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Mr. Market Turns Investment Banker

Summary

Intuition ends where statistics begin.

Anscombe's quartet.

Picture the graph and graph the picture.

Mr. Market arrives at a sharp investor’s house one day and explains that his nervous condition has temporarily kept him out of the public markets although he has 100% interests in small businesses available. He comes in for coffee and butters her up by stating that he has a company with 11 salesmen that need a leader with her skillset. He knows that she has a passion for statistics and selling so he has brought along a book prepared by his team of MBA’s to give her the assurance that she needs to purchase the business.

The next day he drops by with a book that shows the algebraic equation of profits to be as follows:

Profits = 3 + .500(sales)

Mr. Market explains that each salesman has a territory to sell the product and is free to negotiate the price. He suggests that occasionally this impacts profitability, but his sharp MBA’s have run the numbers repeatedly and the profit equation is always the same. He suggests that the profit equation will hold regardless of the sales number if the makeup of the salesmen stays the same because the salesmen all produce a specific margin based on their negotiating skills.

The company appears to be scalable and profitable, but she asks for the break down by salesman and then replies with the answer that the company is interesting but lacks potential.

The next day Mr. Market appears with a different company and she asks the same question. Once again there are 11 salesmen with the same profit equation. Again, the answer is no.

Mr. Market uses low cost transportation the next two days and arrives with two more companies with the same profit equation utilizing 11 salesmen. The investor is becoming frustrated and then decides that a series of questions will bring the morning visits to a conclusion.

She asks:

Are all the salaries the same?

Mr. Market says yes.

Can I fire any particular salesman?

The answer is no.

Do the salesmen communicate with one another?

No.

Can I ask them to communicate with one another?

Yes.

The investor then rethinks her decisions and tells Mr. Market that she will purchase the fourth company that he offered subject to a particular individual becoming head of sales. Mr. Market then begins to get the documents.

Aftermath

Mr. Market appeared with 4 different companies with the exact same profit equation and statistics. The mean of x(sales) was 9 in all four cases and the variance was 11. The mean of y(profit) was 7.5 while the variance was 4.12. The correlation coefficient between the variables was .816 for all four companies offered by Mr. Market. How did the investor decide?

The Quartet

https://plot.ly/~MattSundquist/2745.png

Above are the four companies offered in clockwise order. Although the statistics are the same for all four, the story told to a shrewd investor is different. Anscombe’s quartet is a pictorial to emphasize that statistics do not tell a story as well as graphs.

The investor recognized the first company as a typical sales graph with several salesman selling more, but it was random if the profitability of the more successful would be under or over the projected profitability. The second company demonstrated that selling more did not equate to more profit margin per dollar of revenue. The third company offered had a superstar salesman unable to produce profits over the projected profit line by not getting premium prices while the some of the others delivered better pricing but little sales. The last company had a superstar able to get price with better than average quantity alongside a few underachievers in terms of margin with healthy sales books. The investor was betting on him sharing his secrets.

A Picture is Worth a Thousand Words (and Means)

Numbers mean so much to an investor in determining the price and the investor means so much to the one with the numbers to justify a price.