Risk takes many forms. You take risk everytime you act, from crossing the street to buying a stock to getting on an airplane to drinking a glass of pasteurized milk.
Generally when people talk about risk, however, they focus on financial risk. This answer therefore addresses both types and measurement of financial risk.
- - Types of Risk -
o Interest Rate Risk: One way to measure interest rate risk is to measure the volatility of interest rates. The easiest way to do this (though not necessarily the most correct) is to look at the historic volatility of interest rates. A more complex way to do this is to use mathemtical models to forecast interest rate scenarios.
o Credit Risk: Credit risk is evaluated by credit ratings agencies, the most common being Moody's, Fitch, and Standard and Poors. These agencies assign credit rates to corporations and bonds, helping the investor and lenders understand the implicit risk of the borrower/issuer.
o Liquidity Risk: Typically the bid-offer spread (the difference between where you buy and sell a product) is a good indication of liquidity risk. For example, if you can buy a stock at $100 and sell it at $99.95, the bid-offer spread is $0.05, and getting out of the trade is considered relatively easy. However, if you could buy a bond at $100 but sell it at $80, the bid-offer spread is $20, and the bond would be considered illiquid.
o Event/Geopolitical Risk: This is a tough one to measure. Increasing global tension is generally reflected in price volatility or a runup in certain types of prices (gold, oil, US Govt bonds), but no one can predict when/where major risk-impacting events will happen.