Idiosyncratic Risk Volatility: Stock Price Informativeness or Price Error?
Abstract
:1. Introduction
2. Literature Review and Hypothesis Development
2.1. Information Environment and Idiosyncratic Volatility
2.2. Information Asymmetry in the Information Environment That Affects Idiosyncratic Volatility
3. Materials and Methods
3.1. Sample
3.2. Variables and Measurements
3.2.1. Idiosyncratic Volatility
3.2.2. Information Environment
- Stock illiquidity (Amihud 2002)This variable measures the daily stock-price response as per the rupiah trading volume. Stock illiquidity is calculated based on the ratio of the absolute return to the trading volume (in rupiah).Abs return is the absolute value of the company’s daily stock return, the trading volume is the number of shares traded, and price is the daily closing price (Lou and Ronnie 2011). A high stock illiquidity ratio indicates low stock liquidity and high information asymmetry, thus indicating a poor information environment. The relationship between illiquidity and information asymmetry is tested further in Hypothesis 2.
- Liquidity riskThe liquidity risk (ILLIQRISK) is the standard deviation of the illiquidity equation. The liquidity risk is the co-variation of its returns with unexpected changes in aggregate liquidity (Lou and Ronnie 2011). A high liquidity risk value indicates a poor information environment (Mitra 2016).
- Information AsymmetryThe information asymmetry variable (SPREAD) was used in this study to determine the quality of the information environment because the development of the information environment is a consequence of information asymmetry (Beyer et al. 2010). Information asymmetry in the information environment indicates a poor information environment. The amount of information asymmetry is calculated based on the following formulation:Spread is the value of information asymmetry, ask is the daily ask closing price, and bid is the bid-closing price. Measurement of each variable in detail can be seen in Table 1.
3.2.3. Control Variable
3.3. Regression Analysis
α6ROAit + α7SIZEit + eit
+ α6ROAit + α7SIZEit + eit
+ α6LEVit+ α7ROAit + α8SIZEit + eit
α5BMit + α6LEVit + α7ROAit + α8SIZEit + eit
4. Results
4.1. Summary Statistics
4.2. Effect of Information Environment on Idiosyncratic Volatility
4.3. The Effect of Information Asymmetry in the Information Environment on Idiosyncratic Volatility
5. Discussion
α4LIQRISK * SPREADit + α5BMit + α6LEVit + α7ROAit+ α8SIZEit + eit
α4LIQRISK * SPREADit + α5BMit +α6LEVit + α7ROAit+ α8SIZEit + eit
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Variable | Measurement | |
---|---|---|
Idiosyncratic Volatility | ||
Absolute and relative Idiosyncratic Volatility | IDVOL (σe2) | Idiosyncratic Volatility based on residual value based on the CAPM equation |
Relative Idiosyncratic Volatility | IDVOLrelative (σe2/σ2) | Idiosyncratic Volatility based on the relative residual value |
Information Environment | ||
Stock liquidity (Amihud 2002 Model) | ILLIQUID | Monthly absolute return/trading volume (in rupiah) |
Stock liquidity risk | LIQRISK | The standard deviation of the illiquid equation |
Information Asymmetry | ||
Bid-ask spread | SPREAD | Difference between buying and selling prices |
Idiosyncratic Determinants | ||
Book to Market | BM | The ratio of book value equity to market value equity |
Leverage | LEV | Debt to asset ratio |
