Article

Risk-Adjusted Returns, Expected Value & Media Buying

by Sam Tomlinson

February 12, 2024

Over the last few weeks, I’ve shared strategic & tactical frameworks on audits, account structures, creative and landers. In many of those cases, I’ve referenced the concept of a risk-adjusted returns – a concept that had more than a few subscribers emailing with questions. 

The result? This issue is all about the ways that the concept of risk-adjusted returns manifests itself in marketing – and how you can put that concept to work in order to make smarter, more profitable decisions for your agency, clients and/or brands. 

Let’s dive in. 

ROI, Risk-Adjusted Returns, Oh My! 

Most marketers are (at least) somewhat familiar with the concept of return on investment “ROI” – after all, the letters “ROI” are smattered across just about every agency website or marketer resume in some form. 

From a financial perspective, ROI is a simple calculation: 

(([Current Value of Investment] – [Initial Cost of Investment]) / [Initial Cost of Investment]) *100%

The result of the above calculation is a percentage return, exactly like what you see on a stock trading platform, Zillow or a betting app: +16% or -24% or +192%. This indicates the overall return on the initial investment: either the investment increased in value (positive) or declined in value (negative). Simple. Easy. Readily-intelligible to just about everyone. 

This simple calculation gets more complex when applied to marketing: unlike with stocks, houses or bets, the current value of the investment is never clear, tangible or liquid (you can’t sell a customer or brand awareness), nor is the cost (is that ad spend, or ad spend + fees, or ad spend + fees + tech, or something else?). Nevertheless, many marketers insist on performing this calculation using the largest-defensible number for the Current Value (usually attributed Revenue) and the smallest-defensible number for the Initial Cost (usually ad spend) – and proudly smack the result on a report or case study. Result: HUGE ROI. 

While just about everything is wrong with the above exercise in financial malpractice, I want to focus on a crucial, oft-overlooked aspect: not all marketing efforts are equal, even if the ROI number is identical. Why? Some carry significantly more risk than others. Some are significantly more volatile than others. 

This is where Risk-Adjusted Returns come in. 

Risk-Adjusted Returns adjust investment performance (or, in our case, marketing performance) for the level and type of risks incurred to produce that return. In finance, there are multiple ways to do this, with the most common being the Sharpe Ratio and the Treynor Ratio.

Without getting into the specifics (and a somewhat lengthy finance lesson), here’s the gist and how this is applicable to advertisers:

The Sharpe Ratio calculates two things: (a) in the numerator, the difference in return between the investment and the risk-free rate of return; (b) in the denominator, the standard deviation of returns over the same period of time. 

The Treynor Ratio functions in much the same way as the Sharpe Ratio, except that the denominator uses a beta coefficient – a measure of the sensitivity of the investment in the market (i.e. riskiness). 

While we don’t have these exact metrics in advertising (yet!, the underlying concepts are incredibly valuable and can be used to create similar ratios for advertising performance. 

Translating Finance To Advertising

There are four core concepts mentioned above, each of which has an approximate corollary in advertising: 

Concept #1: Investment Return = I have an unpopular opinion here (we’re all surprised): marketing ROI should be calculated as follows: 

Incremental Contribution Dollars Above Baseline] + [Net Present Unrealized Contribution Dollars of Customers Acquired Above Baseline – [Total Cost Of Initiative] / [Total Cost Of Initiative]

[Incremental Contribution Dollars Above Baseline] = this is the incremental return produced by the initiative, in excess of what the brand would have received if nothing was done. 

[Net Present Unrealized Contribution Dollars of Customers Acquired Above Baseline] = one of the challenges with marketing is that customers spend over time; in fact, a hallmark of a great brand is the ability to drive repeat purchases or recurring revenue (in the case of SaaS). A fair return calculation should factor in expected (thus, unrealized) future contribution dollars, discounted back to present value. The discount adjusts for both the time-value of money and the inherent risk present in a future cashflow (i.e. the customer might churn, or might pass away, or might move out of your service area). 

[Total Cost Of Initiative] = It drives me bonkers when agencies consider only the costs of advertising in their calculations; doing so isn’t legitimate. Instead, we need to consider the full set of costs incurred for this initiative – ad costs, agency/freelancer fees, tech costs, etc. Everything incremental that was spent on the initiative during the time period must be considered. 

