversification effects from introducing hedge funds into a traditional portfolio of stocks and bonds. Our results make it clear that in terms of skewness and kurtosis equity and hedge funds do not combine very well. Although the inclusion of hedge funds may significantly improve a portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds includes a definite trade-off between profit and loss potential. Our results also emphasize that to have at least some impact on the overall portfolio, investors will have to make an allocation to hedge funds which by far exceeds the typical 1-5% that many institutions are currently considering.

Hedge funds, asset allocation, diversification, skewness, kurtosis, optimization, mean-variance

Abstract:
In this paper we study the possible role of managed futures in portfolios of stocks, bonds and hedge funds. We find that allocating to managed futures allow investors to achieve a very substantial degree of overall risk reduction at limited costs. Apart from their lower expected return, managed futures appear to be more effective diversifiers than hedge funds. Adding managed futures to a portfolio of stocks and bonds will reduce that portfolio's standard deviation more and quicker than hedge funds will, and without the undesirable side-effects on skewness and kurtosis. Overall portfolio standard deviation can be reduced further by combining both hedge funds and managed futures with stocks and bonds. As long as at least 45-50% of the alternatives allocation is allocated to managed futures, this again will not have any negative side-effects on skewness and kurtosis.

Abstract:
Disappointing performance is leading hedge fund investors to look for cheaper alternatives. Hedge fund indexation has been suggested as a possible solution. Unfortunately, investable hedge fund indices are nothing more than funds of funds in disguise, with performance similar or even worse than real funds of funds. The core problem of hedge fund indexation is that as long as one still invests in hedge funds, the cost factor that indexation is meant to eliminate will still be there. In this paper we use our FundCreator technology to generate returns with statistical properties very similar to those of hedge fund indices, but without actually investing in hedge funds. The proposed strategies only trade liquid futures contracts and therefore not only offer investors an accurate replica, but at the same time solve many other problems typically surrounding hedge fund investments, such as illiquidity, lack of transparency, limited capacity, etc.

Hedge fund, FundCreator, Indexation

Abstract:
Most previous tests of hedge fund performance have failed to model the exposure of hedge fund returns to systematic non-normality risks, nor have they taken the tactical asset allocation decisions of hedge funds managers into account. This paper shows that failure to account for these features leads to incorrect statistical inferences on the performance of 1 out of 4 hedge funds and overstates hedge funds' alpha by 1.54% on average. Put another way, hedge funds offer abnormal returns that are 23.1% lower than commonly accepted.

Hedge funds, performance evaluation, alpha, systematic skewness, systematic kurtosis, tactical asset allocation

Abstract:
Most previous tests of hedge fund performance have failed to model the exposure of hedge fund returns to systematic non-normality risks, nor have they taken the tactical asset allocation decisions of hedge funds managers into account. This paper shows that failure to account for these features leads to incorrect statistical inferences on the performance of 1 out of 4 hedge funds and overstates hedge funds' alpha by 1.54% on average. Put another way, hedge funds offer abnormal returns that are 23.1% lower than commonly accepted.

Hedge funds, performance evaluation, alpha, systematic skewness, systematic kurtosis, tactical asset allocation

Abstract:
In this paper we study the persistence and predictability of several statistical parameters of individual hedge fund returns. We find little evidence of persistence in mean returns but do find strong persistence in hedge funds' standard deviations and their correlation with the stock market. Persistence in skewness and kurtosis is low but this could be due to the small size of the sample used. Despite the observed persistence, our study also shows that in absolute terms hedge funds' risk profiles are not easily predicted from historical returns alone. The true value of a hedge fund's track record therefore appears not to lie in its use as a predictor of future performance and risk, but primarily in the insight that it provides in a fund's risk profile relative to that of other funds in the same strategy group. The availability of a track record is important, but for a different reason than many investors think.

Abstract:
In this paper we investigate whether it is possible for a fund of hedge funds to not only offer investors access to a diversified basket of hedge funds but to provide skewness protection at the same time. We study two different strategies. The first is for a fund to buy stock index puts and leverage itself, in line with the skewness reduction strategy proposed earlier in Kat (2002). In general, the latter strategy is too dependent on the actual asset allocation strategy followed by investors to allow a fund to be constructed that is optimal for all investors at the same time. However, for investors that invest more or less equal amounts in stocks and bonds and who keep their hedge fund allocation below 30% such a fund can indeed be structured. The second strategy is for a fund to buy put options on itself. We show that this does allow a fund to offer skewness protection to different types of investors at the same time, but compared to the optimal strategy the protection will be somewhat less accurate. Under both strategies the fund of funds is likely to incur a significant loss in expected return. As long as the hedge fund allocation stays below 30%, however, the loss of expected return on investors' overall portfolios will remain limited.

