## Dealing With Risk

**Risk analysis** is the systematic study of **uncertainties** and **risks** we encounter in business, engineering, public policy, and many other areas. **Risk analysts** seek to identify the risks faced by an institution or business unit, understand how and when they arise, and estimate the impact (financial or otherwise) of adverse outcomes. **Risk managers** start with risk analysis, then seek to take actions that will **mitigate** or **hedge** these risks.

Some institutions, such as **banks** and **investment management** firms, are in the business of taking risks every day. Risk analysis and management is clearly crucial for these institutions. One of the roles of **risk management** in these firms is to **quantify** the financial risks involved in each investment, trading, or other business activity, and allocate a **risk budget** across these activities. Banks in particular are required by their regulators to identify and quantify their risks, often computing measures such as **Value at Risk (VaR)**, and ensure that they have adequate **capital** to maintain solvency should the worst (or near-worst) outcomes occur.

#### Quantitative Risk Analysis

**Quantitative risk analysis** is the practice of creating a **mathematical model** of a project or process that explicitly includes uncertain parameters that we cannot control, and also *decision variables* or parameters that we *can* control. A quantitative **risk model** calculates the impact of the uncertain parameters and the decisions we make on outcomes that we care about -- such as profit and loss, investment returns, environmental consequences, and the like. Such a model can help business decision makers and public policy makers understand the **impact of uncertainty** and the consequences of different decisions.

#### Models and Simulation

One way to learn how to deal with uncertainty is to perform an experiment. But often, it is too dangerous or expensive to perform an experiment in the "real world" so we resort to using **models** -- such as a scale model of an airplane in a wind tunnel. With a model, we can perform many **experiments** to **simulate** what could happen in the real world. For example, subjecting our model airplane to various air currents and forces, we might learn how an actual aircraft design is likely to behave in the real world. We can introduce **uncertainty** into our experiments by allowing some conditions to vary randomly. A single experiment that involves a randomly generated condition might not tell us very much, but if we perform a **simulation** that consists of *many* such experiments (or **random trials**), and collect **statistics** about the results, we can learn quite a lot.

If we have the skills and **software tools** needed to create a mathematical model of a project or process on a computer, we can perform a simulation with many trials in a **very short time**, and at **very low cost**. With such advantages over experiments in the real world, it's no wonder that computer-based simulation has become so popular. For business models, Microsoft Excel is an ideal tool for creating such a model -- and simulation software such as Frontline Systems' **Risk Solver** can be used to get maximum insight from the model.

#### Monte Carlo Simulation

**Monte Carlo simulation** -- named after the city in Monaco famed for its casinos and games of chance -- is a powerful mathematical method for conducting quantitative risk analysis. **Monte Carlo methods** rely on **random sampling** -- the computer-based equivalent of a coin toss, dice roll, or roulette wheel. The numbers from random sampling are "plugged into" a mathematical model and used to calculate outcomes of interest. This process is repeated many hundreds or thousands of times. With the aid of software, we can obtain statistics and view charts and graphs of the results.

Monte Carlo simulation is especially helpful when there are several **different sources of uncertainty** that interact to produce an outcome. For example, if we're dealing with uncertain market demand, competitors' pricing, and variable production and raw materials costs **at the same time**, it can be very difficult to estimate the impacts of these factors -- in combination -- on Net Profit. Monte Carlo simulation can **quickly analyze thousands** of 'what-if' scenarios, often yielding surprising insights into what can go right, what can go wrong, and what we can do about it.