As a mathematician, I am still surprised when I discover an economic concept that originally seemed “fixed in reality”, is actually dynamically defined by people. One such example is the idea of value. At first glance, money may appear to be a neutral and unbiased metric, considering people’s reliance on it to weigh various daily decisions. However, its true value hinges on the willingness of others to trade for it, suggesting a changing nature.
➰Value of X The highest price that someone is willing to pay for X, usually expressed as a monetary value. This price depends on the people involved and their current context.
The concept of an equivalent exchange is essential to the concept of value. If you were willing to pay one dollar for a cup of coffee, it implies that you value it more than keeping that dollar for yourself. Conversely, if you refuse to pay two dollars, you can infer that, given your current context, its value falls somewhere between one and two dollars. However, value is not static; it can fluctuate. After spending an hour staring at a screen projection in your third meeting of the day, you may be willing to pay four dollars for the same mug.
In the realm of business, choosing between options typically involves evaluating their worth from the organization’s point of view. You want to invest in projects that are the most profitable from the organization’s point of view. If you could accurately evaluate the value of alternatives, making these kinds of decisions would be a breeze!
Beyond the typical uncertainty surrounding choices, there are two obstacles to correctly valuing alternatives:
How can you quantify more intangible concepts, such as “performance”?
How do organizations communicate and implement a consistent value framework throughout the organization?
This week I’ll present a tool that can address both challenges, give some examples, and discuss how it makes decision-making easier.
Building value frameworks
To determine the value of something, one can use their instinct while considering factors such as recent expenses, personal finances, and how much you want something in that moment. While informal, this method focuses on what matters most to you. For larger purchases, you might start applying a more structured approach, but the focus remains on what you value.
When applying this approach to your organization, it can be challenging to adopt the business’s perspective, rather than your own. Many managers have the power to make resource allocation decisions, but few understand exactly how the business values any specific amount of money, its value framework. Therefore, communicating this framework to employees is crucial for executives.
Returning to the definition of value, you can define the business’s value framework by clarifying what constitutes an equivalent exchange between two aspects of the business. Most of the time, the main aspect of interest will be the resources to be invested. A good value framework will put an aspect’s value in relation to another and act as a conversion mechanism between the two.
Other possible aspects include quality, promptness, innovation, work-life balance, performance, reliability and anything else that the business values. The following subsections show some examples of a good tool to achieve those equivalent exchanges.
Risk-reward map
Last week, I mentioned that different alternatives can have different risk profiles. To make an informed choice, it’s crucial to take into account the organization’s risk tolerance. One straightforward approach to represent this is a map of indifference.
The map charts the expected rates of return of an investment for a given level of risk. To illustrate, suppose your firm will only consider an investment with a 20% probability of a loss if its expected return is above 40%. That threshold is then plotted on the map and represents the upper limit beyond which investments with a 20% likelihood of a negative return are admissible for the company. The organization should not invest in any project that falls below that threshold.
Here’s how you can build a map of indifference for your business:
Determine the investment size. Since the organization’s risk tolerance varies with the investment amount, you must construct a map for each of the various typical size of investment for your organization.
Choose a definition of risk. Interesting risk definitions include the possibility of losing the entire investment, the probability of earning a negative return (as used in the subsequent example), or the probability of earning less than the organization’s hurdle rate. This will be the first aspect of the map of indifference.
Identify the threshold of indifference. Using the next figure as an example, ask yourself (and possibly other decision-makers) if the organization is willing to make an investment that has a 20% chance of a negative return if the expected return is 60%.
In this case, the organization would, so lower the return to 20% and ask yourself the same question again.
At 20%, the business feels like this would be too risky, so raise your estimate.
Eventually, going back and forth below and above the right value, you’ll approach the correct threshold value, here 35%. It is the lowest point at which the investment would still be considered viable.
Sample more threshold values. Repeat step 2 for different probabilities of a negative return. This results in samples of the curve of indifference.
Draw the curve. Interpolate the points sampled.
A mapping of the impact of the probability of a negative return to the expected return needed to fund a project. Each point represents a threshold value defined in step 2 and 3. The line that interpolates the thresholds is drawn in step 4 and called the curve of indifference.
➰Curve of indifference The curve that interpolates points between the two aspects of the business as represented in a map of indifference. An organization presented with two investments on this curve would be indifferent to choosing one over the other, valuing them equally.
In the end, you will have a clear curve that separates investments that you would make from those you wouldn’t, based on their level of risk. This will be an effective way of conveying your risk tolerance to other business leaders.
