A bear market is defined as a downward trending market, but a bear market rally is a bit different. A bear market rally is a period in which stock prices increase during a bear market. Although this might seem counter intuitive, the increase is short lived, follows a period when the markets declined and is then followed again by another market decline which results in a significant downward trend.
While there are no specific standards for the concept of a bear market rally, the general definition is that there is an overall market increase of 10-20% during the conditions of a bear market. This trend is common during downward movement of the stock markets, and you can find such examples by looking at the way the markets move even in the worst financial times. Even after the famous 1929 Dow Jones crash a bear market rally occurred before the final decline in 1932.
It is important not to mistake a sucker rally for a bear market rally. A sucker rally will initially appear as a rise in the market, but the trend is much shorter. The idea is that the rally lasts long enough for the “suckers” to make purchases right before the market dives again. Determining which is which is often difficult even for those in the investment field. For investors who get in during either rally the risks are significant since there is little way to predict just when the bottom will fall out of the market again, potentially leaving them with stocks which are suddenly worth much less then they were at purchase.