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Home > Financial Risk Management Best Practice > Quantifying Corporate Financial Risk

Financial Risk Management Best Practice

Quantifying Corporate Financial Risk

by David Shimko

Executive Summary

  • Standard pro forma cash flow analysis considers risk in a crude way, usually with a subjectively determined upside and downside to cash flows.

  • Stochastic analysis generates a large number of scenarios to give a better understanding of risk interactions, business linkages, optionality, and contracts designed to mitigate risk.

  • Simple models can be built in spreadsheets, but one must take care to model financial assets, commodity prices, interest rates, and exchange rates appropriately.

  • Stochastic pro-formas can lead to better capital budgeting, valuation, and risk management decisions, particularly when risk is important to decision-making.

  • Even the most sophisticated models are still subject to model risk; and they do not likely capture all the risks affecting an enterprise.

Example of a Stochastic Pro Forma

Consider the case of a company that has experienced six months of cash flows this year and wants to forecast the next six months. The usual way to do this is to predict a cash flow growth rate—expected, high, and low—and to base the analysis on these choices. A sample cash flow projection might be illustrated graphically in Figure 1.

In reality, of course, several different cash flow patterns might emerge for the last six months of the year. Using the same risk model, we could run a large number of simulations and see what the outcomes might be. Eight possible outcomes are plotted in Figure 2.

Clearly the stochastic analysis, albeit more realistic, is not as simple and not as attractive at first blush as deterministic analysis. And there are many situations where stochastic analysis is not needed. Yet there are certain results that one can get from stochastic analysis that cannot be gained from deterministic analysis. Table 1 gives some examples.

Table 1. Incremental analyses produced by stochastic pro formas

Analysis Sample question
Probabilities of outcomes What is the likelihood we will need to borrow?
Risk of outcomes What is the most likely range for annual cash flows at year-end?
Interactions If we invest more in capital expenditures only when cash flows are up, how do we reflect that in the analysis, and what impact does it have?
Options Our loan contracts have floating rates, but the rates are capped. How does this affect the probabilities of different cash flow levels?
Worst case We probably won’t have the worst case revenues and the worst case costs in the same year; how does that reflect on our expectation of the worst case?
Events There is a 10% chance we get a major contract that will increase our cash flows significantly. How do we incorporate this in the model?
Risk mitigation The treasurer wants to lock in foreign exchange rates for our foreign buyers. How will this affect cash flow volatility?
Capital structure What is our capacity to make interest payments on debt with 99% certainty?

Stochastic analysis is needed in situations where risk assessment is required, where the future company decisions depend on an unknown variable, where options are present, and when the company wants to study risk mitigation strategies.

Stochastic modeling of the income statement can be done at the aggregate level as it has been demonstrated here, or the components can be broken down into smaller components, such as the prices of products, inputs, interest rates, foreign exchange rates, and the like. The benefit of breaking down the income statement into its market-driven components is that we can find much more information on market-quoted prices and rates. This historical information is usually used as a starting point in determining how best to model these prices and rates.

Modeling Market Risk

Risk analysts need to spend significant time and effort to model the risk of the inputs to their stochastic models correctly. Incorrect specifications for market prices will lead to incorrect results. There are several models available to model market price risk. The choice of the best model generally is made by looking at the market’s historical performance and making judgments about market price behavior.1

For example, if our risk model depends on fluctuations in the stock market index, a popular approach is to represent the index as following a random walk in percentage terms. Thus, any given day’s return is normally distributed with a constant mean and standard deviation, and statistically independent from the previous day’s return. This approach was popularized in the Black–Scholes (1973) and Merton (1973) papers on option pricing. The random walk works reasonably well, except that with specialized knowledge one could argue that the average return should not be constant, the volatility should not be constant, and there are sometimes events which cause stock prices not to be normally distributed. For this reason, the S&P 500 index may reasonably follow a random walk, but the stock of a small pharmaceutical company will not, since it is prone to occasional major events such as FDA drug approval or discovery of legal liability.

Other market prices, such as interest rates, do not follow random walks. Overly high and overly low interest rates tend to correct over time to equilibrium levels. Although that equilibrium level may change over time, the general character of interest rates is that they are mean-reverting—i.e., they revert to a long-run mean over time. The same is true of commodity prices. High commodity prices stimulate production, which causes future prices to fall. Low prices discourage production, causing future prices to rise. Therefore, interest rates and commodities need to be modeled in a similar way. Some currencies exhibit mean-reverting behavior and some do not.

Finally, every market price may have unique characteristics. The volatility of natural gas and heating oil changes by season. Power prices spike rapidly when generation fails and bounce back immediately as generation comes back on line. Careful modeling of critical market price inputs will lead to the best models of stochastic results.

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Further reading


  • Black, Fischer, and Myron Scholes. “The pricing of options and corporate liabilities.” Journal of Political Economy 81:3 (May–June 1973): 637–654. Online at:
  • Merton, Robert C. “Theory of rational option pricing.” Bell Journal of Economics and Management Science 4:1 (Spring 1973): 141–183. Online at:


  • Most of the literature in “stochastic processes” is extremely technical and not suitable for the average business reader. Even “stochastic processes in finance” tends to lead to models of security prices and interest rates for building value-at-risk models and option pricing models.
  • The topic “financial statement simulation” in an internet search engine leads to simulation software providers, such as Palisade, Finance 3.0, and @Risk. These providers offer written materials to supplement their software services. In addition, the reader is invited to request additional materials from the author.

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