Return on assets | ROA | Earnings to assets ratio |
Company size | SIZE | Asset log |
Observations | Mean | Median | Maximum | Minimum | Std. Dev. | Skewness | Kurtosis | |
---|---|---|---|---|---|---|---|---|
A. Idiosyncratic volatility | ||||||||
IDVOL (σe2) | 1229 | 1.605 | 1.597 | 5.506 | 0.001 | 0.997 | 0.536 | 3.160 |
IDVOLrelative (σe2/σ2) | 1229 | −4.093 | −2.321 | 2.346 | −55.146 | 5.64 | −3.482 | 21.299 |
B. Information environment | ||||||||
ILLIQUID | 1229 | 7.149 | 7.183 | 17.556 | 3.459 | 0.957 | 8.096 | 105.225 |
LIQRISK | 1229 | 0.001 | 0.001 | 0.105 | 0 | 0.004 | 15.721 | 332.413 |
C. Information asymmetry | ||||||||
SPREAD | 1229 | −3.228 | −3.421 | 3.063 | −8.208 | 1.693 | 9.640 | 170.969 |
D. Firm characteristics | ||||||||
BM | 1229 | 0.894 | 0.8 | 18.3 | −88.9 | 4.36 | −13.991 | 242.696 |
LEV | 1229 | 0.191 | 0.139 | 3.575 | 0 | 0.214 | 23.617 | 707.926 |
ROA | 1229 | 0.029 | 0.028 | 1.303 | −2.641 | 0.164 | −3.213 | 80.049 |
SIZE (Asset = in millions Rupiah) | 1229 | 9,740,000 | 2,450,000 | 352,000,000 | 54,500,000 | 25,200,000 | 7.554 | 82.777 |
IDVOL | ILLIQUID | LIQRISK | SPREAD | BM | LEV | ROA | SIZE | |
---|---|---|---|---|---|---|---|---|
IDVOL | 1000 | |||||||
ILLIQUID | 0.396 *** | 1000 | ||||||
LIQRISK | 0.296 *** | 0.864 *** | 1000 | |||||
SPREAD | 0.137 *** | 0.170 *** | 0.083 *** | 1000 | ||||
BM | 0.175 *** | 0.104 *** | 0.068 *** | 0.028 *** | 1000 | |||
LEV | 0.343 *** | 0.278 *** | 0.139 *** | 0.058 *** | −0.081 *** | 1000 | ||
ROA | 0.203 *** | 0.088 *** | 0.0605 *** | 0.084 *** | 0.078 *** | −0.042 | 1000 | |
SIZE | 0.550 *** | 0.563 *** | 0.321 *** | 0.182 *** | 0.194 *** | 0.433 *** | 0.181 *** | 1000 |
Variables | Statistic | Probability * |
---|---|---|
IDVOL | 244.091 | 0.000 |
ILLIQUID | 209.985 | 0.000 |
LIQUIDRISK | 206.108 | 0.000 |
SPREAD | 216.789 | 0.000 |
BM | 215.794 | 0.000 |
LEV | 210.752 | 0.000 |
SIZE | 214.795 | 0.000 |
ROA | 213.792 | 0.000 |
1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|
Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | |
prob | prob | prob | prob | prob | prob | |
Chow—test | 1273.883 | 1249.134 | 1657.361 | 1463.090 | 1548.716 | 1431.298 |
0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
Hausman—test | 10.300 | 28.498 | 23.834 | 44.066 | 11.129 | 34.671 |
0.001 | 0.000 | 0.000 | 0.000 | 0.004 | 0.000 |
A. IDVOL (σe2) | ||||||
1 | 2 | 3 | 4 | 5 | 6 | |
Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
ILLIQUID | 0.457 | 0.472 | 0.692 | 0.721 | ||
14.591 *** | 15.490 *** | 26.448 *** | 25.730 *** | |||
LIQRISK | 44.207 | 39.150 | 75.976 | 97.785 | ||
10.591 *** | 6.033 *** | 22.788 *** | 18.533 *** | |||
BM | −0.003 | −0.006 | −0.006 | |||
−0.177 | −0.382 | −0.525 | ||||
LEV | 0.150 | −0.432 | 0.107 | |||
0.490 | −1.295 | 0.436 | ||||
ROA | −0.267 | −0.678 | −0.054 | |||
−1.273 | −2.908 *** | −0.314 | ||||
SIZE | −0.099 | −0.044 | −0.076 | |||
−0.760 | −0.309 | −0.728 | ||||
Controls | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.533 | 0.596 | 0.510 | 0.505 | 0.728 | 0.734 |
F-stat | 4.008 *** | 4.689 *** | 3.728 *** | 3.544 *** | 7.997 *** | 7.861 *** |
B IDVOLrelative (σe2/σ2) | ||||||
Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
ILLIQUID | 81.016 | 91.891 | 27.566 | 481.261 | 472.707 | |
5.777 *** | 5.279 *** | 4.817 *** | 8.920 *** | 7.891 *** | ||
LIQRISK | 47.681 | 123.161 | 114.379 | |||
