Mean‐variance efficiency of the market portfolio and futures trading

We derived an intertemporal capital asset pricing model in which the mean‐variance efficiency of the market portfolio is neither a necessary nor a sufficient condition. We obtained this result by modeling a frictionless, continuously open financial market in which nonredundant futures contracts are available for trade, in addition to cash assets. Introducing such contracts modifies the way investors optimally allocate their wealth. Their portfolios then comprise the riskless asset, a perturbed mean‐variance‐efficient portfolio of cash assets, and a perturbed mean‐variance‐efficient portfolio of futures contracts. Furthermore, a (3 + K) mutual fund separation is obtained, with K being the number of economic state variables, in lieu of the usual (2 + K) fund separation. Mean‐variance efficiency of the market portfolio is a necessary condition only when cash assets are the sole traded assets. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:329–346, 2001     

Optimal portfolio composition and the CAPM

It is commonly assumed that the CAPM implies that all investors hold a balanced portfolio, “the market portfolio,” and investors just determine the proportion of their wealth held in the market portfolio and the risk-free asset. That this is patently at odds with observed investor behavior is sometimes used to justify rejecting the CAPM. However, by assuming that substitute securities exist, in this paper we still obtain the CAPM, although investors neither hold all of the assets in the market nor a balanced shareholding in the assets they do hold.     

Bernoulli speculator and trading strategy risk

In a continuous‐time model of a complete information economy, we examine the case of a “pure” speculator who chooses to trade only on forward or futures contracts written on interest‐rate‐sensitive instruments. Assuming logarithmic utility, we assess whether his strategy exhibits the same structure as when he uses primitive assets only. It turns out that when interest rates follow stochastic processes, as in the model of Heath, Jarrow, and Morton (1992), where the instantaneous forward rate is driven by an arbitrary number of factors, the speculative trading strategy involving forwards exhibits an extra term vis‐a‐vis the one using futures or primitive assets. This extra term, different from a Merton–Breeden dynamic hedge, is novel and can be interpreted as a hedge against an “endogenous risk,” namely the interest‐rate risk brought about by the optimal trading strategy itself. Thus, only the strategy using futures (or the cash assets themselves) involves a single speculative term, even for the Bernoulli speculator. This result illustrates another major aspect of the marking to market feature that differentiates futures and forwards, and thus has some bearing on the issue of the optimal design of financial contracts. Real financial markets being, in fact, incomplete, the additional “endogenous” risk associated with forwards cannot be hedged perfectly. Since using futures eliminates the latter, risk‐averse agents will find them attractive in relation to forward contracts, other things being equal. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 507–523, 2000     

Hedging under counterparty credit uncertainty

This study investigates optimal production and hedging decisions for firms facing price risk that can be hedged with vulnerable contracts, i.e., exposed to nonhedgeable endogenous counterparty credit risk. When vulnerable forward contracts are the only hedging instruments available, the firm's optimal level of production is lower than without credit risk. Under plausible conditions on the stochastic dependence between the commodity price and the counterparty's assets, the firm does not sell its entire production on the vulnerable forward market. When options on forward contracts are also available, the optimal hedging strategy requires a long put position. This provides a new rationale for the hedging role of options in the over‐the‐counter markets exposed to counterparty credit risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 248–263, 2008     

Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.     

Home bias and high turnover: Dynamic portfolio choice with incomplete markets

Why do investors trade a lot in foreign assets and hold so little of them in their portfolios? This paper shows that both observations can arise naturally in the presence of nondiversifiable nontraded consumption risk when each country specializes in production, preferences exhibit consumption home bias, and asset markets are incomplete. Using a general equilibrium two-country, two-sector (tradable and nontradable) model of the world economy with production I show that low diversification occurs because variations in relative prices (i) increase the riskiness of foreign assets and (ii) facilitate risk-sharing across countries. Large and volatile capital flows are necessary to take advantage of international risk premia differentials that occur in response to productivity changes in the nontradable sector. I characterize the optimal portfolio holdings, the evolution of the investment opportunity set, the risk premium, and the dynamics of capital flows using a new methodology for solving dynamic general equilibrium models with incomplete markets and portfolio choice.     

