Distinctions and Concepts: Risk/Reward Modeling

(This is the first in a series of posts talking about a concept/or tool for how to think about something, distinguished from most of my other posts by being (probably! I haven’t finished writing the first post!) relatively short and easily digestible, but also by being probably less meaningfully useful than, say, my Five Conditions for Improvement, or my PIP sorta-presentation. It’s meant more as a snack than as a meal)

When thinking about a decision to be made, one of the obvious things we do if we’re trying to deal with the decision rationally, is trying to understand the likely risk and likely reward of going in a certain direction. I might choose to leave my job to pursue another one, presumably because there are some benefits I’m thinking of in the new job. But there are also risks in the new job. How do I balance them? Heck, how do I actually think about the risks and rewards and visualize them?

Imagine I’ve been with my current employer for a while. I’m well-liked and respected. I’m part of a team where I understand how others work and we work well together. The company is public, stable, and successful. I’m considering moving to another company, a startup that is far less stable and not yet successful. I’m obviously not part of that team yet. My compensation is heavy on equity that may never be worth much (or may be worth a lot more than my compensation at my current employer). This is complicated!

Benefits
Each positive aspect of the new job compared to the current one — each reason I might want to take this new role — has a certain magnitude and a certain likelihood. While we may be tempted to think of magnitude and likelihood as being on a 0–100 scale, that’s probably too granular. Let’s just use 1–3 here, where 1 is low magnitude or likelihood, 2 is medium magnitude/liklihood, and 3 is high magnitude/likelihood. Of course, likelihood and magnitude are completely independent of each other. So why am I switching? Let’s put some numbers on the benefits.

I like working with a smaller team. It’s a minor benefit — call it a 1 magnitude — but of course right now that’s guaranteed to happen (this 50 person startup is smaller than the 100,000 person company I may be choosing to leave). So the likelihood of this benefit is 3. So if we think of specifing magnitude and likelihood as a tuple, it’s (1,3).

This new role is new to me, and I think it’s going to potentially open up my career to many more intersting roles in the future. The magnitude of this benefit is pretty significant — maybe 2? But the likelihood is smaller. I might just be confusing people who look at my CV because this is such a shift. I might be going into blockchain and it may just be a fad. Let’s say the likelihood of this being huge for me is a 2, so as a tuple we have (2,2)

Lastly, compensation! This could go big! This could give me retirement money! So that’s definitely a 3 on magnitude, but the odds of that are honestly somewhat low — let’s call it a 1, so we have (3,1).

So now we have three tuples — (1,3), (2,2), (3,1). Let’s put them on a graph!

Hey, that’s cool.

Let’s talk about the risks for a moment

Risks

If we think of ‘magnitude’ as signed — so ‘positive magnitude’ is a positive outcome and ‘negative magnitude’ is a negative outcome, then ….

I don’t really know what kind of leader I’m going to report to. We’ve had some chats but I’m not sure I’ve read them well. For me, that’s a particularly significant problem, because under a leader who’s bad for me I’m going to fail utterly. So the risk here is pretty high — -3 magnitude — and the likelihood is, say, 2 because I did get to chat with them. Tuple is (-3,2)

I’m taking a meaningful compensation hit. I don’t actually care that much about that, because either way I’m doing fine, money-wise, but that’s a sure thing, so … magnitude -1, likelihood 3, or (-1,3)

If we’re just dealing with these risks, and we think of ‘magnitude’ as signed — so ‘positive magnitude’ is a positive outcome and ‘negative magnitude’ is a negative outcome, we can do the same charting we did earlier for risks, and get (converting the above magnitudes to negative):

And, of course, we can combine these two graphs for a more holistic one:

OK, that’s cool.

A few things I like about modeling risk/reward this way:

1. It’s easier to distinguish low-likelihood risk/reward from higher-likelihood risk/reward;
2. It’s easier to distinguish likelihood from magnitude
3. For me, at least, graphing the decision trade-offs this way allows for some intuitive leaps. For example, if I’m at least somewhat risk-averse, I notice that while the benefits of moving forward only have a relatively lower likelihood of significant positive outcome (+3 magnitude only has a 1 likelihood), I have a significant risk (-3) with a more significant likelihood (2). That makes me pretty concerned. On the flip side, if I am not affected by loss aversion, I could simply choose to look at the area under the graph (green vs red) above and notice that for benefits I get an area of 6 while for risks I get an area of 5, so roughly speaking this decision is more likely to work out for me than not.

Examples
I want to talk more about (3) above — I find that human beings have a better intuitive understanding of tradeoffs sometimes when it’s visual, rather than numerical. Once you’ve been exposed to the above model, you can very quickly and intuitively understand what these hypothetical graphs look like:

This is probably a bad tradeoff unless you’re very fond of risk — it suggests that the most likely positive outcomes are outweighed by the most likely negative outcomes. “High risk, low reward”

This is a pretty balanced situation, where your most likely positive outcomes are not amazing, but also the most likely negative outcomes are not disasterous — “low risk, low reward”

Also balanced, but far more rewarding — or catastrophic! — situation. “High risk, high reward.”

Questions You May Be Asking

(Cribbed liberally from the feedback I got when posting the first draft of this post):
How do I use this information? “OK, so the graph for this decision is, for example, high risk, high reward (last graph above). How do I use this information?” Well, that’s sort of up to you. This isn’t really a way to lead you down the path toward a particular decision, it’s more a way to visualize the high-level balance between risk and reward (and likely kinds of risks and rewards).

What about multiple risks/rewards? “In the analysis leading to the graphs above, we only graphed at most one risk/reward factor per given magnitude. What about multiple risk/reward factors per given magnitude?” Honestly, I’m not sure what you should do, but I tend to then just break up the bars into multiple bars, one for each factor. For example, imagine a situation where you have two risks — (-3,2) and (-1,3) — but instead of three potentially positive outcomes you have four — (1,3)(1,3),(2,2),(3,1) (in plain English this means you have two very high likelihood minor benefits). You could model that this way:

And if you want to do the same ‘area’ calculations we talked about above still consider each bar to have the same width, so risk is still (-3*2 + (-1*3) (a total of 9 risk points) and reward is (1*3+1*3+2*2+3*1) (a total of 13 reward points)

Where Can I Learn More? While to the best of my knowledge I came up with this myself without any obvious source work, this is a relatively simple approach to risk where the field of risk managmeent and security assurance go much more deep into this. In risk management, the concept of a Risk Matrix is a much more full-featured approach to modeling the risk side of the graphs above.

This Isn’t Hard!

This doesn’t need to be a very significant effort — for most decisions in which I’ve used this methodology, it’s a 5 minute framework exercise — but at least for me, I’ve found this helpful. Try it — and let me know what you think.