## Abstract

Despite the introduction of sophisticated stock market indices, investors often trade portfolios of the flawed indices to change their exposure to the market. In this study, we show that these transactions cause significant mispricing in individual stocks, especially during periods of significant market movement. As an influential, albeit flawed, stock index, we focus on the Nikkei 225. We find index constituents that are excessively weighted on the index, experience buying (selling) pressure when the stock market surges (falls), and experience price corrections after such periods of change. In contrast, non-constituent stocks do not experience such trading pressure.

This is a preview of subscription content, log in to check access.

## Notes

- 1.
Free-float-adjusted market capitalization is calculated by taking the equity’s price and multiplying it by the number of shares available in the market. The free-float method is intended to exclude locked-in shares such as those held by promoters and governments.

- 2.
- 3.
Most investors trade S&P 500 index futures to control their exposure to US stock markets rather than Dow Industrial Average futures. Thus, the Dow index is famous but not influential on the returns of index constituents.

- 4.
During the investigated period (Sep. 1993–Dec. 2013), the average daily trading value of Nikkei futures is approximately 300 times greater than that of TOPIX futures.

- 5.
Akeda (1990) mentions the possibility that the returns of high-priced illiquid constituent stocks are influenced by Nikkei 225 portfolio transactions. In line with his prediction, Adachi (1991) shows that in the early 1990s (when the Japanese asset price bubble burst), the prices of illiquid overweighted stocks excessively commove with (are excessively sensitive to) Nikkei 225 index values.

- 6.
Consistent with this prediction, Liu et al. (2012) report the high-beta characteristic of penny stocks (low-priced stocks).

- 7.
Most stocks have a face value of 50 (JPY). However, some stocks have face values of 500, 5000, or 50,000. Since 2001, the index used the deemed face value, which is estimated by considering past face value, corporate events, and capitalization changes, among others.

- 8.
Index divisor is a parameter to adjust for stock splits, capitalization changes, and so on.

- 9.
Approximately, the number of trading days over 1 month.

- 10.
The original definition of Amihud illiquidity is the absolute value of a stock’s return divided by its dollar trading value (Amihud 2002). However, to reduce the currency effect on evaluating illiquidity, the denominator is set to yen trading volume.

- 11.
Since the change in overweighting over one day is quite limited, the effect of overweighting as of day \(t-1\) on stock returns \(R_{i,t+1} (\beta _{\mathrm{OW}_{1,t}})\) is almost equal to the effect of overweighting as of day

*t*on stock returns \(R_{i,t+1} \) \((\beta _{\mathrm{OW}_{{\mathrm{0,t}}+1}})\). - 12.
OWN has a value of zero for Nikkei 225 constituents.

- 13.
To reduce the influence of outliers, the descriptive statistics for the effects of overweighting are based on winsorized values (at their first and 99th percentiles).

- 14.
The results are reported in Sect. 5.1.1.

- 15.
While the regression analysis considers heteroskedasticity in the effect of overweighting by performing WLS regression, the analysis does not adjust heteroskedasticity. Thus, the result might be excessively influenced by the outliers of \(\beta _{\mathrm{OW1}}\) and \(\beta _{\mathrm{OW2}}\). Thus, we winsorized the effect of overweighting at their first and 99th percentiles to reduce the influence of outliers on our results. Hereinafter, when we analyze the average effects during periods of market surges and falls, we report the winsorized means.

- 16.
That is, the results in Sect. 4.1 indicate that \(\beta _{\mathrm{OW1}_{0,t+1}}\) and \(\beta _{\mathrm{OW2}_{0,t+1}}\) are positively associated with \(\hbox {MR}_{t+1} \). However, since the 1-day-change in OW is quite limited, \(\beta _{\mathrm{OW1}_{1,t}}\) and \(\beta _{\mathrm{OW2}_{1,t}}\) are almost equal to (at least strongly positively correlated with) \(\beta _{\mathrm{OW1}_{0,t+1}}\) and \(\beta _{\mathrm{OW2}_{0,t+1}}\), respectively. Therefore, it is highly likely that \(\beta _{\mathrm{OW1}_{1,t}}\) and \(\beta _{\mathrm{OW2}_{1,t} } \) are positively associated with \(\hbox {MR}_{t+1}\).

