Stock volatility indicates how much the value of the stock changes during the course of a certain period of time. if the stock's value keeps going up and down on regular bases over the course of 90 days, it has high volatility. But if it the stock's value remains the same over the course of 90 days, it has low volatility. While volatility can make a stock risky, that isn't necessarily the case. In fact, with the right investment strategy, it can make the stock more profitable than it would otherwise be.
The Question of Risk
When an investor buys stock, he or she inevitably takes a risk. After all, the stocks represent the portions of the company's profits. The investors buy stocks assuming that they will rise in value as the company continues to increase it's profit margin. But that won't necessarily be the case. For one reason or another, the company's profits may plunge. They may recover over time, but they may not. In the worst-case scenario, the company's losses grow to the point where it has to declare bankruptcy, leaving the investor with completely worthless stock.
For the purpose of the stock market, risk signifies that odds that it's value will unexpectedly drop. While every stock contains some element of risk, some stocks are riskier than others. The risk is usually judged based on market conditions, recent events in United States and throughout the world and the company's policy decisions. It is constantly reevaluated as those factors change, allowing investors to adjust their strategies accordingly.
Risk vs. Volatility
As mentioned in the introduction, volatility is the measure of how much the value of the stock changes over time. Volatility is measured by comparing the financial performance over a certain period in the past over the financial performance over the same period in the present day. If the value doesn't change much, the stock's volatility is low, but if it changes significantly, the stock's volatility is high.
Many investors assume that if the stock has high volatility, it must be risky. However, it isn't necessarily the case. That is because the volatility is more limited in scope. Comparing the financial performance assumes that all the other factors are the same, which is not always the case.
The Unexpected
For example, the damage caused by Hurricane Katrina caused hotels throughout New Orleans area to suddenly lose customers, causing unexpected plunge in profits. Government contractors responsible for the clean-up, on the other hand, got an unexpected boost. Furthermore, sudden losses do not have the same effects on every company. Some companies may have leaders that are savvy enough to navigate through the trouble spots without undercutting the company's overall performance.
In short, just because an investment is volatile doesn't mean it's risky. The investors will need to look at a bigger picture to determine if there is any risk. And, if there is low risk, they can actually use volatility in their favor. They can do this by measuring pattern of volatility and see if there are certain periods when the stocks' value as lower/higher than average. They can use this knowledge to buy stocks when their value is low and sell them while they are high. And, since the risk is low, they are much less likely to lose money in the process.
【我的备注】我们经常使用股票价格变化率的方差/标准差作为衡量股票波动性的方法，即衡量股票风险的方法。但股票的风险并不能仅靠波动性来衡量。比如股票由于某个事件出现大幅下跌，这个下跌会大大增加方差/标准差的值，会让人认为这个股票的风险很大。但我们应该考虑这个事件发生的概率有多大。所以人们在在险价值（VaR，Value at Risk）的基础上，又提出了条件在险价值（CVaR，Conditional Value at Risk）的概念。
关于条件在险价值（Conditional Value at Risk），需要先理解在险价值。知乎上有比较全面的在险价值的解释。条件在险价值的计算要比在险价值的计算更复杂。
百度百科上关于它的概念，我觉得还是十分恰当的。
从价格条件出发，研究在一定价格水平上股票收益率的统计分布特征，并以此为基础来研究VaR理论及其应用，使在险价值理论更加符合市场的实际情况。
另外有一个小细节，在险价值和条件在险价值的缩写中的“a”一定要小写。如果大写了就是VAR，即Vector Autoregression（向量自回归模型），这是时间序列分析中常用的一个多变量模型。