Hedge fund, fund of funds, skewness, put option, leverage

Abstract:
In this paper we discuss a number of important questions to ask when analysing a new alternative diversifier from either a stand-alone, asset-only or asset-liability point of view. The framework is simple, but highly effective. Apart from the new diversifier's statistical properties, it emphasizes the importance of properly accounting for parameter uncertainty and illiquidity; two elements very often ignored by investors. It also shows the importance of taking the correct perspective when evaluating a new diversifier. What looks good from a stand-alone perspective need not look good in a portfolio context and vice versa. Application of the above framework to funds of hedge funds, commodities and synthetic funds underlines the advantages and disadvantages of these diversifiers and clearly points at synthetic funds as the most and funds of hedge funds as the least attractive of the three.

Diversification, alternative investments, hedge funds, commodities, synthetic funds

Abstract:
In this paper we use a scenario-based ALM model to study the effects on the risk-return profile of defined benefit pension funds from including options in the pension fund portfolio. Our results show that properly constructed option strategies can add substantial value to pension fund management. The results are robust with respect to variations in horizon, equity risk premium and volatility assumptions. The optimal strategy, however, should be determined in an asset-liability context and not ad hoc, as the intuitively most appealing strategies are not necessarily the most effective. In addition, we find that different types of funds may require significantly different option strategies. What works well for one fund may be less effective or even counter-productive for another. Overall, incorporating options appears an efficient way of improving long-term pension fund health and therefore the sustainability of defined benefit pension schemes.

Pension fund, derivatives, options, asset-liability management, scenarios

Abstract:
Over the last 20 years, investors have come to approach investment decision-making in an increasingly mechanical manner. Optimisers are filled up with historical return data and the 'optimal' portfolio follows almost automatically. In this paper we argue that such an approach can be extremely dangerous, especially when alternative investments such as hedge funds are involved. Proper hedge fund investing requires a much more elaborate approach to investment decision-making than currently in use by most investors. The available data on hedge funds should not be taken at face value, but should first be corrected for various types of biases and autocorrelation. Tools like mean-variance analysis and the Sharpe ratio that many investors have become accustomed to over the years are no longer appropriate when hedge funds are involved as they concentrate on the good part while completely skipping over the bad part of the hedge fund story. Investors also have to find a way to figure in the long lock-up and advance notice periods, which make hedge fund investments highly illiquid. In addition, investors will have to give weight to the fact that without more insight in the way in which hedge funds generate their returns it is very hard to say something sensible about hedge funds' future longer-run performance. The tools to accomplish this formally are not all there yet, meaning that more than ever investors will have to rely on common sense and doing their homework.

Hedge Funds, Investment, Mean-Variance, Skewness, Alternative Investments

Abstract:
With the arrival of synthetic funds, investment management no longer has to resemble a visit to The Mongolian Barbeque. Investors no longer have to go through the usual process of finding and combining individual assets and funds into portfolios in an, often only partially successful, attempt to construct an overall portfolio with the characteristics they require. They can now design and create their ideal diversifier or overall portfolio by themselves and avoid the many pitfalls and excessive fees that surround popular new asset classes, such as hedge funds, private equity, etc. Undoubtedly, investors will need time to come to grips with the concept, but given these benefits, there is no doubt synthetic funds have a bright future ahead of them.

Synthetic fund, hedge fund, portfolio management, asset allocation

Abstract:
Since the publication of our first paper on hedge fund replication in 2005, our FundCreator methodology has met with many positive reactions. There have also been some negative responses though. With investors clearly becoming confused as a result of the amount of disinformation that is being circulated, in this short paper we address the 10 most common points of criticism. We argue that most of these are largely unjustified and fairly trivial at best and no reason whatsoever to doubt the capability of FundCreator to deliver exactly what it promises: returns with predefined statistical properties.

Hedge fund, synthetic fund, replication

Abstract:
In this paper we use the FundCreator hedge fund return replication technique recently introduced in Kat and Palaro (2005) to evaluate the net-of-fee performance of 875 funds of hedge funds and 2073 individual hedge funds, up to an including November 2006. Comparing fund returns with the returns on FundCreator-based dynamic futures trading strategies with the same risk and dependence characteristics, we find that no more than 18.6% of the funds of funds and 22.5% of the individual hedge funds in our sample convincingly beat the benchmark. In other words, the majority of hedge funds have not provided their investors with returns, which they could not have generated themselves by mechanically trading a diversified basket of liquid futures contracts. Over time, we observe a substantial deterioration in overall hedge fund performance. In addition, we find a tendency for the performance of successful funds to deteriorate over time. This supports the hypothesis that increased assets under management tend to endanger future performance.

