### Abstract

Two experiments in the stability of stock statistics This paper announces support in the form of the Spearman rank correlation test for the hypothesis: stock variance is a stable commodity, but the covariance of stocks varies randomly. Among the consequences of this hypothesis are: 1. Arbitrage equations involving covariances do not constrain the marketplace. 2. Variance is a stable commodity whose price is set by the arbitrage opportunities it presents. 3. Portfolio theories depending on estimates of future stock covariances are not at present useful theories. The result is not unexpected, however the conclusions challenge some of the existing literature. 1

### Citations

1244 | Generalized Autoregressive Conditional Heteroskedasticity
- Bollerslev
- 1986
(Show Context)
Citation Context ...d observed variance and thesefficient market hypothesis. In addition, there has been much work done using the ARCH model introduced by Engle [2] and the extension GARCH model introduced by Bollerslev =-=[1]-=-. These heteroscedastic models assume that stock price is a gaussian normal random variable with time varying variance, the variance predicted according to the parameters of the model. This paper atta... |

946 |
Autoregressive Conditional Heteroscedasticity with Estimates of the Variance
- Engle
- 1982
(Show Context)
Citation Context ...been undertaken by Shiller [7] in order to bring into accord observed variance and thesefficient market hypothesis. In addition, there has been much work done using the ARCH model introduced by Engle =-=[2]-=- and the extension GARCH model introduced by Bollerslev [1]. These heteroscedastic models assume that stock price is a gaussian normal random variable with time varying variance, the variance predicte... |

591 |
Portfolio Selection: Efficient Diversification of Investments
- Markowitz
- 1959
(Show Context)
Citation Context ...of Mathematics and Computer Science University of Miami 1 had no predictability, they would also be of no value as an asset. The theory by which an optimal portfolio is calculated is due to Markowitz =-=[6]-=-. For that theory, variance and covariance information is required. One possibility would be to calculate the historical variances and covariances of a universe of stocks and bring these values forwar... |

319 |
Rank Correlation Methods
- Kendall
- 1970
(Show Context)
Citation Context ...r }, any r ∈ R. We wish to compare these two rankings in order to reject the possibility that there is no significant influence of the past on the future. Spearman’s rank correlation coefficient [3], =-=[5]-=- is the correlation of ranks under the two orders: � � 6 r∈R Rankα(r) − Rankβ(r) rR = 1 − �2 . (N + 1)N(N − 1) Similarly, consider S = R (2) the collection of all distinct stock pairs, and select a si... |

49 |
Mathematical statistics
- Freund
- 1992
(Show Context)
Citation Context ...βi = r }, any r ∈ R. We wish to compare these two rankings in order to reject the possibility that there is no significant influence of the past on the future. Spearman’s rank correlation coefficient =-=[3]-=-, [5] is the correlation of ranks under the two orders: � � 6 r∈R Rankα(r) − Rankβ(r) rR = 1 − �2 . (N + 1)N(N − 1) Similarly, consider S = R (2) the collection of all distinct stock pairs, and select... |

1 |
and Oskar Morgenstern. Predictability of Stock Market Prices
- Granger
- 1970
(Show Context)
Citation Context ...chieved by taking two independent, random orderings. The problem of prediction of stock price movements has been previously studied from the timeseries standpoint. The work of Granger and Morgenstern =-=[4]-=- uses the classical techniques of Fourier Analysis to study the spectral qualities of stock price movements. A very detailed study of stock price variance has been undertaken by Shiller [7] in order t... |

1 |
Experimental stock market data. http://www.ai.mit.edu/stocks/. 0.8 0.6 0.4 0.2 Trial Time Period Experiment Variance Covariance Random 1 93.3 vs. 93.4 3.42 0.21 1.44 2 93.3 vs. 93.4 4.32 −1.58 −0.55 3 93.3 vs. 93.4 3.63 −0.23 −0.90 4 93.4 vs. 94.1 4.44 0.
- Torrance
(Show Context)
Citation Context ...t experiment, summarized in Figures 1 and 2, uses a data set of 212 stocks containing records of at least 280 closing prices since October 30, 1993. The data was taken from MIT’s Stock Market Project =-=[8]-=-. We use this data to test quarter and semi-annual data streams running from the third quarter of 1993 until the fourth quarter of 1994. This data is of limited depth in time, but does give us a large... |