Tipology : Glossary

Risk is a subjective situation in which uncertainty, an objective situation, takes on its own configuration. The measurement of risk can be either probabilistic or frequentist. The first depends on the probabilities, or probability distribution, of occurrence assigned to a set of possible future events. The second is defined as the number of favourable cases over the number of possible cases. From an economic point of view, risk can take various forms. We speak of risk when we speak of bankruptcy risk, exchange rate risk, maturity risk, country risk, systemic risk, systematic or non-diversifiable risk, diversifiable risk, etc.. Each of these risk categories has its own specific scope. Linked to risk is also, via the expected utility theory, risk aversion. It is, like risk, a subjective situation in which each individual/agent operating in the market is faced each time he/she is confronted with two alternatives: one certain and one uncertain. Depending on their risk aversion, individuals will choose one or the other situation according to the utility that will be determined. Each individual will always manage to define a threshold of indifference between the two alternatives by defining what is called the certain equivalent. This is the value that makes the risk-averse/proposing/indifferent individual neutral with respect to choosing the certain situation over the uncertain one. Once risk aversion/propensity and its certain equivalent have been defined, one can define a much-used measure in economic analysis which is the risk premium. It is the amount that is demanded by a risk-averse individual in a situation of uncertainty. The risk premium can also be estimated with models such as the CAPM. The risk premium can also be used to estimate what is called excess returns where the difference in return between a risky asset and a risk-free asset is a function of the non-diversifiable risk, measured by βeta, and the market risk premium.

The concept of investors' risk aversion thus defines how they demand extra profits or compensatory returns for greater uncertainty. Moreover, the notion of the cruciality of risk and the assumption that riskier investments, in order to be considered profitable, must have a higher return profile in comparison to less unscrupulous transactions, are rather intuitive. The expected return on each investment can, therefore, be expressed as the sum of the risk-free rate and an extra return to compensate for this greater uncertainty (risk premium). To describe the risk premium, it is therefore appropriate to distinguish the two basic components of risk:
- systematic risk
- specific risk.

Systematic risk, or also non-diversifiable risk, arises from the realisation that there are dangers and problems that affect the entire economy, posing a threat to all assets (in the CAPM model, systematic risk is measured by the β indicator). This is the reason why equities show a tendency to synchronise movements and the motivation behind investors' exposure to “market uncertainty”, regardless of the number of shares held.

Specific risk, on the other hand, inserts the impending dangers on the individual asset considered. It is an element that can be reduced by means of appropriate diversification techniques of the financial assets constituting the portfolio (see LMC and SML) and, moreover, can be measured through the use of suitable statistical indices of variability, among which we recall, for example, the mean square deviation.

Risk is also taken into account when talking about premium puzzles. Among the phenomena that appear to be difficult to solve is one: why did the US stock market offer such a high average annual return (around 8 % in real terms) for most of the 20th century? This conundrum is known as the equity premium puzzle. The questions that can arise are such as "why has the volatility of the stock market return been so much higher than that of the growth rate of per capita consumption?" or "why has the market interest rate been (real) less than 1 %?". The puzzle is based on precisely these kinds of questions. It is difficult to generate from a rational expectations model an economic system characterised by low volatility for consumption but high volatility for stock returns and a low average interest rate in real terms. For years, theorists have tried to understand why only a small proportion of investors buy shares, or why people with a long-term time horizon hold fixed-income bonds. It is well known that the real returns offered by different financial assets can differ considerably, even when averaged over an extended period of time. Economists explain this by attributing these differences to the varying intensities with which the yield of a security covaries with the typical investor's consumption function. If this covariance is high, the sale of shares leads to a reduction in the variance of the typical investor's consumption flow.

Bibliography
SALTARI E., 1997, Introduction to Financial Economics, NIS (La Nuova Italia Scientifica), Rome
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, March
MEHRA R., PRESCOTT E. C., 1985, The Equity Premium: A Puzzle, in Journal of Monetary Economics, Vol. 15, pp. 145-161

Editor: Rocco CICIRETTI (march 2025)