Department of Finance and Statistics

This study investigates whether a Fama-French five-factor asset pricing model can explain average returns in the Nordic markets. Further, this study compares the fivefactor asset pricing model’s performance to that of a CAPM and Fama-French threefactor model. The study rejects all models’ descriptions of average returns on the sample. All models perform well in explaining the average returns of portfolios sorted on size and book-to-market ratio, and portfolios sorted on size and investment. However, the models have large difficulties in explaining the average returns of portfolios sorted on size and profitability. While the five-factor model provides a more mean-variance efficient portfolio from its explanatory variables, it fails to improve the intercepts produced in regressions on three factors. Moreover, this study provides more evidence of a disappearing size effect and finds that small stocks in the Nordic markets generally have lower market betas than big stocks.

In earlier studies, scientists have attempted to identify genetic and environmental factors affecting the rate of multiple maternities among humans. We contribute to these studies by analysing the frequencies of multiple maternities in sibships containing triplets. Use of the Hellin transformation is included in evaluation of the triplet rate. Our results indicate greater frequencies of repeated multiple maternities in the sibships than expected, based on population frequencies. The excesses obtained are more marked in triplet maternities than in twin maternities. The transformed triplet rate shows results similar to the twinning rate. The findings also indicate that in families, the influence of maternal factors on the frequencies of multiple maternities is stronger than the influence of paternal factors.

Purpose: To estimate the prevalence of pseudoexfoliation syndrome or exfoliation syndrome (ES) in a cross-sectional study and during a long-term follow-up, and to analyse how ES has been inherited in a large pedigree on an isolated population of Ko¨kar island in southern Finland. Methods: In a population-based study conducted between 1960 and 1962, a comprehensive ophthalmological examination was performed on 595 subjects (85% of the population). From then until 2002, 965 subjects were examined at least once. A pedigree was constructed for all ES-affected subjects according to genealogical studies. The genetic contribution to ES was investigated in this pedigree by segregation analysis and the heritability of the intraocular pressure (IOP) quantitative trait estimated using SOLAR and SAGE software. Results: In the cross-sectional study, the prevalence of ES was 8.1% for 247 subjects over 50 years of age (males 7%, females 9%) and increased to 18.4% for 70 subjects over 70 years of age (males 13%, females 25%). In addition, two females less than 50 years of age were ES-affected. Between 1960 and 2002, 76 (14.3%) of 530 subjects over 50 years of age had ES [23 males (10%) and 53 females (18%)]. Exfoliation glaucoma (EG) was found more often in males (11 patients, 48%) than in females (13 patients, 25%) whereas primary open-angle glaucoma (POAG) was almost as frequent in males (seven patients, 3%) as in females (five patients, 2%). The relative risk (RR) of glaucoma (ES versus no ES) was 11.9 [95% confidence interval (CI) 6.2-22.9] for all the subjects -14.6 for males (95% CI 6.3-34.0) and 11.8 for females (95% CI 4.4-31.6). Seventyfive pedigrees of 78 ES-affected patients were linked together into one large pedigree with 110 nuclear families. The segregation ratio of ES was 18% (8% for males, 24% for females) when both parents were unaffected, and 16% (9% for males, 27% for females) when at least one parent was affected. The heritability of IOP was estimated to be 30%. Conclusion: In this population-based family study, ES is consistent with an autosomal dominant trait with incomplete penetrance, where the penetrance is more reduced in males than in females. However, the presence of ES was a greater risk factor for developing glaucoma in males than in females.

In earlier studies, scientists have attempted to identify genetic and environmental factors affecting the rate of multiple maternities among humans. We contribute to these studies by analysing the frequencies of multiple maternities in sibships containing triplets. Use of the Hellin transformation is included in evaluation of the triplet rate. Our results indicate greater frequencies of repeated multiple maternities in the sibships than expected, based on population frequencies. The excesses obtained are more marked in triplet maternities than in twin maternities. The transformed triplet rate shows results similar to the twinning rate. The findings also indicate that in families, the influence of maternal factors on the frequencies of multiple maternities is stronger than the influence of paternal factors.

