Risk is a subjective situation where objective uncertainty becomes effective. Risk can be measured in a probabilistic manner or in terms of frequency. The probabilistic manner to measure risk depends on the probability assigned to a certain number of future events, whereas frequency is associated with the number of possible cases divided by the total number of future events.
From an economic point of view, risk can take on diverse forms: the risk of bankruptcy, exchange, maturity, country, systematic and non-systematic risk. Each of these categories of risk has its own specific field of application. Risk is also associated with risk aversion through the expected utility theory. Risk aversion is a subjective situation which agents in the market face each time they have to choose between alternatives: one is certain and the other is uncertain. Depending on risk aversion, individuals choose one of the two alternatives by analysing the utility associated with it. Moreover, each agent’s attitude towards risk defines a value where he/she is indifferent between the two. This value is called the certainty equivalent. It is the lowest value that will compensate an individual for participating in a venture with uncertain outcome.
After defining the aversion/propensity risk situation and the certain equivalent, it is possible to define another risk measure used in the economic analysis: risk premium. Risk premium is the extra-value requested by individuals with different levels of risk aversion, to face an uncertain event instead of a certain one. This value can be estimated through theoretical models such as CAPM.
Risk premium can also be used to define excess return. Excess return is the difference between the expected return of a risky investment and a risk-free investment. It depends on non-diversifiable risk measured by in the CAPM model, and the market risk premium. 
isk aversion defines how individuals request extra-return to compensate for the higher level of uncertainty. This is crucial in defining the risk aversion of each individual. Moreover, each investment must be assessed by using the return-risk valuation in order to be considered worthy with respect to the other investment. Each expected return can be assessed by using the risk-free rate and the extra-return (risk premium) used to compensate the higher level of uncertainty. We can distinguish between two fundamental risk components:
systematic risk; 
- specific risk.
Systematic risk, also known as non-diversifiable risk, is related to the exogenous situation non-directly related to the specific asset (in the CAPM model, this risk is measured by ). This is the reason why stocks show co-movements in the trend. This is common in the market and is called market uncertainty. It is not related in any way to any particular stock or portfolio. 
Specific risk is directly related to the characteristics of a specific investment. It can be reduced by the diversification process of financial assets when creating portfolios (see CML, and SML). It can be measured by using a variability index such as the average square root.
Risk is also taken into consideration when speaking of the premium puzzle. This phenomenon is hard to resolve from an economic perspective. Why did the US stock market have such a higher return (8% on areal base) for most of the 20th century? This enigma is called equity premium puzzle. Other questions that may arise are of the following kind: "why is the volatility of stock returns higher than the pro-capita consumption growth rate?", or "why is the real interest rate in the real market lower than 1%?". 
Using a rational expectation model, it is difficult to generate an economic system characterised by contained volatility for consumption and high volatility in stock returns, with a low interest rate in real terms. Through the years, economists have tried to understand either why only few investors buy stocks or why individuals with long-term investment strategies hold fixed income assets.
It is known that financial asset returns in real terms can differ consistently even if they are evaluated in the long run. By using the different intensity of stock return covariance with the standard consumption function, it is possible to theoretically define these differences. If covariance is high, the supply of stocks determines a reduction in the variance of standard consumer consumption flow. 
Saltari, E., 1997, Introduzione all’Economia Finanziaria, NIS (La Nuova Italia Scientifica), Roma;
Brealey, R. A., Myers, S. C., 2000, Principles of Corporate Finance, Irwin/Mc Graw Hill, New York;
Sharpe, W. F., 1964, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, in Journal of Finance, Vol. 19(3), pp. 425-442;
Mehra, R., Prescott, E. C., 2003, The Equity Premium in Retrospect, in NBER Working Paper No. W9525, Marzo;
Mehra, R., Prescott, E. C., 1985, The Equity Premium: A Puzzle, in Journal of Monetary Economics, Vol. 15, pp. 145-161.
Editor: Rocco CICIRETTI