Why Can’t You Just Give Me The Number?

Why Can’t You Just Give Me the Number? An Executive’s Guide to Using Probabilistic Thinking to Manage Risk and Make Better Decisions
by Patrick Leach

Decisions can be based on a deterministic calculation only in conditions of certainty, that is to say the input parameters are known quantities. But strategic decisions are often made in a context of uncertainty and complexity, where a definite answer is unknowable, so we must turn to probabilistic thinking.

Uncertainty. “I make the case that all value generated by business executives comes—directly or indirectly—from how they manage uncertainty. Without uncertainty, a share of a company’s stock is effectively a bond, with guaranteed future cash flows. Guaranteed bonds don’t need management. But stocks (or rather, companies issuing stock) certainly do.”

Probability. “We usually characterize uncertainties with an estimate of the range of values we believe the parameter could have, plus a probability distribution to show how likely we believe the various values in that range to be.”

“p₁₀ / p₅₀ / p₉₀ [are] the values corresponding to the 10^th, 50^th, and 90^th percentiles, respectively, of a probability distribution. Just as your child’s SAT percentile of 87 means that she did better than 87% of all the students who took the test, so the p₃₃ value of a distribution means that 33% of all the possible values lie below the given number (and, conversely, 67% lie above it).”

Risk Neutrality. “Expected Value [is] the probability-weighted sum of all possible outcomes… Risk neutrality, as the name implies, means judging each opportunity based solely on its Expected Value.”

“For example, suppose Project A has a sure NPV [net present value] of $4 million. Project B is not so certain—it has a success-case NPV of $25 million, a failure-case NPV of -$2 million, and a probability of success of 28%… Companies that consistently choose their Project Bs will out-perform those that choose their Project As in the long run.”

“However, there’s a catch to this: you have to be able to afford to lose. More than likely [72% chance], if you embark on Project B, you’re going to lose $2 million. If that’s going to break the company or put it in dire financial stress, you obviously should not consider Project B.”

“In fact, you have to be able to afford to lose numerous times. Statistics will tell you that if you launch eight independent projects, each exactly like Project B, you’ll have about a 93% chance of making money—but even that’s no guarantee. There’s still a 7% chance that at the end of your eight Project Bs, you will have lost $16 million.”

“Provided a company has the financial staying power to attempt many projects, the road to optimal performance is to evaluate projects in a risk-neutral manner.”

Risk Culture. “If the corporate culture expects success on all projects and punishes failure at this level, project managers will, of course, be strongly motivated to choose safe alternatives over uncertain ones, regardless of the relative expected values. And the company’s return to shareholders will lag behind that of a company that truly understands uncertainty and implements its risk tolerance at the appropriate level.”

Motivation. “You simply cannot expect your people to generate p₉₀ results on average. By definition, the P₉₀ is that value you expect to achieve or exceed only 10% of the time… The best motivational goals are challenging, but reachable. Put people in a position where they fail significantly more often than they succeed, and productivity tends to drop.”

“There is evidence to indicate that people are most highly motivated to attain a goal which they have roughly a 50/50 chance of achieving. Set the goal at, say the p₂₀ (too easy), there’s no challenge to it. Set it at the p₉₀ (too hard), and people won’t even try… Thus, the case for the median—the p₅₀—as a production target is based on the notion that this goal will provide maximum motivation for team members.”

Portfolio Management.  “The company’s tolerance for uncertainty and risk should be implemented at the corporate portfolio level, not at the individual project level (or even the individual business unit level). Failure to do this—choosing ‘safe’ projects with lower EVs because the company is unwilling to accept a significant probability of failure on any individual project—is a recipe for under performance at the corporate level.” This is analogous to how venture capital funds operate.

“Risk neutrality at the project level leads to optimal returns at the portfolio level.”

“In general, we have a number of assets and projects under management, and we’re interested in maximizing the return on the group as a whole. This is portfolio management… This is what value generation is all about: delivering consistent value to shareholders by investing in high-EV projects or assets.”