The French mathematician Bertillon reasoned that the number of dizygotic (DZ) pairs would equal twice the number of twin pairs of unlike sexes. The remaining twin pairs in a sample would presumably be monozygotic (MZ). Weinberg restated this idea and the calculation has come to be known as Weinberg's differential rule (WDR). The keystone of WDR is that DZ twin pairs should be equally likely to be of the same or the opposite sex. Although the probability of a male birth is greater than .5, the reliability of WDR's assumptions has never been conclusively verified or rejected. Let the probability for an opposite-sex (OS) twin maternity be p O , for a same-sex (SS) twin maternity p S and, consequently, the probability for other maternities 1 − p S − p O . The parameter estimatesp O andp S are relative frequencies. Applying WDR, the MZ rate is m = p S − p O and the DZ rate is d = 2 p O , but the estimatesm andd are not relative frequencies.

The sex ratio at birth (SR) is defined as the number of males per 100 females and is almost always around 106. John Graunt (1620Graunt ( -1674 was the first to compile data showing an excess of male births to female births and to note spatial and temporal variation in the SR. John Arbuthnot (1667-1735) demonstrated that the excess of males was statistically significant and asserted that the SR is uniform over time and space. Arbuthnot suggested that the regularity in the SR and the dominance of males over females must be an indication of divine providence. Nicholas Bernoulli's (1695-1726) counter-argument was that chance could give uniform dominance of males over females. Later, Daniel Bernoulli (1700-1782), Pierre Simon de Laplace (1749-1827) and Siméon-Denis Poisson (1781-1840) also contributed to this discussion. Attempts have been made to identify factors influencing the SR, but comparisons demand large data sets. Attempts to identify associations between SRs and stillbirth rates have failed to yield consistent results. A common pattern observed in different countries is that during the first half of the twentieth century the SR showed increasing trends, but during the second half the trend decreased. A common opinion is that secular increases are caused by improved socio-economic conditions. The recent downward trends have been attributed to new reproductive hazards. Factors that affect the SR within families remain poorly understood. Although they have an effect on family data, they have not been identified in large national birth registers.

Interest in the distribution of birth weight arises because of the association between birth weight and the future health of the child. A common statistical result is that the birth weight distribution differs slightly from the Gaussian distribution. Methods: A standard attempt has been done to split the distribution into two components, a predominant Gaussian distribution and an unspecified "residual" distribution. Results: We considered birth weight data among triplets born in Finland in and compare the birth weight among stillborn and live-born triplets. The stillbirth rates are 119.1 per 1000 births for males, 124.6 for females and 121.8 for all. The sex differences are not significant. The still birth rate for the period 1905-1930 was 119.5 and for the period 1931-1959, 124.2. We identified a strong association between birth weight of the triplets and their survival. The weight distribution for male triplets is described well by the Gaussian curve, while for females a slight deviation from the Gaussian distribution is discernible.

Purpose: To review the literature of autosomal recessive cornea plana (RCP) and to perform a clinical and genetic study on this disorder in Finland. The 78 Finnish RCP patients represent the majority of RCP cases worldwide; outside Finland only 35 cases have been reported. Methods: Families with RCP, particularly in northern Finland, have been followed up by the senior author since the 1950s and extensive genealogical studies have been made.

To investigate exfoliation syndrome (ES) in order to elucidate gender distribution and the roles of genetic and climatic factors in its manifestation. We studied the gender distribution of ES and the association between ES and the appearance of certain climatically induced disorders (pterygium, climatic droplet keratopathy) and the size of pingueculae in populations living in the Arctic region, in temperate regions and in tropical regions. This involved a total of 11 samples taken in eight different countries, comprising 2206 persons of both genders over the age of 50 years. A total of 1051 males were investigated for ES and 147 of them (14.0%) were found to have it. The corresponding figures for females were 1093 and 177 (16.2%). After standardization according to age, no systematic difference between the genders was found in the study. The frequency of ES varied greatly. It was not observed at all in the Inuit (Eskimos) but was found most frequently (about 30%) among the Saami (La...