When making a decision, you can also use this map to visually plot decision alternatives, and assess which alternatives have the most favourable risk-reward trade-off for your business. The best admissible alternative would be the one that maximizes the distance to the curve.
A map of indifference with three alternatives under consideration. Alternative A sits just above the threshold of admissible alternatives, while B is well below. Alternative C is the clear winner due to its distance from the curve.
Performance-freshness map
Maps of indifference are also useful when comparing two different aspects of a business where there are no simple conversion methods. For example, when reading from a distributed database, software developers must balance freshness (how up-to-date the queried data is) with the speed (how quickly users can get an answer) afforded by caching data from the database, for quicker retrieval if the data is needed again.
Suppose you are supporting a web service that serves important data to users. When requesting data, users expect to get their data quickly (referred to as the query’s performance) and to have access to the most up-to-date data (referred to as the data’s freshness).
It follows that users wouldn’t appreciate waiting for a data centre that is currently down (as it could be hours before the connection is reestablished) to ensure they can access the freshest information. However, they wouldn’t tolerate reading business-critical data that is too outdated either.
Between those extremes, where subtleties are more challenging to articulate, a map of indifference can be a valuable tool to evaluate and communicate how the organization thinks of this balance.
To create this map, imagine having a magic wand that can instantly increase performance, measured in milliseconds (ms) of reduced latency, while reducing freshness, measured by what percentage of the retrieved information is out of date (% stale reads). How much freshness would you be willing to sacrifice to reduce latency by 50 ms, or 100 ms, or 200 ms? You can use the same steps outlined in the previous section to create this map as well.
An example of a map of indifference that relates performance and freshness of data.
Points along the curve of indifference should be equally valuable to you. If you were willing to expend valuable resources to move from one point to another on the curve, then you are not truly indifferent about where you are on the curve. If you’re willing to pay to move along the curve, then by definition, the new point holds greater value than the original one for you.
To achieve a more precise depiction of value, a typical enhancement is to display more than one curve at once on the map.
Map of indifference with multiple curves of indifference. The darker line is unchanged and represents indifference between various trade-offs. The paler lines also denote indifference; however, scenarios on each of them are considered more valuable than the ones on the line below them. The greater the distance to the dark line, the more valuable a scenario is considered.
These curves will each represent a different exchange, between any two aspects of the business, that would be considered equivalent. These other curves can take on a variety of shapes, and together can define something resembling a topographical map of your organization’s value framework.
Indifference transitivity
Suppose your sales team has carried out a survey reporting on customers who stopped using the product due to issues with the freshness of the data provided by your web service. By analyzing the responses to the survey, you can create an indifference curve linking revenue to data freshness.
Maps that include financial information are especially useful. In this case, the map would help you choose a justifiable amount to invest in reducing data staleness to reduce loss of revenue.
The majority of corporate choices revolve around finances. For productive comparisons, strive to construct maps of indifference with a dedicated axis for your financial investment, whenever feasible.
Another reason for this is that maps of indifference have an interesting and important property: they are transitive. This property lets you link two maps and associate concepts without requiring a direct relationship. For example, if there is a mapping from performance to freshness and another one from freshness to revenue, you can combine them to create a new map from performance to revenue.
Indeed, this is an excellent way to review your curves of indifference. If you have a strong conviction that a transitive mapping does not align with how the company values trade-offs between the two dimensions, then it’s likely that at least one component of the transitive relationship is incorrect. This could also indicate that the organization does not consistently carry out its value assessments across all aspects of the business.
Certain monetary equivalence
Now that you have a tool to convert the value assessment of different aspects of the business, I’d like to share with you a useful target for these conversions: certain monetary equivalence.
➰Certain monetary equivalence The guaranteed cash value that someone would accept now rather than taking a chance on a greater and riskier return in the future.
It is a useful common denominator that can be used to convert between all aspects of the business:
Investments, using net present value: “Would you prefer $110 in one year, or $100 today?”
Risks, using prospect theory or maps of indifference: “Would you prefer a 70% chance of receiving $1000, or a 100% chance of receiving $600?”
Aspects of the business, using maps of indifference: “Would you prefer a 1% decrease in stale reads, or a $50,000 cash infusion?”
Modelling a decision by assigning a monetary value to its various factors allows you to quantify the trade-offs between competing alternatives and, even more excitingly, between competing objectives.
In fact, having such an explicit representation of equivalent exchanges could lead you to re-evaluate the importance of certain business aspects, and potentially align them more closely with your organization’s mission and values.
How does your company convey its tolerance for risk? If you have decision-making authority, how would a map of indifference help you allocate resources? I would appreciate it if you could share your thoughts in the comment section.
I’ll see you again next week!
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