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Abstract:
This article studies the relative investment performance of several stock-valuation measures. The first is mispricing based on the valuation model developed by Bakshe and Chen (1998)and extended by Dong (1998) (hereafter, the BCD model). The BCD model relates, in closed form, a stock's fair value to (i) the firm's net earnings per share (EPS). (ii) the expected future EPS growth and (iii) long-term rate. The second is a value/ price (V/P) ratio based on the Lee-Myers-Swaminathan (1999) residual-income model. The other measures are all indirect valuation indicators, including book/market (B/M), earnings/price (E/P), size, and past return momentum. These measures are shown to possess distinct properties. For example, the B/M, E/P and V/P ratios are highly persistent over time: high (low) B/M stocks tend to maintain high (low) B/M ratios. But, the BCD model mispricing is highly mean-reverting: an overpriced group will eventually become underpriced (in about 1.5 years on average), and vice versa. More importantly, the BCD model mispricing, momentum, size V/P and B/M are, in decreasing order, significant ex ante predictors of future returns. The best investment strategy is to combine the BCD model mispricing with momentum rankings. Indeed, if one would hold an equally-weighted portfolio of stocks that are the most underpriced and that have top momentum, the average monthly return from 1979 to 1996 would have been 3.18 percent, with a monthly Jensen's alpha of about 1.5 percent.

Stock Valuation, Book/Market, Earnings/Price, Firm Size, Price Momentum, Stock Returns, Investment Management

Abstract:
Existing studies on market seasonality and the size effect are largely based on realized returns. This paper investigates seasonal variations and size-related differences in cross-stock valuation distribution. We use three stock valuation measures, two derived from structural models and one from book/market ratio. With each measure, we find that the average level is the highest in midsummer and the lowest in mid-December. Furthermore, the valuation dispersion (or, kurtosis)across stocks increases towards the year end and reverses direction after the turn of the year, suggesting increased movements in both the under-and-overvaluation directions. Among size groups, small-cap stocks exhibit the sharpest decline in valuation from June to December and the highest rise from December to January. For most months, small-cap stocks have the lowest valuation among all size groups. In a typical month, small-cap stocks show the widest cross-stock valuation dispersion, meaning they are also the hardest to value. Overall, large stocks enjoy the highest level of valuation uniformity and are the least subject to seasonal valuation variations.

Abstract:
This article develops and empirically implements a stock valuation model. The model makes three assumptions: (i) dividend equals a fixed fraction of net earnings-per-share plus noise; (ii) the economy's pricing kernel is consistent with the Vasicek term structure of interest rates; and (iii) the expected earnings growth rate follows a mean-reverting stochastic process. Our parameterization of the earnings process distinguishes long-run earnings growth from current growth and separately measures the characteristics of the firm's business cycle. The resulting stock valuation formula has three variables as input: net earnings-per-share, expected earnings growth and interest rate. Using a sample of individual stocks, our empirical exercise leads to the following conclusions: (1) the derived valuation formula produces significantly lower pricing errors than existing models both in-and out-of-sample; (2) modeling earnings growth dynamics properly is the most crucial for achieving better performance, while modeling the discounting dynamics properly also makes a significant difference; (3) our model's pricing errors are highly persistent over time and correlated across stocks, suggesting the existence of factors that are important in the market's valuation but missing from our model. In addition to pricing stocks, we can apply the model to back out market expectations about the firm's future from its stock price, allowing us to recover the relevant information embedded in the stock price.

Abstract:
This paper provides evidence on the significant impact of illiquidity or non-marketability on security valuation. A
typical listed company in China has several types of share outstanding: (i) common shares that are only tradable on stock exchanges, (ii) restricted institutional shares (RIS) that are not tradable and can only be tansferred privately or through irregularly scheduled auctions, and (iii) state shares that are only transferable privately. These types of share are indentical in every aspect, except that market regulations make state and RIS shares almost totally illiquid. Our analysis focuses on the price differences between RIS and common shares of the same company, using both auction and private-transfer transactions for RIS shares. Among our findings, the average discount for RIS shares relative to their floating counterpart is 77.93% and 85.59%, respectively based on auction and private transfers. The price for illiquidity is thus high, significantly raising the cost of equity capital. This illiquidity discount increases with both the floating shares' volatility and the firm's debt/ equity ratio, but decreases with firm size, return on equity, and book/price and earnings/price ratios (based on the floating share price). However, RIS share price can either increase or decrease with the quantity being transacted, depending on whether it is through a private placement or an auction.

