Deriving Investor Sentiment from Options Markets

Transcription

1 Deriving Investor Sentiment from Options Markets Chikashi TSUJI February 28, 29 Abstract The purpose of this paper is to introduce the put call ratio (PCR) as an investor sentiment index, and show the results of several illustrative analyses in Japan. After deriving the PCR from the Nikkei 22 index options data, we demonstrate that market timing strategies using the PCR are effective in Japan. This evidence suggests that the PCR operates as a contrarian indicator for the option s underlying asset, Nikkei 22, in Japan. Keywords: put call ratio, investor sentiment, market timing. JEL classification : G12; G1. This paper has been prepared for the annual report of the Data Bank Project of the University of Tsukuba. The author is grateful to the Osaka Securities Exchange (OSE) for providing the data used in this study. The views are those of the author and not necessarily those of the OSE. The author also greatly appreciates the generous financial assistance of the Data Bank Project of the University of Tsukuba, which is led by Professor Kazuo Kishimoto. The author also especially thanks Kazuhiko Nishina because the idea and intuition for writing this paper is derived from several talks in Professor Dr. Nishina s laboratory at Osaka University when the author participated in a seminar there. Correspondence: Chikashi TSUJI, Associate Professor, Department of Social Systems and Management, Graduate School of Systems and Information Engineering, University of Tsukuba. Address: Tennodai, Tsukuba, Ibaraki 3-873, Japan. 1

2 1 Introduction The put call ratio (PCR) is generally viewed as a short-term, leading technical indicator of sentiment that implies the direction of future moves in the stock market. Most contrarians use the PCR as a contrarian indicator because they believe that options trading is dominated by the less sophisticated public rather than by professionals. For this reason, they believe that public investors are generally wrong about the market, especially at significant turning points. Analysts consequently use the PCR to identify the consensus as a result of the herding of public investors, then execute trading strategies to bet on the opposite direction. For example, analysts consider that an increase in the volume of put options relative to the volume of call options indicates that public investors are predominately bearish. Therefore, contrarians interpret this PCR move as a sign of future bullish movement. In contrast, analysts believe that a decline in the volume of put options relative to that of call options suggests that public investors are predominately bullish about the market. Hence contrarians view the optimism of public investors, who have little specialized information, as a bearish signal. As argued later, analysts advocate a variety of PCR values as buy and sell signals. These signals are used to set up such positions as long or short in stock portfolios or options. Several studies have analyzed the PCR in the US as a sentiment indicator of stock markets. We cite, for example, Billingsley and Chance (1988), Pan and Poteshman (26), and Lakonishok et al. (29). 1 However, in Japan, we are not aware of prior research using the PCR. Hence, in this paper, very rough and preliminary as it is, we survey the situation of the PCR in Japan while providing some empirical examples and actual PCR data. 1 There are other studies of investor sentiment in the US, though not using the PCR. These include Solt and Statman (1988), Neal and Wheatley (1998), Fisher and Statman (2), Bandopadhyaya and Jones (26), and Baker and Wurgler (26), amongst others. 2