Hedge fund, fund of funds, performance evaluation, replication

Abstract:
We present an extension of the traditional Sharpe ratio to allow for the evaluation of non-normal return distributions. Combining earlier work in this area with stochastic simulation, we develop a procedure that allows for the construction of a benchmark for the evaluation of the performance of funds with a non-normal return distribution, while maintaining the operational ease of the Sharpe ratio. Similar to the latter, our procedure only requires the risk-free rate of interest rate, the distribution of the market index and an assumption about the type of return distributions to be evaluated. Unlike the Sharpe ratio, however, we are not restricted to normality but are able to handle any reasonable type of distribution. Since our benchmarking procedure is based on the no-arbitrage assumption, it also provides insight into the conditional arbitrage-free value of one distributional parameter in terms of another. We show that in case of the Johnson Su distribution the relationship between skewness and mean return is more or less flat. Skewness and median return on the other hand exhibit a strong negative relationship.

Abstract:
Although the inclusion of hedge funds in an investment portfolio can significantly improve that portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness and higher kurtosis. In this paper we show how this highly undesirable side-effect can be neutralized by allocating a fraction of wealth to out-of-the-money put options on the relevant equity index. Based on monthly return data over the period 1994-2001 we show that investors who want to fully eradicate the negative skewness of portfolios containing stocks, bonds and hedge funds will have to sacrifice a not insignificant part of their expected return. Investors who limit themselves to neutralizing only the additional skewness caused by the inclusion of hedge funds will be able to do so at much more favourable terms, however. The latter only need to allocate a small fraction of wealth to index puts and accept a drop in expected return that is unlikely to exceed 1% per annum, depending on the hedge fund allocation. This means that in the current low interest rate environment the costs of eliminating the unwanted skewness effect of hedge funds need not be prohibitively high.

hedge funds, skewness, diversification

Abstract:
In this paper we use a scenario-based ALM model to study the impact of different interest rate derivatives strategies on the risk-return profile of a defined benefit pension fund. The results show that properly constructed hedging strategies using swaps and swaptions can add substantial value. Increased risk perception due to fair value accounting and regulation can be dealt with effectively via these techniques. The results are robust with respect to the assumed interest rate mean reversion level. An expected rise in interest rates is therefore no reason to refrain from hedging.

Pension fund, swap, swaption, hedging, interest rate risk

Abstract:
In this paper we report on a new class of derivative products which we refer to as 'equity-linked savings products' (ELSPs). ELSPs require investors to pay periodic installments in return for a predefined equity-linked payoff at maturity. We discuss the structuring, hedging, pricing and marketing aspects of a variety of ELSPs. We pay particular attention to the case of The Netherlands where ELSPs are currently very popular with an estimated USD 2 billion issued over the last three years. Reverse engineering of a recent issue shows that the profit margins that product providers may be able to achieve on ELSPs are extremely high.

Exotic Options, Investments

Abstract:
Interest rates are currently at a historical low. Since in the longer run interest rates will return to their historical average, this implies that bond prices are about to fall. Popular investment advice therefore says that investors should shorten the maturity of their bond portfolios to minimize their losses. This argument, however, skips over the fact that longer-dated bonds pay higher coupons as well as the fact that a substantial rise in interest rates may take quite some time to occur. We examine the combined impact of both and conclude that the current interest rate environment in no way implies that investors should rebalance towards short-dated bonds. Extensive scenario analysis confirms that in an overall portfolio context a longer-dated bond portfolio is more efficient than a short-dated bond portfolio, especially when long-dated liabilities are present.

Interest rates, bonds, yield curve, ALM

Abstract:
In this paper, we study the multivariate return properties of a large variety of commodity futures. We find that between commodity groupings (such as metals, energy, etc.) correlations are very low and mostly insignificant whereas within groups they tend to be much stronger. In addition, commodity futures are roughly uncorrelated with stocks and bonds. Still, correlations may vary somewhat over the different phases of the business cycle, suggesting that not all commodities make equally good diversifiers at all times. Copula-based tests do not indicate any deviant behavior in the tails of the joint return distribution of commodity futures and stocks or bonds. Contrary to equities and bonds, we show that commodity futures returns are positively correlated with unexpected inflation (i.e., 25% on average with CPI inflation as opposed to -30% for equities and -50% for bonds). There are significant differences between the various commodities, however, with energy, metals, cattle, and sugar offering the best hedging potential. Altogether, assuming that the observed regularities will persist, our results confirm that a well-balanced commodity futures portfolio could offer a worthwhile diversification service to the typical traditional investment portfolio.