5.360 *** | 6.933 *** | 5.140 *** | ||||
BM | 0.013 | 0.012 | 0.013 | |||
0.595 | 0.531 | 0.626 | ||||
LEV | 0.052 | 0.131 | 0.090 | |||
0.113 | 0.287 | 0.203 | ||||
ROA | 0.472 | 0.300 | 0.194 | |||
1.511 | 0.938 | 0.628 | ||||
SIZE | 0.014 | −0.047 | 0.030 | |||
0.074 | −0.238 | 0.161 | ||||
Controls | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.871 | 0.869 | 0.871 | 0.870 | 0.873 | 0.872 |
F-stat | 88.092 *** | 79.822 *** | 88.768 *** | 81.441 *** | 96.733 *** | 87.879 *** |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|
Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | Chi-Square | |
prob | prob | prob | prob | prob | prob | prob | prob | |
Chow—test | 1624.450 | 1481.900 | 1248.798 | 1181.671 | 1681.561 | 1480.202 | 1481.342 | 1340.250 |
0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
Hausman—test | 4.993 | 13.413 | 21.191 | 38.634 | 25.199 | 44.555 | 16.628 | 34.359 |
0.025 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.001 | 0.000 |
A. IDVOL (σe2) | ||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
SPREAD | 1.555 | 3.106 | 1.799 | 0.082 | 0.056 | 0.069 | 0.064 | 0.060 |
14.960 *** | 2.571 ** | 7.949 *** | 2.965 *** | 1.872 * | 1.826 * | 2.325 *** | 2.019 *** | |
ILLIQUID | 0.472 | 0.498 | 516.708 | 518.293 | ||||
14.857 *** | 15.560 *** | 12.101 *** | 11.462 *** | |||||
LIQRISK | 44.260 | 39.164 | 212.349 | 214.702 | ||||
10.583 *** | 6.018 *** | 13.444 *** | 13.021 *** | |||||
BM | 0.016 | 0.020 | 0.003 | |||||
0.507 | 0.825 | 0.109 | ||||||
LEV | 0.118 | 0.109 | −0.396 | |||||
0.319 | 0.350 | −1.215 | ||||||
ROA | −0.635 | −0.181 | −0.625 | |||||
−3.362 *** | −0.863 | −2.858 *** | ||||||
SIZE | −0.124 | 0.033 | −0.068 | |||||
−0.781 | 0.253 | −0.495 | ||||||
Controls | No | Yes | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.489 | 0.500 | 0.559 | 0.610 | 0.519 | 0.515 | 0.584 | 0.582 |
F-stat | 3.522 *** | 3.514 *** | 4.308 *** | 4.822 *** | 3.820 *** | 3.638 *** | 4.557 *** | 4.395 *** |
B IDVOLrelative (σe2/σ2) | ||||||||
Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
SPREAD | 1.566 | 3.285 | 0.085 | 0.081 | 1.545 | 0.072 | 0.062 | 0.057 |
14.840 *** | 1.636 * | 17.690 *** | 2.897 *** | 69.536 *** | 1.862 *** | 2.209 *** | 1.915 * | |
ILLIQUID | 0.537 | 0.512 | 522.161 | 524.537 | ||||
3.286 *** | 15.836 *** | 12.074 *** | 11.435 *** | |||||
LIQRISK | 18.001 | 39.001 | 214.061 | 216.707 | ||||
4.229 *** | 5.915 *** | 13.380 *** | 12.956 *** | |||||
BM | 0.013 | 0.020 | −0.007 | 0.002 | ||||
0.410 | 0.804 | −0.405 | 0.085 | |||||
LEV | 0.110 | 0.111 | −0.454 | −0.401 | ||||
0.294 | 0.353 | −1.338 | −1.213 | |||||
ROA | −0.644 | −0.181 | −0.718 | −0.636 | ||||
−3.359 *** | −0.855 | −3.028 *** | −2.867 | |||||
SIZE | −0.138 | 0.024 | −0.053 | −0.078 | ||||
−0.852 | 0.184 | −0.363 | −0.557 | |||||
Controls | No | Yes | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.474 | 0.498 | 0.608 | 0.606 | 0.490 | 0.505 | 0.563 | 0.573 |
F-stat | 3.374 *** | 3.491 *** | 4.948 *** | 4.755 *** | 3.516 *** | 3.544 *** | 4.267 *** | 4.276 *** |
A. IDVOL (σe2) | ||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
ILLIQUID | 0.469 | 0.490 | 0.691 | 0.723 | 0.678 | 0.670 | 0.698 | 0.722 | ||
14.681 *** | 15.504 *** | 25.500 *** | 24.723 *** | 21.17 *** | 19.844 *** | 25.716 *** | 24.715 *** | |||
LIQRISK | 62.331 | 63.705 | 75.938 | 97.744 | 100.082 | 98.728 | 73.608 | 94.064 | ||