Basically: the return on a marketing investment should consider ONLY the incremental return produced (i.e. the reasonable return in excess of what the brand would have received if nothing was done) PLUS the net-present unrealized LTV of incremental customers acquired, and it should factor in all the costs associated with the initiative – not just ad spend, but agency fees, tech costs, etc. 

Concept #2: Risk-Free Return = Baseline Performance  = any initiative performance should not just be measured against doing nothing, but also against the performance of a known, mature channel (usually Meta or Google). 

Concept #3: Standard Deviation of Return  = This one is about as straightforward as it gets, if you have the above performance metrics and a basic knowledge of excel (or the ability to use GEMINI or ChatGPT), you can calculate a standard deviation of return. 

Concept #4: Beta Coefficient / Riskiness = Finally, there’s the Beta Coefficient. In finance, this is the Covariance of the Investment + the Market, divided by the Variance of the Market. In advertising, we can do the same thing using the return of the individual platform and the return of either (a) the advertiser’s full marketing mix OR (b) a core platform. 

These are certainly not hard-and-fast definitions (and this is very much a work-in-progress evolution), but using them unlocks new ways to view your marketing investments, which (in turn) leads to new ways to allocate your marketing capital. 

One of the core outputs of this way of thinking is that it reinforces the financial benefits to scaling core platforms vs. diversifying away from them, especially at low levels of spend (less than $50k – $100k USD per month). The reasons are simple – larger platforms (like Google, Amazon & Meta) are far less volatile and far less risky than smaller platforms (like Pinterest, LinkedIn, Criteo, etc.); when you adjust your returns from each platform for that risk + volatility, larger platforms look comparatively better, even if the top-line return numbers are comparable. 

From a marketing perspective, this may seem crazy, complex and new; but I don’t think it’s any of those things. We have most of the data required to compute the above metrics; we just need to put it together in the right way. 

When you do, the result is a different way to look at your ad spend, platform investments and priorities that considers things like volume, variability, volatility and expected returns – all of which allow you (the savvy business owner, media buyer, whatever) to make better, smarter and more profitable decisions.

Thinking In Bets + Maximizing Expected Returns

My ultimate aim in pushing marketers to explore how financial concepts can be applied to marketing is simple: I want marketers to make smarter, more financially-informed decisions. 

Part of that is getting better data from which to make marketing investment decisions – that’s what risk-adjusted returns are all about. It’s a different, more robust data point that can inform how we allocate dollars and assess performance. It isn’t the be-all, end-all. But it is a step in the right direction. 

The other part of that is thinking in bets – a phrase borrowed from former decision-theorist-turned-pro-poker-player Annie Duke. 

Duke’s primary contention – and something I couldn’t agree with more – is that most choices we make are decisions under uncertainty. They are bets. Whether that decision happens in the context of a hand of poker or setting a daily budget on Meta or deciding how much to spend on YouTube is not relevant. What is relevant is the uncertainty and the risk inherent in making any of those decisions. 

Adjusting our returns for the risk we assumed is one step in making smarter decisions. Learning to think in bets and potential outcomes is a second step in the same direction. 

In finance, economics and mathematics, expected returns are defined as the sum of the products of potential returns * the probability of each potential return. That may sound complicated in theory, but in practice it’s quite simple:

Assume we have a Meta advertising initiative. There’s a 10% chance that we spend $10,000, receive zero sales, and are out the entire $10,000 in ad spend (total loss). There’s a 20% chance we spend $10,000 and break even (such that the net revenue less COGS and less costs of service/delivery equals the marketing investment). There’s a 50% chance that we spend $10,000 and receive $15,000 in contribution dollars, and there’s a 20% chance that we spend $10,000 and receive $25,000 in contribution dollars. I can summarize that as follows: 

Scenario #1:

The expected value of this Meta advertising initiative is $11,500 in contribution dollars, defined as revenues less all variable costs of revenues (COGS, Cost of Delivery, Transaction Costs, etc.) less advertising expenses. 

Objectively, that’s pretty excellent – most people would be delighted if they invested $10k and made an additional $11.5k in expected profit. But, there’s risk here: 30% of the time, the investment is a total loss or a break-even. Acknowledging the inherent uncertainty of how a given campaign will (or will not) perform is essential in making better, more informed decisions. 

