Measuring the Risk - Volatility

 
When it comes to investment, in addition to the return on the investment, the other thing that we are always interested in knowing is that how much risk we are taking to make a specific investment. But exactly what is risk? How can we quantify the risk?

Risk VS. Uncertainty

Although there is no clear distinction between the risk and uncertainty, we can use Frank Knight’s distinction as the starting point: Risk has an unknown outcome, but we know what the underlying outcome distribution looks like. Uncertainty also implies an unknown outcome, but we don’t know what the underlying distribution looks like. For example: Amazon is going to announce its fourth quarter earnings in January 31, 2012. As of writing, we don’t know what the price movement of amazon stock is after the earning is announced, but we do have the past history to measure the likelihood of the price movement after earning is announced. That’s the risk. On the other hand, current European sovereign debt crisis posts an uncertainty for us because the outcome is unknown and there is no past history for us to gauge the likelihood of the outcome

Measuring the Volatility of the Stock as the Risk

Although there is no way to measure the uncertainty of a particular stock, we can measure the volatility of the stock according to the past history of price movement to represent the risk of investing in the stock. The volatility of the stock is simply the standard deviation of the price movement for a certain period of time:

Calculate the Risk of the Market (S&P 500)

You can calculate the risk of the market (S&P 500) or any particular stock/ETF you are interested in by following steps:
1. Get the stock historical price data: Use Stock Historical Data Download to download the past 10 years, monthly price movement for symbol S&P 500 (^GSPC)
2. Calculate the monthly price % change based on the monthly price movement
3. Uses the Excel function (STDEV.S) to calculate the volatility for you. Remember you have to times the number by sqrt(12) to make it annualized volatility
You can download the sample excel here
Following is the S&P 500 volatility distribution based on last 10 years, 5 years, 3 years, and 1 year data

The volatility ranged from 16% to 18.9%.
As we can see, the volatility of the stock changes if we use the different intervals of past history
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