3 2 Construction of the Put call Ratio Option volume data from the Nikkei 22 option index used to construct the monthly PCRs at the end of each month are from the Osaka Securities Exchange (OSE). The formula for deriving the PCR at time t: PCR t is as follows. 2 PCR t = 1 N NX V P 1 t+1 i + V t+1 i P 2 V C1 t+1 i + V t+1 i C2 1, (1) i=1 where Vt+1 i P 1 : volume of put option of the near maturity contract; V P 2 t+1 i : volume of put option of the second nearest maturity contract; Vt+1 i C1 : volume of call option of the near maturity contract; Vt+1 i C2 : volume of call option of the second nearest maturity contract, and N denotes the number of business days at the end of each month. We set N =in this paper. We also note that all options we use here are out of the money options that are nearest to being at the money. Our sample period is January 199 to February 2, and the trends of the Nikkei 22 and the PCR are shown in Figure 1. 3 Illustrative Analysis This section explains the data s characteristics and several results for simple market timing analysis. First, we display the descriptive statistics of the PCR in Japan in Table 1. This table shows that the PCR has positive skewness and slightly higher kurtosis than the normal distribution. Next, in Table 2, we show several percentile values of the PCR. These figures are used for our various market timing strategies. Billingsley and Chance (1988) used 1 6 and 7 4 strategies for S&P 1 Index Option (OEX), and 7 4 and 6 4 strategies for Chicago Board Options Exchange (CBOE) equity options. 3 Based on 2 There seem to be several versions of the method of deriving the PCR used by each financial institution or technical analyst. However, there seem to be no significant differences between those formulas. 3 For example, from the OEX options data, a PCR greater than 1 (7) is considered bullish, a ratio less than 6 (4) is considered bearish, and ratios in between are considered neutral. Hence in the 1 (7) 6 (4) strategy, when the PCR is over 1 (7), it is a signal to buy, while when the PCR falls below 6 (4), it is a sign to sell. 3

4 these values, we set up the following eight strategies. 1) 1 6 strategy, 4 2) (1 9 percentile) strategy, 3) (1 8 percentile) strategy, 4) (2 8 percentile) strategy, ) (2 7 percentile) strategy, 6) (3 7 percentile) strategy, 7) (3 6 percentile) strategy, and 8) (4 6 percentile) strategy. Finally, empirical results are shown in Table 3. The table indicates the situation of profit and loss in each transaction by using the PCR. Table 3 demonstrates that 1) the 1 6 strategy records a profit of average yearly return of.77% and a profit of gross percentage return of 8.77%, respectively with transactions. Similarly, in order: 2) the strategy shows a profit of average yearly return of.86% and aprofit of gross percentage return of 13.47%, respectively with 11 transactions; 3) the strategy exhibits a profit of average yearly return of 1.46% and a profit of gross percentage return of %, respectively with 1 transactions; 4) the strategy displays a profit of average yearly return of 2.83% and a profit of gross percentage return of 43.3%, respectively with 23 transactions; ) the strategy shows aprofit of average yearly return of 3.327% and a profit of gross percentage return of.4%, respectively with 33 transactions; 6) the strategy records a profit of average yearly return of 3.86% and a profit of gross percentage return of 4.382%, respectively with 39 transactions; 7) the strategy indicates a profit of average yearly return of 3.27% and a profit of gross percentage return of 3.491%, respectively with 4 transactions; and 8) the strategy exhibits a profit of average yearly return of 3.8% and a profit of gross percentage return of %, respectively with 3 transactions. Figure 2 displays the loss and profit situation from each transaction of each strategy. 4 We tried 7 4 and 6 4 strategies; however, they did not work for the Nikkei 22 Index options. In the 1 6 strategy, when the PCR is over 1, we buy the Nikkei 22, and when the PCR falls below 6, we sell the Nikkei 22. 4

5 Figure 1. The trends of the NIKKEI 22 and the put-call ratio Percent Yen PCR (Lef t scale) NIKKEI22 (Right scale)

6 Table 1. Descriptive statistics of the put-call ratio in Japan Statistic Whole sample period Jan. 199 to Feb. 2 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Observations Notes : 1. The full sample period is from January 199 to February 'Std. Dev.' denotes the sample standard deviation. Sub-sample period Jan. 199 to Dec Sub-sample period Jan to Feb. 2 Table 2. Percentile values of the put-call ratio in Japan Whole sample period Sub-sample period Sub-sample period Percentile 1% Jan. 199 to Feb Jan. 199 to Dec Jan to Feb % % % % % % % % % % % % % Notes: 1. The full sample period is from January 199 to February The figures in the table display the percentile values from the distribution of the PCR in Japan. Table 3. Profits and losses from the market timing strategies using the put-call ratio Strategy The number of times of transactions Yearly average percentage return Gross percentage return Notes : 1. The analyzed sample period is from January 199 to February 'Yearly average percentage return' means the average yearly return from each strategy in the whole sample period. 3. 'Gross percentage return' means the gross percentage return from each strategy in the whole sample period.

