## Risk Measures

Risk manifests in many different ways and so are risk measures. The following are some of the most frequently used risk measures.

**Standard Deviation**

This risk measure must be considered in combination with the average return. Because shifting the daily price of an asset uniformly up or down will not change the standard deviation. It measures the fluctuation of the asset price around the average return and is among the first used in measuring the risk due to its simplicity. One drawback is that it treats positive and negative deviation from the mean the same while investors usually only consider deviation to the downside to be a risk.

**Value at Risk **

Value at risk is one of the alternatives addressing the shortcoming of risk in terms of standard deviation. It provides a probability (say 5%) of loss exceeds a certain level (say 20%). Value at risk is widely used by financial institutions to assess the risk of their portfolio consisting of risky assets. However, to compute value at risk one needs to know the full picture of probability distribution of the risky assets involved which in general can only be estimated. So in practice what is calculated is only an approximation. Moreover, value at risk only assess the risk of loss exceeds a certain level not how large the loss will be.

**Maximum Drawdown **

Maximum drawdown is a more direct risk measure. It is simply the largest percentage loss from its peak of an investment in a given period of time. This measure provides an important guidance to the trader when determining her risk exposure (e.g., the leverage level) in order to avoid ruin. In practice, she has to build in enough cushions for safety because maximum drawdown after all only tells us what happened in the past.