- 17.
\(\beta _{\mathrm{AOW2}_{0,t}}\) is not significantly positive when the market is up. However, the average value of \(\beta _{\mathrm{AOW2}_{0,t}}\) is significantly negative and our additional analysis shows that \(\beta _{\mathrm{AOW2}_{0,t}}\) is significantly higher when the market is up than when the market is down. Thus, our results still support the view that the effect of overweighting is positively associated with market returns.

- 18.
Since \(\beta _{\mathrm{VOL1}_{t}}\) and \(\beta _{\mathrm{VOL2}_{t}}\) are serially correlated, we perform an OLS regression with a Newey–West-adjusted standard error.

## References

Adachi, T.: Stock price movements and futures trading (Kabuka hendou to sakimono torihiki). In: Nihon no kabuka hendou ni taisuru Kenkyu: Japan Securities Research Institute (1991). (in Japanese)

Akeda, M.: Acceptable trade size in index investing (Indekkusu baibai no tekisei kibo). Secur. Anal. J.

**28**(5), 1–10 (1990). (in Japanese)Amihud, Y.: Illiquidity and stock returns: cross-section and time series effects. J. Financ. Mark.

**5**, 31–56 (2002)Arnott, D., Hsu, J., Moore, P.: Fundamental indexation. Financ. Anal. J.

**61**, 83–99 (2005)Atkins, A., Dyl, E.: Price reversals, bid-ask spreads, and market efficiency. J. Financ. Quant. Anal.

**25**, 535–547 (1990)Barberis, N., Shleifer, A., Wurgler, J.: Comovement. J. Financ. Econ.

**75**, 283–317 (2005)Boyer, B.: Style related comovement: fundamentals or labels? J. Financ.

**66**, 307–332 (2011)Campbell, J., Hilscher, J., Szilagyi, J.: In search of distress risk. J. Financ.

**63**, 2899–2939 (2008)Corwin, A., Schultz, P.: A simple way to estimate bid-ask spreads from daily high and low prices. J. Financ.

**67**, 719–760 (2012)Greenwood, R.: Excess comovement: evidence from cross-sectional variation in Nikkei225 weights. Rev. Financ. Stud.

**21**, 1153–1186 (2008)Herbst, A., Mccormack, J., West, E.: Investigation of a lead–lag relationship between spot stock indices and their futures contracts. Futures

**7**, 373–382 (1987)Iqbal, Z., Dheeriya, L.: A comparison of the market model and random coefficient model using mergers as an event. J. Econ. Bus.

**43**, 87–93 (1991)Kawaller, G., Koch, P., Koch, T.: The temporal price relationship between S&P 500 futures and the S&P 500 index. J. Financ.

**42**, 1309–1329 (1987)Liu, Q., Rhee, G., Zhang, L.: Too good to ignore? A primer on listed penny stocks. Working Paper, University of Hawaii, Honolulu (2012)

Markowitz, H.: Portfolio Selection: Diversification of Investments. Wiley, New York (1959)

Roll, R.: A simple implicit measure of the effective bid-ask spread in an efficient market. J. Financ.

**39**, 1127–1139 (1984)Sharpe, W.: Risk-aversion in the stock market: some empirical evidence. J. Financ.

**20**, 416–422 (1965)Stoll, R., Whaley, R.: The dynamics of stock index and stock index futures returns. J. Financ. Quant. Anal.

**25**, 441–468 (1990)Tse, K.: Lead-lag relationship between spot index and futures price of the nikkei stock average. J. Forecast.

**14**, 553–563 (1995)

## Acknowledgments

Many thanks to an anonymous referee, the editor, Johnnie Johnson, Kotaro Inoue, and Seichiro Iwasawa for their comments on a draft.

## Author information

### Affiliations

### Corresponding author

## Additional information

Publication of this paper was supported by a grant-in-aid from Zengin Foundation for Studies on Economics and Finance.

The opinions expressed herein solely represent the views of the authors and do not reflect the opinions of any organizations to which the authors belong.

## Rights and permissions

## About this article

### Cite this article

Miwa, K., Ueda, K. Price distortion induced by a flawed stock market index.
*Financ Mark Portf Manag* **30, **137–160 (2016). https://doi.org/10.1007/s11408-016-0269-5

Published:

Issue Date:

### Keywords

- Stock market index
- Price-weighted index
- Trading pressure
- Stock mispricing

### JEL Classification

- G14
- G17
- G23