Beyond the Risk Premium: A First Principles Approach to Valuation

Join me on a journey to uncover a systematic, transparent, and reliable method for quantifying the value of risk and uncertainty without the need for an arbitrary “risk premium.”

In this article, I describe a much better, systematic method of valuation by adopting a first principles approach, distilling the essence of financial valuation into four fundamental building blocks, and proposing a practical, step-by-step process that shifts the focus from tweaking discount rates to truly understanding and quantifying risks within cash flows.

Gain valuable insights that will change the way you think about risk and uncertainty in financial valuation, whether you're a seasoned finance professional or an aspiring analyst.

What Do We Really Know for Sure About Financial Valuation?

Financial valuation is a critical aspect of making informed decisions about investments, projects, and businesses. The concept of a "risk premium" is often used to adjust valuations for the inherent risks in these ventures. However, is this the best approach? In this chapter, I will examine the fundamental principles of financial valuation and present an alternative perspective on incorporating risk in valuation. I will focus on the four building blocks that I believe are undeniably true and relevant.

1. Future Cash Flows

The first principle of financial valuation lies in the recognition that financial value stems from future returns, or more specifically, future cash flows. Past performance, such as the previous 10 years or the last quarter's results, does not guarantee future value. Therefore, it is essential to focus on estimating future cash flows rather than relying on historical financial figures. To do this, one must have a deep understanding of the business model or the mechanics behind the numbers.

2. Time Value of Money

The second principle is the time value of money. The concept states that the longer we have to wait for an amount of money, the less it is worth to us in the present. Discounting future cash flows is a technique used to translate the timing information into a single present value. However, it should not be used to translate risk information into value.

3. Consideration of Risk

Risk is the third fundamental principle in financial valuation. The riskier an investment or project, the less an investor would be willing to pay for it. In essence, the more uncertain a cash flow is, the less it is worth. While risk matters in valuation, the challenge lies in accurately translating riskiness into value.

4. Valuation of Uncertainty

The fourth principle is the valuation of uncertainty, a concept developed in finance through the Binomial Option Pricing Model. This model, also known as the Cox-Ross-Rubinstein Model, was first proposed by William Sharpe in 1978 and formalized by Cox, Ross, and Rubinstein in 1979. The basic idea of an option is to eliminate the downside risk while retaining the potential for upside gains. This can be seen as an insurance policy that protects against negative values below a certain threshold.

The question then becomes: How much would one have to pay for this option? The value of this "riskiness" determines how much less than the expected value should an investor be willing to pay if they have to bear the risks themselves.

Where to Account for Risk? Discount Rate or Cash Flows?

When it comes to financial valuation, a commonly debated topic is whether risk should be accounted for in the discount rate or in the cash flows themselves. This chapter will explore the rationale behind each approach and argue for incorporating risk directly into the cash flows rather than using a risk premium in the discount rate.

The Appeal of the Risk Premium

The primary reason why it is so tempting to use a risk premium for valuation is its simplicity. Adding a risk premium to the discount rate does achieve the desired effect: the higher the discount rate, the lower the present value. However, determining the appropriate risk premium is a significant challenge. It is often difficult to justify the chosen risk premium, and the process can become more akin to astrology than astronomy.

Changing Perspectives: Geocentric vs Heliocentric Approach

To shift our perspective on accounting for risk, consider the analogy of the geocentric versus the heliocentric models of the solar system. At first glance, it may seem intuitive to assume that the sun revolves around the Earth, given our observations from the ground. However, this theory is limited and leads to a more complex and less accurate understanding of celestial mechanics.

In the same way, using a risk premium on top of the discount rate may provide a simple method of accounting for risk, but it lacks accuracy and can lead to arbitrary decision-making. Instead, adopting a more systematic approach would involve accounting for risks and uncertainties in the cash flows themselves. This is akin to recognizing that the Earth revolves around the sun, providing a more accurate and comprehensive understanding of our solar system.