Abstract:
This paper investigates whether one can profit from the size, book-to-market, or momentum anomaly, when price-impact costs are taken into account. A non-linear price-impact function is individually estimated for 5173 stocks to assess the magnitude of trading costs. Compared to constant proportional transaction costs (as typically assumed in the literature), a concave price-impact function tends to assign a higher impact cost to mid-size trades and a lower impact to large-size trades. We implement long-short arbitrage strategies based on each such anomaly, and estimate the maximal fund size possible before excess returns become negative. For all anomalies, the maximal fund sizes are small in order to remain profitable. Markets are therefore bounded-rational: price-impact costs deter agents from exploiting the anomalies.

Stock market anomaly, Price-impact function, Arbitrage, Fund size limit

Abstract:
The fundamental valuation equation of Cox, Ingersoll and Ross was expressed in terms of the indirect utility of wealth function. As closed-form solution for the indirect utility is generally
unobtainable when investment opportunities are stochastic, existing contingent claims models involving general stochastic processes were almost all derived under the restrictive log utility assumption. An alternative valuation equation is proposed here that depends only on the direct utility function. This alternative valuation approach is applied to derive closed-form
solutions for bonds, bond options, individual stocks, and stock options under both power utility and exponential utility functions. Allowable processes for aggregate output, firms' dividends, and state variables are quite general and empirically plausible. The resulting interest rate and stock price dynamics have many empirically plausible properties. Our bond and stock option pricing models with stochastic volatility and stochastic interest rates have most existing models nested. The stock option pricing model is also shown to have the ability to reconcile certain puzzling empirical regularities such as the volatility smile.

Abstract:
This paper examines the information embedded in both the stock and option markets prior to takeover announcements. During normal periods, buyer-seller initiated stock volume imbalances are significant predictors of next-day stock returns and option volume imbalances are uninformative. However, prior to takeover announcements, call volume imbalances are strongly positively related to next-day stock returns. Cross-sectional analysis shows that those takeover targets with the largest
pre-announcement call-imbalance increases experience the highest announcement-day returns. The largest increase in
buyer-initiated trading activity is in short-term
out-of-the-money calls that subsequently experience the largest returns. Collectively, these findings are consistent with the hypothesis that, in the presence of pending extreme informational events, the options market plays an important role in price discovery.

Abstract:
This paper studies the equilibrium valuation of foreign exchange-contingent claims. The basic framework is the continuous-time counterpart of the classic Lucas (1982) two-country model, in which exchange rates, term structures of interest rates and, in particular, factor risk prices are all endogenously determined and empirically plausible. This endogenous nature guarantees the internal consistency of these price processes with a general equilibrium. In addition to
the domestic and foreign nominal interest rates, closed-form valuation formulas are presented for exchange rate options and exchange rate futures options. Common to these formulas is
that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are provided analytically. It is shown that most existing currency option
models are included as special cases.

Abstract:
This paper studies the equilibrium valuation of foreign exchange-contingent claims. The basic framework is the continuous-time counterpart of the classic Lucas (1982) two-country model, in which exchange rates, term structures of interest rates and, in particular, factor risk prices are all endogenously determined and empirically plausible. This endogenous nature guarantees the internal consistency of these price processes with a general equilibrium. In addition to the domestic and foreign nominal interest rates, closed-form valuation formulas are presented for exchange rate options and exchange rate futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statistics are provided analytically. It is shown that most existing currency option models are included as special cases.

Abstract:
This paper first demonstrates that, in a discrete time framework, rational momentum can exist in an economy that has autocorrelated risk and convex dividend policies. It then uses this framework to examine the momentum role of firms. When firms actively create positive productivity shocks and increase overall production scale accordingly, outputs will be convex in productivity. This productivity convexity can generate momentum because a positive productivity shock helps a firm to have both higher realized past return and higher expected return (due to increased exposure to productivity risk). Empirically, productivity-based return components (PBR) usually explain more than 50% of international index momentum return. This result is robust in the presence of other risk factors. Macroeconomic variables also have a certain explanatory power for momentum, partially through PBR. Finally, as a robustness check, PBR also explains about 30% of industry momentum in the US.

