5 Steps to Making Investment Decisions Like a Statistician

This is a guest post by Dale Gilliam. Dale is the CEO of Troubadour Research & Consulting.  Troubadour offers strategy consulting, analytics, and market research for startups, capital investment firms, and marketing consultancies. Dale can be found on Twitter @data_modeler and LinkedIn.

You know how in the insurance industry, actuaries crunch a lot of data to come up with probability estimations for how likely they are (and how much) to pay on a claim?  They use that to determine what your premium should be.  Have you ever wondered about how you could use some of those same principles to help in making investment decisions?  The point of this post is to show how, in 5 steps, you can do something similar.

First, I want to define an investment decision as any business decision that has some amount of money on the line.  It doesn’t necessarily have to be whether or not to invest in a company or development of a new product; it could also relate to how or how much.  For example, if you’re developing a mobile app, the decision question could be:  Do we develop the first version of the app for iOS only, Android only, or both iOS and Android?  Each option has its pros and cons but ultimately depends on the demand for the app.  If it explodes in a big way, you may wind up losing potential sales by not being on all platforms, but if demand lags for a while, you may wish you had only put resources into developing for one platform.

So the first step is:

Step 1: Create a pay-off table.

This can actually be the most time-consuming part, and it requires a fair amount of knowledge and/or knowledge-gathering.  For our purposes, our friends at Globe Runner SEO have allowed us to use them as an example.  Globe Runner SEO is a digital agency specializing in SEO, online advertising, and content marketing.

Eric at Globe Runner SEO recently contacted us about offering some insight into his latest decision: whether he should open a sales outpost in Houston or Austin.  The first six months is fraught with risk, since the salesperson hired to man the outpost may not work out and then he would need to begin the search for a replacement.  With Houston being further away, the cost of hiring the wrong person is greater since travel costs for training would be greater.  However, Houston is a bigger market, and some internet research suggests that it may be more profitable as well.

So what we need to consider are:

1)     What would it look like if the salesperson failed and needed to be replaced;

2)     What if they were a decent hire (worth keeping); and

3)     What if they turned out to be exceptional?

4)     Also, what are the chances of each of those happening?

We build a pay-off table that addresses these questions.

Payoffs

Fail

Decent

Exceptional

Austin outpost

-$30K

$20K

$70K

Houston outpost

-$35K

$20K

$100K

Probability of happening

50%

40%

10%

 

So this says that if we open an Austin outpost, a failed salesperson would cost the company a net of $30K, but if she turned out to be exceptional, would net the company a $70K profit by the time six months is up.  Further, there is a 50/50 chance that the salesperson (in either location) works out, but 4 out of 5 times the salesperson will simply be acceptable.

Step 2: Optimistic and Conservative Choices 

The first step in analysis is simply looking at the best and worst case scenario.  If we’re feeling optimistic or feeling aggressive in the investment decision then Houston is the better choice, since it earns the most at the top end.  If we’re more pessimistic or conservative, Austin is the better choice since it minimizes the potential for loss.

This step in analysis may seem very obvious, and it is, but I’ve run decision analyses before where the same option was recommended regardless of how risk averse you were feeling.  That kind of result serves to remind us that sometimes investments seem like they can be good, but running a few numbers clearly shows that you should invest elsewhere.

Step 3: Minimize Any Regrets You Could Have

Step 2 didn’t produce a clear winner, so we’ll apply another criterion: regret.  In this case, we want to minimize the amount of regret we could possibly have.  So let’s say we hire someone in Austin that turns out to be exceptional; we might say “Oh, if only we’d hired in Houston we would have made another $30K!”

Regrets

Fail

Decent

Exceptional

Austin outpost

$0

$0

$30K

Houston outpost

$5K

$0

$0

 

What does this decision criterion tell us?  It suggests Houston would be a better decision since we would only regret $5K if the salesperson didn’t work out, but in Austin there’s a chance we would regret $30K.

So far, Houston 2 – Austin 1.

Step 4: Determine the Expected Value

Now is when we start to feel like an actuary or Vegas statistician.  We assigned some probabilities to each state of nature – the thing we ultimately can’t control.  The expected value is calculated by multiplying each payoff by the probability and then summing it up for that row.

Expected Value

Fail

Decent

Exceptional

Calculation

EV

Austin outpost

-$30K

$20K

$70K

-30*.5+20*.4+70*.1=

$0

Houston outpost

-$35K

$20K

$100K

-35*.5+20*.4+100*.1=

$500

Probability of happening

50%

40%

10%

 

Calculating the expected value is like playing the odds.  In this case, if we played out this scenario many, many times, the Austin outpost would average out to produce exactly $0 in profits (keep in mind, this is just a short-term expectation).  On the other hand, a Houston outpost would average out to $500 profit for each salesperson.

Houston extends the lead, 3 – 1.

Step 5: Strengthen Your Assumptions

Remember that payoff table we created in the beginning?  Those payoff values and probabilities were assumptions – essentially educated guesses – that we made.  To this point we have spent no money on trying to shore up these assumptions.  A few steps that we can take in the analysis would be to:

  1. Perform a risk assessment
  2. Perform a sensitivity analysis
  3. Calculate the value of perfect information
  4. Calculate the value of imperfect information

Looking at payoffs is one thing, but the risk assessment will show you how much of a gamble you are taking.

The sensitivity analysis takes a hard look at the probabilities we’ve put in by testing how we might have chosen differently if we started with different probabilities.  For example, if we had started with 60/30/10 instead of 50/40/10, but the analysis from Step 4 would have lead us to the same conclusion, then we can feel pretty good.  We just want to be sure the decision isn’t sensitive to the guesses we’ve made.

Imagine a gypsy offered you a crystal ball that would essentially tell you which decision will make you the most money.  The value of perfect information is the most you should pay for this crystal ball.  Since you likely will not be offered such a crystal ball, assume that this is the maximum price you should pay for any advice or information to help with this decision.  If you pay more, you KNOW you are overpaying.  The value of imperfect information involves a bit more calculating (and Bayes theorem, for all of you statistics lovers out there), but will tell you the maximum value of additional information.  You might be surprised how much market research can be worth if your decision means making or losing a million dollars!

These assessments are too involved to cover in this post, but see below for some additional reading or contact us at Troubadour if you need help with an existing decision.

In our case of opening a sales outpost, the value of the crystal ball would be $2500 and the value of a consultant who could help predict the success of the salesperson would be $1500.  My recommendation to Eric has been to open a Houston branch because it has the highest expected value.  In this case, losses are short term, and the hiring process will be repeated by growing the team at the Houston office.  In this scenario, it reminds me of the Vegas slot machine.  If the machine is played only once, there is a good chance it will lose money.  But after being played over and over, all it does is make money.

For further reading, this textbook offers a very nice overview and walkthrough of decision analysis and other types of quantitative models for business: Quantitative Methods for Business by Anderson/Sweeney/Williams/Camm/Cochran/Fry/Ohlmann.

Image Credit: “Spin – Wheel of Fortune” by Conor Ogle

  • Show Comments

  • Rick Galloway

    4/5 times its acceptable…. interesting finding.. Good post

Comments are closed.

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