Incorporating Risk into Cash Flows

By incorporating risk directly into the cash flows, we can develop a more accurate and systematic valuation methodology. This approach involves analyzing the potential risks and uncertainties associated with each cash flow and simulating the projected amounts accordingly. This method is more consistent with the fundamental principles of financial valuation discussed in the previous chapter, as it only builds on future cash flows, the time value of money, the consideration of risk, and the valuation of uncertainty.

The Missing Piece: How to Determine the Value of Risk?

The challenge of determining the appropriate — in fact, negative — value of risk for uncertain cash flows can be addressed by taking a different approach: instead of adding layers of complexity, use a single, risk-free benchmark rate and incorporate risk information directly into cash flows. This method is simple, clear, and elegant.

The way to achieve this is by discounting every single scenario generated through Monte Carlo simulations, resulting in a distribution of Net Present Values (NPVs) that reflects the potential range and probability of outcomes. While this distribution provides a better understanding of inherent risks, determining the fair value of the asset remains an issue.

Option Pricing Theory to the Rescue

Option pricing theory offers a solution. The fair value of a set of uncertain cash flows is the price one would pay for insurance or an option that covers shortfalls below the average value. This "insurance" price can be calculated using the weighted average of all cases where the NPV falls below the average.

The Binomial Options Pricing Model (BOPM) or Cox-Ross-Rubinstein model, which uses a binomial tree with discrete time steps and price movements, can be employed for this purpose. However, the BOPM has various restrictions that make it difficult to apply in real-life situations. Instead, a Monte Carlo simulation that follows the principles of option pricing theory, without the limitations of the BOPM, can be used.

A Short Recap: How Does BOPM Work Again…?

The Binomial Option Pricing Model (BOPM) is a widely used numerical method for valuing options, which are financial instruments that give the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a specific date. The BOPM was first proposed by William Sharpe in 1978 and later formalized by John Cox, Stephen Ross, and Mark Rubinstein in 1979.

BOPM works by dividing the time to expiration of the option into discrete intervals or steps and constructing a binomial tree (or lattice) to represent the possible price movements of the underlying asset. At each node of the tree, the asset price can either move up or down by a specific amount, with corresponding probabilities. The model then calculates the value of the option at each node, starting at the final time step (at expiration) and working backward through the tree.

At the final time step, the option's intrinsic value is calculated by comparing the underlying asset's price with the option's strike price. Moving backward through the tree, the option's value at each node is determined by taking the weighted average of the option's value in the subsequent nodes, factoring in the risk-free interest rate and the probabilities of the price movements.

Applying it in Real Life

The Binomial Option Pricing Model, however, has certain limitations and assumptions that may not be applicable to all real-life situations. This is where Monte Carlo simulation comes into play. Monte Carlo simulation is a powerful, flexible technique that can be used to model complex, uncertain systems by simulating random variables and generating a large number of scenarios.

By using Monte Carlo simulation, we can overcome the limitations of the BOPM and apply option pricing theory to a wider range of scenarios without the underlying restrictions. Monte Carlo simulation generates numerous possible price paths for the underlying asset, incorporating various sources of uncertainty and risk. The option's value can then be calculated for each simulated price path, and the results can be aggregated to determine the option's fair value.

Monte Carlo simulation equivalent to Binomial Option Pricing Model

In summary, valuing uncertainty involves using Monte Carlo simulations to discount potential future scenarios, considering option pricing theory to determine the fair value of uncertain cash flows, and focusing on incorporating risk information directly into the cash flows. This systematic approach provides a more accurate, transparent, and reliable method for valuing risk in businesses, projects, and investments.

Turning Risk into Value — A Practical Approach

In the previous chapters, I established the importance of incorporating risk directly into cash flows rather than using a risk premium in the discount rate. I also demonstrated how proven option pricing theory can be used to determine the (negative) value of risk within the cash flows.

In this chapter, I will provide a practical approach to incorporating risk into financial valuation, detailing its essential components and outlining the steps required to implement it in financial modeling.

