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This paper examines the predictability of implied required rate of return (R
_{OI}) of individual stock in the cross-section of stock returns. The required rate of return of each stock is implied using its corresponding stock options and used in estimating the fundamental value of stock. The study finds that stocks with low price to fundamental value have higher future returns. The inferred R
_{OI}OI

It has been documented that the implied volatility of stock exhibits predictability of stock returns. Bali and Hovakimian [

I derive the option implied rate of return, as in Câmara, et al. [_{OI} is used to discount the future payoff. Previous studies have documented that the option prices reflect the market’s expectations; the R_{OI} implied by the options is thus forward looking and should provide accurate estimation of the fundamental value than those estimates using backward-looking required rate of return computed using historical data.

The three years analysts’ forecasts of the earnings and dividends per share obtained from I/B/E/S for estimating residual incomes are discounted back using the computed R_{OI} to determine the fundamental value. Then, the price to fundamental value ratio (PFV) is computed for each stock. The securities prices diverge from their intrinsic values due to the existence of information asymmetry and market inefficiency. As the overreacted security prices would eventually gravitate back to its intrinsic value according to fundamental analysis, this timing varying PFV can act as a benchmark to determine the individual overpriced and underpriced securities. This paper provides empirical evidence that the PVF estimated using optionimplied rate of return exhibits superior predictive power of future stock return.

Price multiples such as the price-to-earnings ratio and market to book value are widely used by practitioners to form contrarian portfolios for exploiting abnormal returns, as researched by Dissanaike and Lim [

Researchers have proposed different models for estimating the required rate of return for stock valuation and capital budgeting. The Capital Asset Pricing Model (CAPM) of Sharpe and the three-factor model of Fama and French [

Pastor and Stambaugh [

This paper develops a new price to fundamental value to predict the cross section of future stock return. The intrinsic value of individual stock is estimated using a required rate of return implied by its corresponding stock options. The results indicate that new price to fundamental value ratio gives outstanding performance in return predictability. The forward-looking information incorporated into the R_{OI} helps giving a more reasonable and accurate estimation of the fundamental value of the security.

The paper also provides evidence that a significant positive return by sorting portfolio using the proposed price to fundamental value ratio. A trading strategy is designed using the price to intrinsic value ratio as a variable to rank the stocks into five portfolios. A zero investment of buying the lowest sorted portfolio and selling the highest sorted portfolio is devised. The performance of the proposed PFV ratio is compared with other fundamental variables such as PE, PB and PD ratios.

The paper is organized as follows. Section 2 discusses the data and methodology. Section 3 presents the empirical findings and analyzes the results. Section 4 concludes the paper.

This paper collects data from three sources. First, the component stocks of the Dow Jones Industrial Average are used by the study. Financial statement data and stock return data are collected on a monthly basis from the dataset of Datastream. This paper examines monthly return from January 1998 to December 2008. Additionally, the factors of the three factor model of Fama/French [

Third, to estimate the option-implied R_{OI}, the paper collects the volatility surface of stock options on a monthly basis of the component stocks of DJIA from the OptionMetrics. For each month, the paper collects 7 to 13 call options with different strike prices for each component stock with a maturity of 1 year for the R_{OI} estimation.

The paper estimates the option implied rate of return by following the methodology of Câmara et al. [_{T} expressed as:

where W_{T} > 0, a and b preference parameters with a < 0 and b > 0. The pricing kernel is then expressed as

where Q_{T} is aggregate wealth and follows a lognormal distribution as

and there is a representative agent with the marginal utility function expressed as where δ and λ are the preference values. The representative agent is risk averse.

The pricing kernel is positive and has a displaced lognormal distribution with expectation. Stock price in a representative agent economy takes the form of

where under the actual probability measure Φ. P_{0} under the equivalent probability measure Λ is expressed as

with the density function in the form of

The density function varies with the preference parameters. By using the equilibrium relation of

The call and put option prices can be expressed as follows:

where

,

,

,

where C and Pu represent the call and put option prices, respectively. P_{0} is the stock price. and w are the risk-free rate and the preference function. r_{OI} and σ are the option implied required rate of return and the stock volatility, respectively. N(*) stands for the cumulative distribution function of the standard normal, K is the strike price, T is the maturity date of the options. By using the data of P_{0}, K and T, the rate of return, σ and w are solved by minimizing the sum of the square of the differences between the market option prices and the model option prices.