To elucidate the causes and mechanisms of twinning and higher multifetal maternities, we have taken advantage of the statistical sources of Sweden, where continuous statistics for the whole population are the oldest available. We found strong secular and regional fluctuations. The rates of multiple maternities were the highest during the last three decades of the 18th century, when the twinning rate was more than 17 per 1,000, the triplet rate was more than 3 per 10,000, and the quadruplet rate was almost 7 per 1 million maternities. During 1849-1873 the twinning rate in Sweden was 14.2 per 1,000, but this rate showed great regional differences, being 18.0 per 1,000 on the island of Gotland and 12.6 per 1,000 in the county of Alvsborg. During this period the twinning rate in the countryside in the county of Stockholm was 20.4, but in the city of Stockholm it was only 14.1 per 1,000. In Sweden after the 1930s there was a marked decrease in the twinning rate, which by the 1960s had fa...

We analyzed the effect of total fertility rate (TFR) and crude birth rate (CBR) on the number of males per 100 females at birth, also called the secondary sex ratio (SR), and on the twinning rate (TWR). Earlier studies have noted regional variations in TWR and racial differences in the SR. Statistical analyses have shown that comparisons between SRs demand large data sets because random fluctuations in moderate data are marked. Consequently, reliable results presuppose national birth data. Here, we analyzed historical demographic data and their regional variations between counties in Sweden. We built spatial models for the TFR in 1860 and the CBR in 1751-1870, and as regressors we used geographical coordinates for the provincial capitals of the counties. For both variables, we obtained significant spatial variations, albeit of different patterns and power. The SR among the live-born in 1749-1869 and the TWR in 1751-1860 showed slight spatial variations. The influence of CBR and TFR ...

In many studies the twinning rate, being strongly dependent on maternal age (and parity), has been standardised according to the maternal age distribution. The direct method requires very informative twinning data for the target population. The indirect method is used when the data for the target population is not sufficiently informative or when the target population is small. We have earlier introduced an alternative indirect technique for standardising the twinning rate. Our technique requires even less of the twinning data. Besides maternal age, parity is an influential factor, and should, if possible, be taken into account. In this study we present the traditional standardisation methods based on both maternal age and parity, we propose a new direct standardisation method and we develop our standardisation methods so that they take into account both maternal age and parity. We apply these standardisation methods to data from Finland, 1953-1964, from St. Petersburg, Russia, 1882...

We consider Benford´s law, also called the first-digit law. Benford (Proc. Amer. Phil. Soc., 78, 1938:551-572) presented the law in 1938, but 57 years earlier Newcomb (Amer. J. Math., 4, 1881:39-40) made the same observation. The problem was identified when they used logarithm tables in performing numerical calculations. They noted that the earlier pages of the tables were more worn than later pages. Consistent with this observation, they noted using numbers starting with low digits more often than numbers with high. Benford considered different data sets and noted that for some this rule is valid while for others it is not. When he combined all data sets, the rule was satisfied. Benford was not the first to observe this curiosity, but Benford´s results aroused more attention. Consequently, in the literature the law was named Benford´s law. This paradox has subsequently been established by other scientists, and it has been confirmed to hold under different circumstances. Benford´s l...

In this study we reconsider the effect of variable transformations on the redistribution of income. Under the assumption that the theorems should hold for all income distributions, earlier given conditions are both necessary and sufficient. Different versions of the conditions are compared. We also consider the consequences if we drop the explicit continuity restriction on the transformations. One main result is that continuity is a necessary condition if one pursues that the income inequality should remain or be reduced. In our earlier studies concerning tax policies the assumption that differentiable transformations satisfying a derivative condition could be reduced to transformations satisfying only a continuity condition.

Background. The distribution of birth weights has been extensively investigated. A common result of these studies is that the distributions differ from the Gaussian. A standard attempt has been to split the distribution into two components: a main distribution assumed to be normal and the other a small correction component. Studies have also shown an association between the distribution of birth weights and gestation age. Methods and results. We consider data from the Åland Islands (Finland) for the period 1885-1998. The birth rate showed significant seasonality, having two peaks, one from March to May and the other from July to September, but only slightly significant seasonality in the birth weights was obtained. We observed significant correlations between birth weight and year of birth, sex of the newborn and type of maternity (single or multiple), condition of the infant (live or stillborn), maternal age and marital status of the mother. We built a multiple regression model and...

Background. The distribution of birth weights has been extensively investigated. A common result of these studies is that the distributions differ from the Gaussian. A standard attempt has been to split the distribution into two components: a main distribution assumed to be normal and the other a small correction component. Studies have also shown an association between the distribution of birth weights and gestation age.