What about boom-or-bust situations, like the below: 

Scenario #2: 

In this case, the expected return is actually higher than the first situation – but look at the underlying distribution: a 75% chance of either a total loss, or a break-even, with only a 10% chance of a 10x return. This is a venture-fund like return distribution – which is fine, if that’s your business. But, from an advertising perspective, the risk-adjusted return of this scenario is significantly inferior to the risk-adjusted return of the first scenario, even though the total expected return here is higher. 

The only way that it makes sense to pursue Scenario #2 is if the budget  is sufficiently large to run this many times over – and lose many times over – because that’s what’s likely to happen. Over the long run, the expected value is positive – but in the short-run, it’s very likely that you’ll post $50,000 – $100,000 in losses before hitting a few home runs. And if you (or your client) can’t stomach that, then you need to find an alternative strategy with a more favorable return distribution. 

This process goes against what so many marketing agencies have trumpeted forever – that we “know” something – a creative, a campaign, a platform, a tactic, whatever – is going to work for a given client. At best, we believe the recommended course of action maximizes the probability of achieving the outcome. At worst, we’re throwing darts in the dark. 

Is It Better To Be Lucky or Good? 

That only gets worse when we fail to differentiate between the impacts of luck (good or bad) vs. the impacts of our skill – another thing marketers are notoriously terrible at doing. 

Like it or not, luck plays an outsized role in most marketing performance – whether that takes the form of a TikTok showing a Stanley Cup still has ice in it after a car fire, or a competitor making a terrible decision resulting in a flood of new customers (like Kyte Baby customers flocking to Mori and others), or leads converting (or not converting) at abnormally high/low rates due to external factors, macroeconomic factors, etc. That’s all luck (at least, let’s hope that wasn’t planned in the case of the Stanley Cup video).

There’s nothing more frustrating than executing something as well as possible, only for bad luck to tank the results. As a concrete example of that, I recently reviewed a lead generation account where everything in December looked legitimately excellent – low cost per lead,  high conversion rates, high lead qualification rates, high MQL-to-SQL conversion rates – except for actual signed deals. For some reason, that number was through-the-floor-low. The client thought the freelancer/agency was to blame – after all, we’re in a results business. 

They asked for my opinion. I disagreed. In this case (and if you’ve read this for awhile, you know I’m not averse AT ALL to criticizing agencies/freelancers), nothing could have been farther from the truth. In fact, the very next month (January), the brand went on to have a record-shattering month. Not good. Not great. Record-shattering. 30% above anything ever in the history of the brand.

What happened? Did the freelancer/agency suddenly get good at their job? Did they engineer some miraculous turnaround with a killer strategy? No and no. In looking at the change history, there were no deviations in management, strategy or approach. There was no “big fix” that turned around the account. What happened was a reversion to the mean in SQL-to-Signed rate. That’s it. 

Conversely, was the freelancer/agency the world’s greatest PPCer now? Also, probably not. In fact, there’s a compelling argument to be made that they were always exceptional, at least in the course of their management of this account. 

The simple-but-difficult-to-accept reality is this: the underlying process in this account was excellent the entire time. The results were skewed by volatility in a single, critical metric (SQL-to-Signed rate), which is almost entirely outside the control of the agency/freelancer. In this case, the brand was unlucky in December, lucky in January, and “above average” over the 62 total days. 

It’d be easy for a brand to look at December’s end results (few signed contracts) and say it was the agency/freelancer’s fault. That would be short-sighted, stupid and wrong. 

Luck plays a disproportionate role in marketing outcomes – more than many of us would like to admit (myself included, sometimes). Yes, it’s true that well-considered strategy, brilliant execution and the like can increase your “lucky surface area” – but that’s all it’s doing. It’s increasing the odds that you’ll be able to capitalize on a fortunate externality. And that has real, tangible value – but it doesn’t have all the value. 

Most outcomes are part luck and part skill. That’s why I’m such a proponent of this way of thinking: it forces us to be intellectually honest with ourselves about what actually transpired. It forces us to think about what else could have happened. And it forces us to make decisions that increase our luck surface area. 

How Does This Impact Ad Platforms?

If media buyers often struggle to think probabilistically, doing so is the default setting of modern ad platforms. Any “smart” or “machine learning driven” bid strategy is a probabilistic engine first and foremost. 

This is why I’m such a proponent of using Cost Caps / Bid Caps / tCPA / tROAS strategies – because doing so forces the platform to think in the same way I do, and make bets in a way that aligns with how I (and my client) are thinking. The act of setting a target – whether it’s a cost cap, bid cap, tCPA, tROAS – is implicit instructions to the ad platform to make a series of bets with an expected value defined by the target. 

