Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock-pairs and time. The results indicate a general trend: whenever the stock index is falling the stock prices are changing in a more correlated manner than in case the stock index is ascending. A thorough statistical analysis of the data shows that the observed difference is significant, suggesting a constant-fear factor among stockholders. PACS numbers:The world is once again experiencing a major financial-economic crisis, the worst since the crash of Oct. 1929 that initiated the great depression of the 1930s. Many citizens are concerned for obvious reasons; we are facing global recession; banks and financial institutions go bankrupt; companies struggle to get credit and many are forced to reduce their workforce or even go out of business. Interest rates are increasing while private savings invested in the stock market evaporate. Large parts of our contemporary societies are deeply affected by the new financial reality.The current financial crisis is one particular dramatic example of collective effects in stock markets [1][2][3]6]; during crises nearly all stocks drop in value simultaneously. Fortunately, such extreme situations are relatively rare. What is less known, however, is that during more normal "non-critical" periods, collective effects do still represent characteristics of stock markets that in particular influence their short time behavior. One such effect will be addressed in this publication, where our aim is to present empirical evidence for an asymmetry in stock-stock correlations conditioned by the size and direction of market moves. In particular, we will present empirical results showing that when the Dow Jones Industrial Average (DJIA) index ("the market") is dropping, then there exists a significantly stronger stock-stock correlation than during times of a raising market. Our results indicate that such enhanced (conditional) stock-stock correlations are not only relevant during times of dramatic market crashes, but instead represents features of markets during more "normal" periods.Distribution of returns is traditionally used as one of the proxies for the performance of stocks and markets over a certain time history [1][2][3]. In the economics, finance and econometrics literature the problem of market sentiment and investor confidence is usually addressed by the use of various indicators. These indicators are either derived from objective market data [4], or obtained by conducting questionnaire-based surveys among professional and individual investors [5]. In the present study we consider thus the first approach, since we believe that the market data (prices and returns) are more objective proxies than questionnaire-inferred data.The basic quantity of interest is...