Liability driven investment with alternative assets: Evidence from Brazil

We study the portfolio choice problem for an asset-liability investor who invests in stocks, equity mutual funds, government bonds, short term interest, hedge funds, listed real estate, and commodities futures available in Brazil. Inflation and real interest play as important risk sources. We estimate the asset classes and liabilities time-varying conditional covariance structure using an asymmetric multivariate dynamic conditional correlation GARCH model and compare the asset-liability portfolio's global minimum variance allocation with Brazilian pension funds' market portfolio. The conditional covariance structure provides insights about the complex dynamic relationships between the asset classes and liabilities. We find that some (though not all) Brazilian alternative assets render strong diversification and liabilities hedging benefits for asset-liability investors. There are significant strategic asset allocation differences between the market portfolio and the liability driven portfolio as given by our model. We, therefore, question the Brazilian pension funds' allocation.     

INVESTING WITH LIQUID AND ILLIQUID ASSETS

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.     

Exports and hedging exchange rate risks: the multi‐country case

This article examines the optimal production, export allocation, and hedging decisions of a risk‐averse international firm that exports to several foreign markets with different currencies. The firm faces multiple exchange rate risks. Optimal decisions are analyzed under two scenarios. In the first, there is a forward market for one currency only. Then, the export allocation to different markets is separable from the firm's preferences and the joint distribution of the exchange rates. In contrast, total production is not separable except for a special case. In the second scenario, there is a forward market for each currency. Then, both production and export allocation are separable. Hedging with forward contracts depends on risk premia and on the joint distribution of the exchange rates. If tradable exchange rate risk is a linear function of untradable exchange rate risk plus noise, there is a conflict between cross hedging and taking a basis risk. If, alternatively, the untradable exchange rate risk is a linear function of the tradable exchange rate risk and noise, there is no such conflict. A speculative position in a biased forward market for one currency can be cross hedged using an unbiased forward market for another currency. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:843–864, 2000.     

Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003     

No chills or burns from temperature surprises: An empirical analysis of the weather derivatives market

This article examines the efficiency of the weather futures market traded on the CME in both HDD and CDD futures contracts in 18 cities across the United States. Efficiency is examined in three ways. First, by comparing the market's implied forecasts for the weather against other forecasts. Second, by looking at whether market's overreact or under‐react to temperature surprises. Third, by looking at weather derivative patterns across cities. We find that generally the market seems very efficient despite its lack of liquidity. We also find risk premia that seem to vary across cities and over time. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:1–33, 2011     

A Markowitz Optimization of Commodity Futures Portfolios

We examine the diversification benefits of using individual futures contracts instead of simply a commodity index. We determine the ex‐ante, ex‐post, and stability results for optimal Markowitz portfolios, investigate the instability between the ex‐ante and ex‐post results, and compare our results to traditional and naïve portfolios. The ex‐ante complete futures portfolio dominates the traditional and naive portfolios and the ex‐post portfolio outperforms the naïve portfolio. The instability between the ex‐ante and ex‐post results is primarily driven by the time‐varying returns of the individual assets rather than by risk. Finally, the Sharpe portfolio results are essentially identical to the Markowitz results. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:343‐368, 2013     

A new perspective on “the new rule”of the current account

In an influential series of contributions, Kraay and Ventura (2000, 2003) offer a “new rule” for the current account: in response to a temporary income shock, the change in the current account is equal to the change in saving times the ratio of net foreign assets to wealth. We analyze the impact of a temporary income shock on the current account in the context of a two-country dynamic general equilibrium model of portfolio choice and show that the new rule does not hold. We also show that the cross-section evidence reported by Kraay and Ventura in favor of the new rule is a feature implied by the steady state of the model that is conceptually distinct from the new rule. We argue that the new rule could only hold in a model with one-way capital flows (only inflows or outflows, but not both), a feature that is strongly counterfactual.     