Commodities, commodity futures, correlation, tail-dependence, SJC copula, inflation

Abstract:
In this paper we study the univariate return properties of a large variety of commodity futures. Our analysis shows that the volatility of commodity futures is comparable to that of US large cap stocks. Yet, with the exception of energy, a consistently positive risk premium is lacking in commodity futures. We also find that for many commodities, futures returns and volatility can vary considerably over different phases of the business cycle, under different monetary conditions as well as with the shape of the futures curve. Skewness in commodity futures returns is largely insignificant, whereas kurtosis is significantly positive and comparable to that of US large cap stocks. In almost all commodities we find significant degrees of autocorrelation, which affects the properties of longer horizon returns.

Commodities, commodity futures, risk premium, volatility, skewness, kurtosis, autocorrelation

Abstract:
Digitals are contracts that pay a fixed amount of money if at maturity the reference index is above (for a call) or below (for a put) some specific value. One can easily extend this concept
to a bivariate setting and create a contract that pays a fixed amount if both reference indices are above (for a call) or below (for a put) certain values. Using these contracts we can create what we call 'C-Bricks', i.e. contracts that pay a fixed amount if at maturity both indices are within some range. We can cut C-Bricks in half in six different ways. This gives rise to what we refer to as 'H-Bricks'. In this article we provide analytical pricing formulas for these types of contracts, assuming we live in the world of Black and Scholes (1973). In the process we also derive pricing results for equivalent contracts that, when alive at maturity, pay the value of one of the reference indices instead of a fixed amount. We refer to those as 'A-Bricks'.

Abstract:
Several authors have published analytical formulas for barrier options. Unfortunately, the specifications of the options studied do not match those of the options typically traded in the OTC market. One major difference concerns the frequency with which the reference index is monitored. Where academics simply assume that the index is monitored continuously, practitioners necessarily have to specify a discrete monitoring frequency. Intuitively, it is clear that discrete monitoring should cause knock-out options to become more and knock-in options to become less expensive. In this article we develop a binomial pricing procedure for the pricing of discrete barrier options, with full as well as partial monitoring. Comparisons with Monte Carlo prices show the method to be very accurate, while requiring only a fraction of the time.

Abstract:
The specifications of the lookback options traded in today's OTC markets do not match the specifications of the contracts studied by academics. In practice, monitoring of the reference index may be done discretely and at the same time be limited to a specific subperiod. In this article we show that in the world of Black and Scholes (1973) discrete lookback options can be priced in closed-form. We derive pricing formulas for a variety of full and partial lookback options where monitoring takes place at non-necessarily equally spaced points in time. Analysis shows that monitoring the reference index discretely instead of continuously may have a very significant effect on the prices of lookback options, but does not introduce new hedging problems.

Abstract:
Derivatives traded in the OTC markets may sometimes involve both asset price risk and exchange rate risk. This article provides an unified treatment of the pricing and hedging of path independent international equity derivatives. After modeling the international economy, we derive a partial differential equation that the pricing formula of any path independent derivative asset exposed to both equity risk and exchange rate risk has to satisfy. We use this result to derive pricing results for a variety of instuments. In addition, we derive and discuss the replication strategies that can be used to hedge these contracts.

Abstract:
Lookback options provide investors with perfect market timing services. However, these options are hardly ever traded because they are much more expensive than ordinary options. The problem with standard lookbacks is that they provide the investor with much more timing than typically required. In other words, the lookback feature can remain limited to only the first (for entry timing) or the last (for exit timing) part of the options' life.
In this article we provide closed-form pricing formulas for such options, fixed-strike as well as floating-strike. Analysis shows how the prices of such 'partial lookback options' respond to a change in the monitoring period. Options with relatively short lookback periods appear to offer a good solution to most timing problems at a reasonable price.

Abstract:
Barrier options come in many forms. In this article we study the pricing of discrete partial barrier options where the barrier level may change deterministically during the monitoring period and monitoring takes place at not-necessarily equally spaced points in time. We provide closed-form pricing formulas for the prices of these options in a Black-Scholes (1973) world. Using these results, we show that monitoring the reference index discretely instead of continuously may have a very significant effect on the prices of barrier options.

Abstract:
With traditional barrier options, life and death of the option are determined by the same reference index as the index underlying the original option contract. It is, however, also possible to structure options where a second reference index determines whether the option knocks in or out. In that case we say the option has an 'outside barrier' and we refer to such options as 'outside barrier options'. In this article we provide closed-form pricing formulas for 8 types of outside barrier options, assuming we live in a two-asset version of the world of Black and Scholes (1973). Analysis of our results makes it clear that, depending on the correlation between both indices in question, outside barrier options can be an interesting alternative for traditional ('inside') barrier options with a reverse barrier.