“Just remember: for very highly skewed distributions, the ‘statistically significant number’ might prove to be very large, indeed. If one new drug out of a hundred makes a billion dollars for the company, and forty-nine of a hundred just break even, and fifty out of a hundred lose $5 million, the EV of each drug of this type is $7.5 million. Very nice, indeed. But how many of these drugs do you need to have in your portfolio in order to be, say, 60% sure that you’ll break even at the very least? As it ends up, you’d better have at least 92 such potential blockbusters in the pipeline. If you want 80% confidence, the number jumps to 161… If you can’t afford to lose money for a very long time, playing statistical roulette like this is a dangerous way to live.”

Value of Information. “Many mangers mistakenly believe that more information is always better…. This is not always the case; sometimes you’re better off making the decision now, despite the uncertainty.” The author quotes Henry Clay: “Statistics are no substitute for judgment.”

“If you’ve already decided what to do, if there is no way that you’re going to change your mind, don’t waste time and money acquiring more information… Analysis of any kind only has value if the decision maker will seriously consider multiple alternatives.”

Conservatism. “You will sometimes hear people advocate conservatism when assessing projects or assets. Estimate the costs high and the revenues low (just to be safe), and you’ll be fine. This is very dangerous. If you consistently underestimate the value of your projects, you will lose out to competitors who (accurately) see greater value and are willing to pay more. Your capital expenses will stay low, but your revenue stream will slowly dissipate. You’ll put yourself out of business, slowly but surely.”

“Only by portraying upside potential and downside risk as accurately as possible can you put yourself in a position to choose optimal strategies.”

Optimization. “Optimizers can only optimize one thing at a time. Conflicting objectives are handled as requirements on certain statistics (other than the one being optimized). For example, if we wanted to maximize the mean NPV, but we also want to have no more than a 5% chance of losing money on the project, we would put a requirement in the optimization process that the p₀₅ of the output NPV curve must be greater than zero. Thus, any simulation run in which the p₀₅ NPV is negative would automatically be thrown out, regardless of how high the mean NPV might be. Problem solved: the optimization program shows you the result with the maximum mean NPV, but only considers those results that have at most a 5% chance of losing money.”

“But this creates a new problem. Suppose an opportunity were to present itself that had a 6% chance of losing money, but had twice the expected NPV of the best simulation run that met the 5% hurdle rate. Would you take it? Of course you would. Such a huge increase in expected value in exchange for such a small increase in risk is a great tradeoff. But if you’ve put a requirement into the model that the p₀₅ NPV must be greater than zero, you’re not even going to see this opportunity.”

Loss Aversion. “We’re not risk-averse; we’re loss averse, and we’ll go to absurd lengths to avoid a loss… The implication for executives and managers in business is huge… We shy away from high-potential long-shot projects that, if they work, could be company-makers. And when we find ourselves mired in a bad project that is losing money hand over fist, as long as there is some chance—however slim—of turning things around so that we don’t end up taking a loss, we’ll hang in there and fight, throwing good money after bad. Admitting that we’ve made a mistake and cutting our losses is often the hardest thing to do in business.”

Flexibility. “Develop scenarios, not a scenario, for the future. There are always multiple possible futures, some more probable than others. A good corporate strategist identifies those outcomes with the highest probability of occurrence and devises a plan that will position the firm to thrive under any of them. By planning for multiple scenarios, you enable your firm to change quickly if the world changes from one scenario to another. You can only do this if you truly understand the key uncertainties that drive value in your business.”

The author covers a number of statistical methods, including: sensitivity analysis and tornado charts, decision trees, efficient frontier to show tradeoffs between competing objectives, and stochastic scheduling for project management. Note: I read the first edition, published in 2006. The link below is for the second edition, published in 2014.

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Leach, Patrick. Why Can’t You Just Give Me the Number? An Executive’s Guide to Using Probabilistic Thinking to Manage Risk and Make Better Decisions. Gainesville, Florida: Probabilistic Publishing, 2014. Buy from Amazon.com.

Disclosure: As an Amazon Associate I earn from qualifying purchases.

Selected books mentioned:

Against the Gods: The Remarkable Story of Risk by Peter Bernstein (1998)

Business Portfolio Management by Michael Allen (1999)

Fooled by Randomness by Nassim Nicholas Taleb (2005)

Classics of Organizational Behavior Third Edition (2001) by Walter Natemayer and Timothy McMahon. Note: There is a Fourth Edition by Walter Natemeyer and Paul Hersey (2011).