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Intertemporal Futures Pricing with Expectation Heterogeneity and Adjustment Effect. Simon H. Yen and Jai Jen Wang Department of Finance National Chengchi University. Abstract.
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Intertemporal Futures Pricing with Expectation Heterogeneity and Adjustment Effect Simon H. Yen and Jai Jen Wang Department of Finance National Chengchi University
Abstract • Intertemporal futures pricing formulas accounting for expectation heterogeneity, adjustment effect and stochastic interest rate are derived. • Relationships among the 3 factors help to explain empirical results such as Contango or normal backwardation.
Perfect Substitutes? • Owing to effective arbitrage linkage, a futures contract and stock index can be viewed as perfect substitutes. • Much literature does not conclude the consistent empirical phenomenon for the cost of carry model.
Discrepancy Attributions • Market frictions • Tax timing options • Asymmetric transaction costs • Additional stochastic factors • Stochastic Convenience Yield • Stochastic Interest Rate
Market Frictions • Tax timing options • futures traders lose tax timing options • Cornell & French (1983), Constantinides (1983), …… • Asymmetric transaction costs • No-arbitrage “band” • Modest & Sunderesan (1983), Klemkosky & Lee (1991), ……
Stochastic Convenience Yield • Gibson and Schwartz (1990) • Important for pricing financial and real assets contingent on the price of oil. • Bhatt and Cakici (1990) • Significant positive relationship between S&P 500 index dividend and mispricing from the cost of carry model.
Stochastic Interest Rate • Differentiates futures and forward prices • CIR (1981), Jarrow and Oldfield (1981), Richard and Sundaresan (1981) …… • Cakici and Chatterjee (1991) • Perform better especially when far away from long-term mean • Not sensitive to the exact specification
Harrison & Kreps (1978) • Unless traders are all identical and obliged to hold a stock forever, speculation would not extinguish, and heterogeneity in expectations yields whereby.
Harris & Raviv (1993) • Traders interpret common information differently and each of them believes in him- or herself. • Empirical regularities • Absolute price changes and volume are positively correlated. • Consecutive price changes exhibit negative serial correlation. • Volume is positively auto-correlated.
Frankel & Froot (1990) • Standard macroeconomic models can not explain dollar path, especially from 1984/6 to 1985/2. • Unexpected deviations are so large to be explained by rational revision such as taste or technology change. • Wide-dispersed forecasts of participants surveyed and tremendous trading volume reinforce the idea of heterogeneous expectations.
Ederington & Lee (1995) • Volatility remains higher after news releases than normal times in T-Bond, Eurodollar, and Deutschmark futures markets. • Such volatility is irrelevant with initial price change. • It means that disagrees among participants exist even in filtering common macroeconomic news.
Frechette & Weaver (2001) • Reject the representative agent hypothesis in U.S. soybean futures market at the 95% level of confidence. • Although the homogeneity assumption has been maintained in the past to ensure model tractability, it is incompatible with what we know to be true about markets.
Standard REE Models • Traders rationally respond to price changes by revising their estimates of other traders’ private signals recursively. • Kyle (1985), Holden & Viswanathan (1992), Foster & Viswanathan (1993), ……
MacKinlay & Ramaswamy (1988) • Mispricing increases on average with maturity, because longer term means • Unanticipated variability of dividend payments; • Larger unexpected interest earnings or costs from marking-to-market flows; • More serious and more expensive replicating errors and adjustment costs.
Yadav & Pope (1994) • Significant arbitrage opportunities after controlling for cash market settlement procedures. • Positive relationships between • Absolute mispricing and time to maturity • Mispricing and index option implied volatility.
Ahn, Boudoukh, Richardson, and Whitelaw (2002) • Some subset of securities in an index may partially adjust, or adjust more slowly, to information because of different transmission mechanisms or perturbation from noise trading. • Such “partial adjustment” effect imposes restriction on trading and causes empirical regularities.
We take heterogeneity as different opinions on future evolution of underlying asset price. • Traders are alike in the same group with the same perspectives about spot price dynamics, but with heterogeneous viewpoints among different groups.
Linear Combination • REE models: equilibrium price has a linear-combination functional form of heterogeneities. • Kyle (1985), Holden & Subrahmanyam (1992), Foster & Viswanathan (1996), … • Others: the similar result or setting • Figlewski (1978), Harris & Raviv (1993), Kogan, Ross, Wang, & Westerfield (2004), …
Related Variables • Number of investment analysts following • Brennan, Jegadeesh, & Swaminathan (1993) • Realized mispricing • Figlewski (1978), Ahn, etc. al. (2002) • Firm size • Merton (1987) and Lo & Mackinlay (1990) • Time to maturity • MacKinlay & Ramaswamy (1988), Yadav & Pope (1994), Hemler & Longstaff (1991)
Interest rate Dynamics • Vasicek’s (1977) Ornstein-Uhlenbeck stochastic process:
Expectation heterogeneity with constant interest rate and without adjustment effect
The cost of carry model is our special case when ξ= 0 or some constant. • Heterogeneity in expectations affects futures pricing through heterogeneous perspectives of dividend yield but not the drift and diffusion terms.
Comparative Statics • A larger degree of heterogeneity reduces the futures prices.
Expectation heterogeneity with stochastic interest rate and constant adjustment effect
Expectation heterogeneity with stochastic interest rate and time-varying adjustment effect
Numerical Examples • The signs of various results of comparative statics are dependent on different combinations of parameters.
Heterogeneity reduces the futures price relative to the cost-of-carry model. • Heterogeneity ~ volatility (Frankel and Froot (1990) and Ederington and Lee (1995)) • Increased volatility lowers basis (f - S).(Chen, Cuny, and Haugen (1995))
Additional components are needed to advance futures pricing models • Not everybody holds the same perspective • Adjusting behavior happens as time goes by • Heterogeneous expectations lowers futures price . And empirical phenomenon depend on the complicated relationships among these factors.