What is Risk?

Analyzing and reflecting risk lies at the core of a valuation analysis, and understanding risk is therefore essential to a robust valuation assessment. In finance, “risk” has specific meaning that differs from the use of that term colloquially, and care must be taken to properly discuss and incorporate risk in a valuation or damages analysis, depending on its type. Finance theory and practice characterizes risk into two types: “non-systematic “or “diversifiable” (or “idiosyncratic” or “asset-specific”) and “systematic” or “non-diversifiable” (or “market”). Non-systematic risks are those that affect the asset being valued but would not affect the market as a whole, whereas systematic risks are risks that affect all assets (except risk-free ones).

The key insight of financial economics is that investors do not value assets in isolation, they value them as part of their portfolios. The more diversified a portfolio, the smaller the impact of any single asset’s idiosyncratic risk on the variability of that portfolio’s returns. Therefore, even though investors are risk-averse (i.e., given two portfolios with the same expected return, they prefer the one with the lowest variance, or uncertainty, over outcomes), they do not discount the value of assets for their idiosyncratic risk because these risks do not have a significant impact on the risk (i.e., the variance) of a diversified portfolio. For example, adding one more coin flip to a bet on the outcome of a “portfolio” of 1,000 coin flips will increase the payoff by the expected value of that coin flip, but will not add to the risk of the portfolio.

Systematic risk affects all assets, and therefore does not disappear in diversified portfolios because it creates correlation among all portfolio assets. No matter how many assets an investor owns, they all react to realizations of systematic risk, such as a global recession or boom, in proportion to their exposure to such risk. The more exposed an asset is to systematic risk, the less valuable it is to an investor, all else constant, because it contributes more variability to the portfolio return compared to the market, and therefore the more it is discounted relative to the expected value of its cash flows.

Systematic risks are risks that affect the average outcome of the cash flows. For example, the risk that the value of an asset would drop along with that of the entire market if the global economy faces a recession is a systematic risk. Consider a hotel company. The hotel company is exposed to changes in the economy that will not “average out” over the whole portfolio of different hotels. When there is a global recession, travel declines. Therefore, the value of a hotel company can be expected to decline at the same time that the portfolio overall can be expected to decline. As another example, for an oil exploration and production business, the average chance of finding oil in drilling an exploration well would remain the same regardless of the overall economy (i.e., it is diversifiable across a large portfolio of wells), but oil prices may change substantially due to global economic conditions—those risks cannot be diversified away even in a large portfolio of wells.

The key learning is this: given two assets that are expected to generate the same average cash flows over a given period of time, the asset with cash flows that are more correlated with the overall market will be priced lower because investors are less able to diversify that risk. Mathematically, given that the expected cash flows are the same, the discount rate for the more correlated asset must be higher to yield the lower price.

What Does This Mean for Valuing an Income Producing Asset?

The discounted cash flow method is based on the principle that the market value of any asset is derived based from its expected ability to generate cash flows in the future, discounted to determine the present value using a discount rate reflecting the time value of money and risk.

Cash Flows. The preferable method for forecasting cash flows is to give due weight to all possible outcomes, bad as well as good, based on their expected probability of occurring. Unbiased cash flows are expected (average) cash flows—not the cash flows that investors may hope for if everything goes well. Thus unbiased cash flows assign realistic weights to all of the outcomes. The cash flows should reflect such expected outcomes for all of the risks of an asset, whatever the source, unless there are legal reasons to disregard certain risks. For example, if there is a 50% chance that future sales will be $0 and a 50% chance they will be $100, the cash flow forecast should be based on expected sales of $50 (50% x $0 + 50% x $100). Determining the probability-weighted cash flows incorporates all risks of the cash flows into the forecast. In practice, investors sometime focus on the most likely scenarios. This can be a reasonable approach, but it can create distortions where there are highly impactful, but low-probability outcomes that are neglected.

Many assets that appear to be risky do not have unusually high systematic risk. For example, a wildcat (i.e., exploration) oil well is typically regarded as riskier than a development well—and it is riskier, if “risk” is defined as uncertainty about future production and cash flows. The wildcat well’s additional diversifiable risks fade away, however, when that one well is drilled by an oil company that drills many wells, and that oil company’s stock is held in a diversified portfolio with dozens or hundreds of other stocks. In other words, an individual wildcat well may face great uncertainty about its future cash flows, but the average cash flows from a large portfolio of wildcat wells drilling on different prospects is much more predictable. This means that holding a diverse portfolio of non-systematic risks allows the investor (and the tribunal) to value them at the average outcome. (Think of a coin toss. The outcome of any one toss is random. But one can say with confidence that the average number of heads in hundreds of tosses will be very close to 50%.)

Discount Rate. This explains why, as a matter of financial economic theory, the discount rate should be calibrated depending on the asset’s exposure to systematic macroeconomic and market risks. The higher the exposure to this type of risk, the higher the discount rate should be. But the discount rate should not be adjusted for asset-specific risks, because these risks “average out” for diversified investors and already should be incorporated into each asset’s expected cash flows.

In practice, this is achieved by employing a discount rate that values the cost of equity component to include a risk-free rate reflecting the time value of money plus an additional rate reflecting the systematic risk of the asset (but not the non-systematic risk). The most common method for determining systematic risk of an asset is the Capital Asset Pricing Model (“CAPM”).

The following diagram summarizes the treatment of risk in valuing an asset using a cost of equity based on CAPM.

	Cost of Equity based on CAPM?	Cash Flows?
Systematic/Market Risks	Yes	Yes
Non-Systematic/Diversifiable Risks	No	Yes

When CAPM is employed to value systematic risk in the cost of equity, all risks, market and macroeconomic as well as asset-specific, have to be accounted for in cash flow forecasts. If market and macroeconomic risks generate more downside than upside outcomes for an asset, then the cash flow forecasts should be reduced until the downside and upside outcomes are in balance (“in balance” means that the forecasts are unbiased in that they reflect a probability-weighted analysis of the expected potential outcomes). Cash-flow forecasts should be adjusted so that asset-specific risks are in balance. Once this has been done, however, further increasing the discount rate to reflect asset-specific risks would double count the impact of those risks and undervalue the asset.

Some financial experts build asset-specific risk into the cost of equity by adding not only a only a premium for systematic risk, but also adding an additional premium for certain aspects of asset-specific risk (i.e., non-systematic risk). This is sometimes referred to as a build-up discount rate. If a build-up discount rate is used, the cash flows should not reflect any risks that have been included in the discount rate but rather should be based on scenarios excluding the asset-specific risks that have been included in the discount rate.

The following diagram summarizes the appropriate treatment of risk in valuing an asset using a build-up interest rate.

	Build-up Discount Rate?	Cash Flows?
Systematic/Market Risks	Yes	Yes, but excluding the risks that have been included in the discount rate
Non-Systematic/Diversifiable Risks	Yes, but excluding the risks that have been included in the cash flow forecast	Yes, but excluding the risks that have been included in the discount rate

The more widely accepted approach is to analyze the expected cash flows addressing how each element of risk will impact the future cash flows and then apply the WACC/CAPM discount rate excluding asset-specific risks. The challenge in practice is that this can lead to a wide range of cash flow outcomes, which can be difficult for the tribunal to understand and unwieldly to apply in the valuation. But what is simply wrong, is to apply a build-up discount rate to expected cash flows that already reflect the same risks because this would double count asset-specific risks and could significantly underestimate the value of the asset.