Abstract:
In this article we use stochastic simulation methods to study the performance of a number of different dynamic portfolio insurance strategies, including option replicating portfolio insurance (ORPI), constant proportion portfolio insurance (CPPI) and a modified stop-loss (MSLI) strategy. We assume the underlying portfolio to be the S&P 500 tracking portfolio with all dividends reinvested upon receipt. The initial time to maturity is one year. Although the differences are mostly small, our results show that ORPI typically offers more attractive results than CPPI or MSLI. Adjusting the floor rule to lock in intermediate profits or adding a constant horizon feature does not lead to superior results.

Abstract:
In this article we study the pricing and hedging of options whose payoff is a polynomial function of the underlying reference index at expiration; so-called power options. Working in the Black-Scholes (1973) framework, we derive closed-form formulas for the prices of general power calls and puts. Parabola options are studied as a special case. Power options can be hedged by statically combining ordinary options in such a way that their payoffs form a piecewise linear function that approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.

Abstract:
In this article we present a model of S&P 500 futures mispricing that is able to capture all major stylized facts observed in actual S&P 500 mispricings behavior. The model itself is inspired by theoretical considerations as well as empirical observations. The model's parameters are estimated by combining stochastic simulation with a neural network. Only a small number of sample statistics is required as input. From the simulated mispricings and futures price series it is clear that the simulated data fit actual S&P 500 mispricings data very well.The approach may easily be extended to other asset classes where the available information on the variables to be modeled is for some reason limited and/or where the model to be estimated is too complex to do so directly.

Abstract:
Future volatility is a key input for pricing and hedging derivatives and for quantitative investment strategies in general. There are many different approaches. This article investigates whether random walk, GARCH (1,1), EGARCH (1,1) and stochastic volatility models of return volatility behavior differ in their ability to predict the volatility of stock index and currency returns over horizons ranging from 2 to 100 trading days. We use close-to-close return data for 7 indices and 5 currencies over the period 1980-1992. The results show that the forecast performance of the different models depends on the specific asset class in question. For stock indices the best volatility predictions are generated by the stochastic volatility model. For currencies on the other hand, the best forecasts come from the GARCH (1,1) model.

Abstract:
This article describes the valuation, hedging and applications of contingent premium options (CPOs). We derive closed-form formulas for path independent and path dependent CPOs that address most cases of practical importance. The resulting hedge ratios show that when it is not possible to hedge these options statically, hedging CPOs may become problematic, especially when the options approach maturity. We also discuss how to structure more specific CPOs, such as money-back and pay-later options. For an investor with a strong view on the price of the underlying asset, these types of options may be an attractive alternative to standard options.

Derivatives, Exotic Options

Abstract:
In this paper we study the pricing of barrier options where the period during which the underlying price is monitored for barrier hits is restricted to only part of the options' lifetime. We derive closed-form formulas for the prices of a number of partial barrier options, including partial asset- or-nothing and cash-or-nothing barrier options. Our results clearly show the importance of the length and the location of the monitoring period for the option price. It is also shown that for options where the monitoring period starts after the options' initial starting date, an alternative interpretation of the barrier condition may lead to a very substantial change in the option price.

Abstract:
We use stochastic simulation methods to study the efficiency of delta-hedging strategies for ordinary, look-back, and Asian call options on the S&P 500 index. Execution is assumed to take place in either the cash or the futures market. Our results clearly show the inadequacy of delta hedging for hedging these options. The outcome of the hedging process is shown to depend heavily on the way the theoretical hedging strategy is operationalized and the gamma characteristics of the option position to be hedged. Apart from discrete hedge rebalancing, our results identify volatility misprediction and, for path-dependent options, the use of hedge ratios derived from Black-Scholes assumptions as the main sources of hedging error risk. Despite mispricings and rollover costs, futures market execution is typically to be preferred over cash market execution.

Abstract:
We compare the binomial pricing methods for lookback options developed by Babbs (1992), Hull and White (1993), and Cheuk and Vorst (1994). The Babbs and the Cheuk and Vorst methods are very similar in nature and essentially two applications of the same transformation. The Hull and White method outranks the Babbs and the Cheuk and Vorst methods in terms of flexibility. From a computational point of view, however, both of the latter methods are much more attractive. Our simulation results show that for full lookbacks the prices generated by the Babbs and the Cheuk and Vorst methods are very accurate, even with only a limited number of time steps. Accurate binomial pricing of partial lookbacks appears problematic, however.