The Relation between Physical and Risk‐neutral Cumulants

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. The empirical observation on skewness research suggests that derivative professionals may also desire to hedge beyond volatility risk and there exists the need to hedge higher‐moment market risks, such as skewness and kurtosis risks. We study two derivative contracts – skewness swap and kurtosis swap – which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the both skewness and kurtosis risk premiums are significantly negative.     

Does deliverability enhance the value of U.S. Treasury bonds?

This study presents the first examination of the value associated with long‐term U.S. Treasury bonds related to their delivery eligibility in the Treasury bond futures market. The opportunity for study has recently become possible given the reduced maturity of Treasury's noncallable bonds in the market. Consistent with rational behavior, deliverable bonds are found to be more valuable than otherwise comparable, ineligible bonds, and the estimated premia are larger than those previously documented for deliverable bills. However, although detectable and statistically significant, the deliverability component of a cash bond's value is somewhat modest in economic terms; some policy implications of this result are discussed. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:264–274, 2008     

Common Risk Factors Versus a Mispricing Factor of Tokyo Stock Exchange Firms: Inquiries into the Fundamental Value Derived from Analyst Earnings Forecasts*

We search for common factors and/or a mispricing factor for Tokyo Stock Exchange firms. We utilize the Edwards–Bell–Ohlson model to compute the firms' fundamental value and divide this value by the firms' market price to construct a new variable called a ‘value‐to‐price ratio’ (VPR). We find that this VPR variable can generate abnormal returns even after adjusting for the risk factors related to portfolio style differences. To find out whether it is indeed a risk factor or simply a characteristic, we construct return difference portfolios of the high VPR stocks minus the low value‐to‐price stocks and call this portfolio the upward‐forecast minus downward‐forecast (UMD) factor. Fama and MacBeth test indicate that the risk premium for this UMD factor is positive. The best model in terms of the adjusted R² value is the four‐factor model in which the UMD factor is added to the Fama and French three factors. GMM Euler condition tests reveal that the UMD factor helps to price assets and that the four‐factor model is not rejected. We conclude the VPR variable contains new information content that is not contained in the conventional Fama and French's three factors.     

Disagreement in a Multi‐Asset Market

This paper provides a simple framework to study the effect of disagreement in a multi‐asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi‐asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk‐free rate can decrease significantly even when the market is overoptimistic and overconfident.     

Who should sell stocks?

Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gains taxes, this policy outperforms both static buy‐and‐hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low or intermediate consumption is substantial.     

International asset pricing with time-varying risk premia

Recent empirical evidence that forward exchange rates are biased predictors of future spot rates can also be interpreted as evidence against the hypothesis of a constant risk premium. Consequently, reconciliation of this evidence with efficient international capital markets requires the existence of time-varying risk premia. This paper modifies Kouri's (1977) asset pricing model to allow time-varying exected returns on assets, eliminates the assumption of a risk-free real asset and derives the characteristics of the risk premia in the forward market as well as the equilibrium yield relationships among the equities and riskless nominal bonds of all countries.     

Pricing efficiency of the S&P 500 index market: Evidence from the Standard & Poor's Depositary Receipts

Standard & Poor's Depositary Receipts (SPDRs) are exchange traded securities representing a portfolio of S&P 500 stocks. They allow investors to track the spot portfolio and better engage in index arbitrage. We tested the impact of the introduction of SPDRs on the efficiency of the S&P 500 index market. Ex‐post pricing efficiency and ex‐ante arbitrage profit between SPDRs and futures were also examined. We found an improved efficiency in the S&P 500 index market after the start of SPDRs trading. Specifically, the frequency and length of lower boundary violations have declined since SPDRs began trading. This result is consistent with the hypothesis that SPDRs facilitate short arbitrage by simplifying the process of shorting the cash index against futures. Tests of pricing efficiency comparing SPDRs and futures suggested that index arbitrage using SPDRs as a substitute for program trading in general results in losses. Although short arbitrages earn a small profit on average, gains are statistically insignificant. A trade‐by‐trade investigation showed that prices are instantaneously corrected after the presence of mispricing signals, introducing substantial risk in arbitraging. Evidence in general supported pricing efficiency between SPDRs and the S&P 500 index futures—both ex‐post and ex‐ante. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:877–900, 2002