7 Figure 2. Profits and losses from the investment strategies using the put-call ratio Panel A 1 6 strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel B strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel C strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel D strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4

8 Panel E strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel F strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel G strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4 Panel H strategy Jan-9 Aug-9 Jul- Feb-1 Sep-1 Apr-2 Nov-2 Jun-3 Jan-4 Aug-4

9 4 Conclusion We have investigated the PCR in Japan and have obtained the results that PCR strategies are effective in equity investments in Japan. The analysis in this paper does not take transaction costs into consideration; however, we obtained similar results when we took the effects of transaction costs into account, although this is not displayed in this paper. The profits gained by our simple trading example are very small; however, in an academic sense, our evidence that we can beat the market by using the irrational herding behavior of public investors contradicts the market efficiency hypothesis. We need to continue further detailed research in the future. Notes for Using Data We limit the use of the attached PCR data in Appendix A to academic research only. Any publications using these data must cite this paper. We are not responsible for any losses or damages following any use of these data for actual investments. Views expressed in this paper are those of the author and do not necessarily reflect those of the Data Bank Project of the University of Tsukuba. 9

10 Appendix A. The put-call ratio data PCR PCR PCR Jan Feb Mar Feb Mar Apr Mar May Apr May Jun May Jun Jul Jun Jul Aug Jul Aug Sep Aug Sep Oct Sep Oct Nov Oct Dec Nov Dec Jan Dec Jan Feb Jan Feb Mar Feb Mar Apr Apr May Apr May Jun May Jul Jun Jul Aug Jul Aug Sep Aug Sep Oct Sep Oct Nov Nov Dec Nov Dec Jan Dec Feb Jan Feb Mar Feb Mar Apr Mar Apr May Apr May Jun Jun Jul Jun Jul Aug Jul Sep Aug Sep Oct Sep Oct Nov Oct Nov Dec Nov Dec Jan Jan Feb Jan Feb Mar Feb Apr Mar Apr May Apr May Jun May Jun Jul Jun Jul Aug Aug Sep Aug Sep Oct Sep Nov Oct Nov Dec Nov Dec Jan Dec Jan Feb Jan Feb Mar Mar Apr Mar Apr May Apr Jun May Jun Jul Jun Jul Aug Jul Aug Sep Aug Sep Oct Oct Nov Oct Nov Dec Nov Jan Dec Jan Feb Jan Feb

11 References [1] Baker, M. and Wurgler, J. (26) Investor Sentiment and the Cross-section of Stock Returns, Journal of Finance 61, [2] Bandopadhyaya, A. and Jones, A. L. (26) Measuring Investor Sentiment in Equity Markets, Journal of Asset Management 7, 3-4. [3] Billingsley, R. S. and Chance, D. M. (1988) Put call ratios and market timing effectiveness, Financial Analysts Journal 1, [4] Fisher, K. L. and Statman, M. (2) Investor Sentiment and Stock Returns, Financial Analysts Journal 6, [] Lakonishok, J., Lee, I., Pearson, N. D. and Poteshman, A. M. (29) Option Market Activity, Review of Financial Studies, forthcoming. [6] Neal, R. and Wheatley, S. M. (1998) Do Measures of Investor Sentiment Predict Returns?, Journal of Financial and Quantitative Analysis 33, [7] Pan, J. and Poteshman, A. M. (26) The Information in Option Volume for Future Stock Prices, Review of Financial Studies 19, [8] Solt, M. E. and Statman, M. (1988) How Useful is the Sentiment Index?, Financial Analysts Journal 44,