10.057 *** | 10.253 *** | 22.621 *** | 18.330 *** | 18.911 *** | 18.610 *** | 21.252 *** | 15.998 *** | |||
ILLIQUID_SPREAD | 4.120 | 6.895 | 1.439 | 0.532 | 25.750 | 19.924 | ||||
2.716 ** | 2.806 *** | 2.298 *** | 2.075 ** | 2.450 *** | 2.283 ** | |||||
LIQRISK_SPREAD | 0.274 | 0.269 | 0.074 | 0.067 | 34.328 | 23.444 | ||||
13.203 *** | 12.192 *** | 3.842 *** | 3.253 *** | 2.602 *** | 2.480 ** | |||||
BM | −0.002 | 0.007 | −0.005 | 0.008 | −0.005 | |||||
−0.140 | 0.283 | −0.433 | 0.397 | −0.428 | ||||||
LEV | 0.101 | −0.382 | 0.133 | 0.103 | 0.120 | |||||
0.338 | −1.198 | 0.535 | 0.400 | 0.483 | ||||||
ROA | −0.129 | −0.610 | −0.050 | −0.093 | −0.051 | |||||
−0.620 | −2.869 *** | −0.289 | −0.538 | −0.294 | ||||||
SIZE | −0.034 | 0.037 | −0.077 | −0.014 | −0.076 | |||||
−0.264 | 0.276 | −0.726 | −0.131 | −0.725 | ||||||
Controls | No | Yes | No | Yes | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.559 | 0.609 | 0.597 | 0.593 | 0.726 | 0.731 | 0.739 | 0.736 | 0.728 | 0.731 |
F-stat | 4.311 *** | 4.873 *** | 4.755 *** | 4.554 *** | 7.891 *** | 7.738 *** | 8.184 *** | 7.791 *** | 7.942 *** | 7.740 *** |
B IDVOLrelative (σe2/σ2) | ||||||||||
Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | Coef | |
t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | t-Stat | |
ILLIQUID | 0.512 | 0.504 | 0.652 | 0.740 | 0.696 | 0.689 | 0.842 | 0.851 | ||
17.126 *** | 15.788 *** | 22.393 *** | 25.096 *** | 21.580 *** | 20.238 *** | 13.431 *** | 13.000 *** | |||
LIQRISK | 62.386 | 63.847 | 47.822 | 98.903 | 101.133 | 99.869 | 105.558 | 104.787 | ||
9.926 *** | 10.118 *** | 13.266 *** | 18.408 *** | 18.973 *** | 18.667 *** | 16.240 *** | 15.828 *** | |||
ILLIQUID_SPREAD | 3.714 | 2.007 | 0.689 | 0.021 | 0.002 | |||||
2.690 ** | 2.001 ** | 2.0962 ** | 2.238 ** | 2.0249 ** | ||||||
LIQRISK_SPREAD | 7.107 | 0.276 | 0.272 | 0.071 | 0.064 | 0.036 | 0.002 | |||
2.824 ** | 13.149 *** | 12.152 *** | 3.682 *** | 3.105 *** | 2.455 ** | 2.0216 *** | ||||
BM | −0.002 | 0.007 | −0.005 | 0.008 | −0.004 | |||||
−0.144 | 0.259 | −0.440 | 0.371 | −0.161 | ||||||
LEV | 0.099 | −0.391 | 0.133 | 0.107 | −0.273 | |||||
0.330 | −1.209 | 0.532 | 0.413 | −0.730 | ||||||
ROA | −0.130 | −0.623 | −0.049 | −0.091 | −0.063 | |||||
−0.616 | −2.883 *** | −0.279 | −0.520 | −0.220 | ||||||
SIZE | −0.041 | 0.029 | −0.085 | −0.024 | −0.009 | |||||
−0.322 | 0.211 | −0.798 | −0.219 | −0.068 | ||||||
Controls | No | Yes | No | Yes | No | Yes | No | Yes | No | Yes |
Adj-R2 | 0.605 | 0.605 | 0.576 | 0.584 | 0.677 | 0.729 | 0.729 | 0.734 | 0.748 | 0.753 |
F-stat | 5.009 *** | 4.812 *** | 4.440 *** | 4.421 *** | 6.447 *** | 7.676 *** | 7.824 *** | 7.713 *** | 7.392 *** | 7.345 *** |
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Widianingsih, Y.P.N.; Setiawan, D. Idiosyncratic Risk Volatility: Stock Price Informativeness or Price Error? J. Risk Financial Manag. 2022, 15, 479. https://doi.org/10.3390/jrfm15100479
Widianingsih YPN, Setiawan D. Idiosyncratic Risk Volatility: Stock Price Informativeness or Price Error? Journal of Risk and Financial Management. 2022; 15(10):479. https://doi.org/10.3390/jrfm15100479
Chicago/Turabian StyleWidianingsih, Yuni Pristiwati Noer, and Doddy Setiawan. 2022. "Idiosyncratic Risk Volatility: Stock Price Informativeness or Price Error?" Journal of Risk and Financial Management 15, no. 10: 479. https://doi.org/10.3390/jrfm15100479