Abstract:
This paper demonstrates that rational momentum can exist in an economy where autocorrelated risk and convex dividend policies are present. It then studies the momentum role of firms. When a firm actively creates positive productivity shocks and accordingly increases its production scale, its output will be convex in productivity. This productivity convexity can generate momentum because a positive productivity shock helps the firm to achieve both higher realized past return and higher expected future return (due to increased exposure to productivity risk). Empirically, productivity-based return components (PBR) on average explain over 50% of the momentum effect in international index returns. This result is robust after adjusting for other risk factors. Macroeconomic variables are also shown to have certain explanatory power for momentum, partially through PBR. Finally, as a robustness check, we find that PBR also explains about 30% of industry momentum in the US.

Abstract:
This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that when sampled intraday (or inter-day), (i) call (put) prices often go down (up) even as the underlying price goes up, and (ii) call and put prices often increase, or decrease, together. Our results are valid after controlling for time-decay and market microstructure effects. Therefore, one-dimensional diffusion option models cannot be completely consistent with observed option-price dynamics; options are not redundant securities, nor ideal hedging instruments---puts and the underlying asset prices may go down together.

Abstract:
This article offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependent entities to the underlying real and monetary variables. Among other features of such economies, inflation can be partially non-monetary and the real and nominal term structures can depend on fundamentally different risk factors. In one extreme, the process followed by the real term structure is independent of that followed by its nominal counterpart.

Abstract:
Any admissible portfolio performance measure should satisfy four minimal conditions: it assigns zero performance to each reference portfolio and it is linear, continuous and nontribial. Such an admissible measure exists if and only if the securities market obeys the law of one price. A positive admissible measure exists if and only if there is not arbitrage. This paper characterizes the (infinite) set of admissible performance measures. It is shown that performance evaluation is generally quite arbitrary. A mutual fund data set is also used to demonstrate how the measurement method developed here can be applied.

Abstract:
Recent empirical studies find that once an option pricing model has incorporated stochastic volatility, allowing interest rates to be stochastic does not improve pricing or hedging any further while adding random jumps to the modeling framework only helps the pricing of extremely short-term options but not the hedging performance. Given that only options of relatively short terms are used in existing studies, this paper addresses two related questions: Do long-term options contain different information than short-term options? If so, can long-term options better differentiate among alternative models? Our inquiry starts by first demonstrating analytically that differences among alternative models usually do not surface when applied to short term options, but do so when applied to long-term contracts. For instance, within a wide parameter range, the Arrow-Debreu state price densities implicit in different stochastic-volatility models coincide almost everywhere at the short horizon, but diverge at the long horizon. Using regular options (of less than a year to expiration) and LEAPS, both written on the S&P 500 index, we find that short- and long-term contracts indeed contain different information and impose distinct hurdles on any candidate option pricing model. While the data suggest that it is not as important to model stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.

Abstract:
Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to bestochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time-series data, (2)out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps.Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not "smile" across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.

Abstract:
Substantial progress has been made in extending the Black- Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps. On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to be stochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta- neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/ volatility with relevant time-series data, (2) out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps. Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not "smile" across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.

Abstract:
We develop a measurement theory of market integration, based on two notions of "integrated markets." First, two markets cannot be perfectly integrated in any sense if one can construct two portfolios, one from each market, that have identical payoffs but different prices. In that case, the law of one price is violated across the markets. Second, they cannot be integrated in a stronger sense if there are cross-market arbitrage opportunities. Two measures of market integration are developed, respectively reflecting these notions. The smaller the measures, the more closely integrated (in the respective senses) the markets. Among other things, they are interpreted as measuring pricing discrepancy between markets.

Abstract:
Closely-integrated markets should assign to similar payoffs prices that are close. This is the idea on which a measurement theory of market integration is developed in this paper. Two markets are said to be perfectly integrated in the weak sense if there is at least one stochastic discount factor that is shared by both markets. Then, the weak integration measure is conveniently defined to be the minimum distance between the respective sets of admissible stochastic discount factors for two markets. This measure is zero if and only if the markets are perfectly integrated in the weak sense, i.e., they assign to similar payoffs prices that are arbitrarily close. The smaller the measure, the more closely-integrated the two markets. In addition, two markets are said to be perfectly integrated in the strong sense if no arbitrage opportunity exists across them. Correspondingly, the strong integration measure is defined to be the minimum distance between the respective sets of non-negative stochastic discount factors for the two markets, and it reflects the extent that arbitrage profits are possible between the markets. The measurement theory can be applied to test market integration without relying on any parametric asset pricing models.