Three Essential Ingredients

Let's first understand the three essential ingredients for this valuation approach:

1. A driver-based planning model: This model is based on the underlying business logic and the key factors driving financial performance. By constructing a model based on the relationships between these drivers, analysts can create financial statements that reflect the potential consequences of various strategic choices and external factors.
2. Monte Carlo simulation: To account for the inherent uncertainties in future outcomes, Monte Carlo simulations employ probability distributions instead of single-point estimates. These simulations generate a wide range of possible scenarios based on the probability distributions of each uncertain variable, providing a more detailed understanding of the potential outcomes and their likelihood.
3. Valuation without discount rate adjustments: Once all risks and uncertainties are incorporated into the model, there is no need for an arbitrary "risk premium" to be added to the discount rate. Instead, a risk-free rate can be used to discount cash flows, focusing on modeling the actual risks and uncertainties within the cash flows themselves and using proven techniques to quantify the value of uncertainty.

I also like to describe these 3 elements in this way:

1. Capturing what we know: We need a driver-based model that focuses on the business logic behind the financial numbers.
2. Addressing what we don't know: Our planning models should use the full range of possible values, rather than relying on single-point estimates.
3. Determining what we would pay for it: Use a risk-free rate as the discount rate and leverage Options Pricing Theory to calculate a single fair value.

8 Easy Steps…

Once we have these three elements, we can follow this simple recipe:

1. Model the effects of everything that influences future cash flows, including factors like market conditions, competition, and regulatory changes. This comprehensive approach will help you identify the key drivers of value and the relationships between them.
2. Represent every risk and uncertainty in the model as probability distributions. This step involves gathering data on historical trends, market research, expert opinions, and other relevant sources to define the range of possible values for each uncertain variable.
3. Run a Monte Carlo simulation to generate (almost) all possible scenarios. By simulating thousands of scenarios, you can obtain a clearer understanding of the potential outcomes and their probabilities.
4. Calculate the Net Present Value (NPV) of future cash flows for each scenario using a risk-free rate. This step helps you estimate the value of each possible future without introducing additional risk through the discount rate.
5. Calculate the average NPV over all scenarios (i.e., the expected NPV or eNPV). This value represents the average of all possible outcomes, weighted by their likelihood.
6. Take the difference between each NPV and eNPV if negative, otherwise zero. This step isolates the downside risk or potential losses associated with each scenario.
7. Calculate the average of (6) over all scenarios (i.e., the "negative value of risk"). This value represents the average downside risk or potential loss across all scenarios.
8. Subtract (7) from (5) to get a risk-adjusted NPV. This final value accounts for both the expected value and the downside risk of your investment, providing a more accurate estimate of its true worth.

To Wrap it up…

In this article, I present a systematic, transparent, and reliable method for quantifying risk and uncertainty in financial valuation. I propose a first principles approach, breaking down financial valuation into four fundamental building blocks and offering a practical method that shifts focus from tweaking discount rates to understanding and quantifying risks within cash flows.

My reasoning starts with the four fundamental, undeniable principles of financial valuation: Future Cash Flows, Time Value of Money, Consideration of Risk, and Valuation of Uncertainty. I discuss the debate between accounting for risk in the discount rate or cash flows and advocate for incorporating risk directly into the cash flows for a more accurate, objective valuation.

I then outline a practical approach to incorporating risk into financial valuation using three essential ingredients: a driver-based planning model, Monte Carlo simulation, and valuation without discount rate adjustments but based on proven option valuation theory. I finally provide a universal valuation approach with 8 easy steps to calculate a risk-adjusted Net Present Value (NPV), which offers a more accurate estimate of an investment's true worth.

In conclusion, this systematic approach provides a more comprehensive method of dealing with risk by incorporating everything we know and believe about risk into the cash flow model. By analyzing the full distribution of potential value, decision-makers can better understand the potential variations and downside risks associated with each alternative, leading to more informed and well-rounded decision-making.