For instance, if I set a tCPA for a qualified lead at $1,000, I’m telling Google to bid in any auction that complies with my target parameters where the expected value (remember that from above?) is equal to or greater than $1,000. 

Thus, if the bid required to show my ad is $90, then Google must project that the expected conversion rate for that user and that query is >= 9.0%. Any expected conversion rate less than 9.0%, or any bid above $90, will result in the expected value of bidding in that auction being less than $1,000, and thus, the bet should not be placed. 

In this particular case, an 11.1% conversion rate isn’t out of the norm – it is a tad higher than the brand’s mean (~8.7%), but well within a standard deviation of that mean (5.7% to 12.2%). The risk-adjusted return is solid, and, quantitative, there’s nothing wrong with Google making that bet. 

Going one step further, as a media buyer, you should be a-OK with this all day – the expected conversion rate is reasonable, the bid is appropriate, and, over the long-run, bidding $90 on these searches is likely to result in a cost per qualified lead of ~$1,000 +/- $50. Go team.  

But what about cases where Google/Meta makes riskier bets? 

Let’s continue with the same example from above: a client with a $1,000 cost per qualified lead target. But, in this case, Google places a $472.00 bid – which implies an expected conversion rate of ~47%. That’s 3+ standard deviations above the mean for this brand. Statistically, there’s a 1-in-1,000 chance that this click will convert at or above that rate. 

Does Google know something I don’t about this user and this query? Most definitely. Is that a bet I’m willing to take? Probably not. 

Why? 

Because the risk-adjusted return of that bet is significantly lower than the risk-adjusted return of the $90.00 click. 

So what do you do about it? 

In this case, move to a portfolio bidding strategy with a Max CPC limit of ~$150.00 (for Google), or a similar bid cap on Meta. This will take those larger bets off the table, de-risking your entire ad spend + improving your risk-adjusted returns. 

The same thing is true for low-volume campaigns/platforms – sure, it’s possible that those platforms will yield some relatively low-cost leads/sales/conversions. But the probability of those platforms/campaigns yielding a consistent flow of those cost-effective leads/sales/conversions is relatively low because they are volume-limited. There just aren’t as many people on Pinterest as there are on Google. There aren’t as many auctions. There aren’t as many buyers. There aren’t as many data points from which Pinterest’s bidding algorithm can optimize. Pinterest is a more volatile market than Google. 

Yes, the total return numbers might look comparable – but (as we’ve seen), total return is often an illusion if it isn’t adjusted for risk and volatility, as well as for costs of management + costs of capital. 

When you add more platforms, you add more complexity – more time spent managing the platform, more time spent on creative, more data fracturing, etc. Likewise, when you have campaigns running on multiple platforms, it creates a capital constraint – I need to reserve a certain portion of my budget for each platform, which means I can’t spend it on another platform – even if the return on the other platform is superior (or, if I do, then I need to continually re-adjust budgets, which adds complexity). 

We can do the same exercise for campaigns, audiences, tactics, initiatives, etc. In each case, we’re focused on understanding and quantifying: 

1. The distribution of the potential outcomes from a given course of action
2. The relative probabilities of those potential outcomes occurring
3. The expected value of each outcome / each decision
4. The riskiness / volatility inherent in those outcomes
5. The role of luck in each outcome

And we’re putting rigor behind that analysis, with the goal of making better, smarter marketing investment decisions.

Capital Allocation & The Zero-Sum Nature of Investment

Fundamentally, marketing (and management/investing) is an exercise in capital allocation. Our job as marketers (or business owners, or investors) is to put our money in the places with the highest risk-adjusted expected returns. 

The reason for that is simple: every investment we make is zero-sum. 

A dollar I invest in Google is a dollar I can’t invest in Meta. A dollar I invest in Microsoft is a dollar I can’t invest in Pinterest. A dollar I spend on advertising is a dollar I can’t spend on R&D, logistics, operations or customer success. 

Everything I’ve discussed in this newsletter boils down to this simple truth: to be an excellent media buyer (or investor, or business owner), it is essential to hone your assessment and decision-making skills. That’s rarely (if ever) pleasant. 

Metrics like expected value and risk-adjusted return provide additional data points to help you make those decisions more dispassionately. And that, over the long run, is what leads to better total returns for your organization/business. 

Until Next Time,

Sam

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