Then, the required rate of return in equation is applied in discounting the future payoff in the residual income valuation model. The fundamental value of the security is expressed as the sum of the current book value and the infinite sum of the present value of expected residual income:

where B_{t} is the book value of equity at time t, FEPS_{t}_{+i} is the forecasted earnings per share for time t + i. The residual income model for the stock valuation is easy to implement and the required forecasted earnings from analysts are readily available in the market.

To facilitate the implementation, equation (9) is simplified into a finite series. The equation is reduced to the following form:

where. The FDPS_{t}_{+i} represents the forecasted dividend per share for t + i. TV is calculated by assuming the residual income as a perpetuity after three years and is expressed as

For each month, the parameters are estimated by minimizing the sum of squared differences between the model and market option prices of all of the component stocks at various strike prices with equal times to maturity in the following form:

where N represents the total number of stocks in the study, and Q_{i} stands for total number of strike prices available for stock i. c_{i} and C_{i} are the market and model option price of stock i at a strike price of K_{j}. A total of 30 sets of fundamental values are then computed for each month. The procedure is repeated for the entire sample period.

Panel A reports the mean excess returns, standard deviations of portfolio formed by the component stocks. The monthly excess returns are calculated as the average monthly return after deducting the risk free rate for the N-months-ahead return, where N stands for a duration of 1, 3, 6, 9, 12 or 18 months. The average monthly excess return in the sample period is 0.29% for a one month holding period. The median value is 0.35% with a maximum of 27.60% and a minimum of −26.37%. The

average excess return for one month investment horizon is higher than others, but it also has higher values of standard deviation and kurtosis as expected. Panel B of

Panel D shows that the autocorrelations of the price multiples were relatively high. The level of autocorrelation at a lag of one month for the price multiples ranges from 0.869 (PE) to 0.938 (PB) but was only 0.849 for PV_R_{OI}. These traditional price multiples have a longer mean reversion compared to the PV_R_{OI}, whose intrinsic value is option implied. Except for the PE ratio, I find similar patterns for the autocorrelation values at longer lags. PV_R_{OI} shows faster mean reversion and was more responsive.

The predictability of various ratios for future returns is examined in this section. The regression considered is in the form of

where R_{t}_{+M} stands for the monthly return at time t for M months ahead. The regression is run for different durations: M = 1, 3, 6, 9, 12 and 18. To derive the conclusion of the overall predictability of the forecasting variable, the paper computes the average regression coefficients of the various M proposed by Richardson and Stock [_{t} is the assigned forecasting variable. The forecasting variables under study are the PV_R_{OI}, PE, PB and PD ratios.

When the price is less than the fundamental value, the price will eventually revert and lead to positive future return. Therefore, the relationship between the P/V ratios and the future return is expected to be negative. _{OI} are negative and significant at the 1% level. This result indicates the return predictability of PV_R_{OI}.

In this section, the paper designs a trading strategy for capturing cross sectional excess returns based on the forecasting power of the P/V ratios. The component stocks are ranked based on the adjusted P/V ratios for each month. The paper proposes two adjusted P/V ratios. The first ratio is estimated by dividing the P/V ratio at time t by its average P/V ratio over the last 12 months.

The arrangement normalizes the 30 ratios and facilitates comparison. The second ratio is same as the first one, except I use 24 months for calculating the average value. To facilitate the comparison with the traditional price multiples, I apply the same methods to the PE, PB and PD ratios for ranking the portfolios.

At month t, the stocks are sorted into quintile portfolios by the adjusted ratios. Based on the findings of previous regression, I expect the lowest (highest) ranked portfolio to be underpriced (overpriced). That will lead to higher (lower) future returns. The paper tries to exploit the excess return by buying the portfolio in the lowest quintile and selling the one in the highest quintile. The portfolio will be held for a horizon from 1 month to 18 months.

Tables 3-6 summarize the performance of the trading strategy using various PV ratios. _{OI}, PE, PB and PD ratios. The rows “R_{ROI}”, “R_{RPE}” “R_{RPB}” and “R_{RPD}” stand for the arbitrage profits generated by taking a short position in Low 1 portfolio and a long position in High 5 portfolio ranked by PV_R_{OI}, PE, PB and PD ratios. The results in panel A indicate that PV_R_{OI} produces significantly positive arbitrage profits across the six horizons with an average return of 0.60%. In addition, when comparing the trading performance across the horizons, the trading performances using PV_R_{OI} ratio over shorter horizons are generally better. Panel A of _{OI} exhibits good forecasting power in short holding period return.

I apply the same trading rules on the price multiples, which are used as proxies for indicating the overpricing and underpricing of stocks. Panels B, C and D summarize the performance of the three price multiples. The PE, PB and PD ratios create arbitrage returns of 0.41%, 0.64% and 0.36%. However, when these returns are compared with the performance of PV_R_{OI}, only the trading strategy using PB-sorted portfolios could compete. PV_R_{OI} outperforms the PE and PD ratios in the trading by 0.19% and 0.24%, respectively. These findings are consistent with previous studies, such as that by Fama and French [

_{OI} adjusted ratio with longer average generates higher excess returns. The average monthly excess return of the six types of horizon is 0.66% for the ratio using the 24-month average compared with the corresponding return of 0.60% for the ratio using the 12-month average.

The results of the PE, PB and PD ratios are summarized in panels B, C and D of _{OI} still outperforms the PE and PD ratios in the trading strategy by 23% and 30% respectively. The gaps are slightly increased using longer term averaged ratios.

I repeat the methodology to examine the trading performances when sorting excess return which is calculated by subtracting monthly return by the risk free rate. Tables 5 and 6 summarize the trading results. The findings for the P/V ratios are similar to those in Tables 3 and 4. However, the arbitrage profits for the P/V ratio and price multiples are lower. Using the 12-month average, PV_R_{OI} outperforms all the price multiples (with arbitrage returns exceeding the three price multiples by 17% (PE), 2% (PB) and 49% (PD)). In addition, the arbitrage return for one month horizon for PV_R_{OI} sorted portfolios is higher than the other five horizons, suggesting stronger predictive power in shorter horizon. This finding using a 24- month average is similar to that using 12-month average except that the PV_R_{OI} only outperforms PE and PD ratios.

By comparing the performance of the PV_R_{OI} ratio with the traditional price multiples from the study of trading performances in Tables 3-6, one can see that the use of option implied cost of equity capital in the estimation of fundamental value improves the predictability of future returns and generates higher trading profits. The result indicates that, the incorporation of this option-implied COE into the equity valuation further improves the predictability of future returns, in particular the return in short investment horizon.

This paper contributes to the literature in two respects. First, a new approach is derived to estimate the fundamental value of stocks using option-implied required rate of return. Traditionally, the cost of equity capital used in the stock valuation is developed based on CAPM. However, this cost of equity capital derived by using historical data is backward looking. As indicated in the existing literature, market stock option prices reflect market expectations and help predict the future volatility of equity. This paper explores the possibility of enhancing the accuracy of valuation using this option implied rate in stock valuation. It is assumed that the superior estimation of

intrinsic value produces P/V ratios that can predict future returns.

Second, the paper develops a trading strategy to assess the profitability of the proposed valuation model. The paper creates two sets of sorting variables. The first one is derived by dividing the current P/V by the average P/V value of the last 12 months. The second one is calculated by dividing the P/V by an average P/V value of the last 24 months. These two adjusted P/V ratios can facilitate direct comparisons between stocks. For each month, the component stocks of the DJIA are ranked into quintiles by the P/V ratio and price multiples. A zero investment is created for each model by buying the lowest sorted portfolio and selling the highest sorted portfolio. The portfolios with the lowest P/V ratios should be underpriced and will generate higher future returns.

The evidence shows that my proposed P/V ratio derived using option-implied rate of return COE outperforms the P/E and P/B ratios in generating higher arbitrage profits in both sorting methods. The PV_R_{OI} ratio consistently generates higher future returns for horizons from 1 month to 18 months. The options-implied rate of return is forward looking and helps produce better arbitrage return.

Because this paper only tests the proposed model on Dow Jones component stocks, which are generally large and popular stocks, future research may explore the predictability and profitability of the model by applying it to small-cap stocks.