Back

Bayesians

Lesson in Course: Medes Newsletter (advanced, 51min)

plc

One sided information

Let's say a man appears with a jar full of quarters.  He offers to sell us the whole jar. Not knowing how many quarters are in the jar, we throw out $20 as an offer based on our best estimate.

Scenario 1 — No transaction

The man says no. We can assume that our offer is too low and there are more than $20 worth of quarters in the jar.

Scenario 2 — transaction closes

The man responds with a resounding yes!  Why are we uneasy and feel like he swindled us? We have less information. The man knew the value of the coins in the jar he sold to us, and we do not know how much we overpaid.

In most primary markets, sellers have complete information advantage over buyers. Whether the market is for used cars, stocks, or even jobs, we can replace the jar with any good or service. Insurance polices are an exception to this rule. As the buyer of the insurance policy, we know our circumstances better than the company.

When in doubt, look for signals

Investors and traders are buyers of stock in companies. They attempt to combat information asymmetry by looking at others.

For example, a market maker likes at-the-money call options expiring in 2 days for stock XYZ.  She makes a market between $85-$88 (buys at $85, and sells at $88) per contract based on her analyses. At the same time, she sees another market maker creating a market between $83-$85 for the same call option.

Could it be that the other market maker has information that she doesn't? To test this, she buys a few contracts for $85. Instead of increasing the price, the other market maker holds steady at $83-$85. It could be likely they know something. Applying Bayesian inference, she adjusts her market to a new spread of $84-$87.

Thomas Bayes

Initial belief plus new evidence = new improved believe.
 The basic mathematical formula takes this form: P(B|E) = P(B) X P(E|B) / P(E), with P standing for probability, B for belief and E for evidence.
 P(B) is the probability that B is true, and P(E) is the probability that E is true. P(B|E) means the probability of B if E is true, and P(E|B) is the probability of E if B is true.

VCs are notorious signal readers. Associates to partners all compare notes with other VCs on a prospective startup. In the private market, information asymmetry is the most exaggerated. The exaggeration helps lend to the power law dynamic in venture returns.

Funds return higher when the investors have more unbiased information. can sift through startups raising money to find the businesses with money-making potential.

It's very difficult to fix adverse selection

I spent the early years of my career in tech building and scaling the valuation line of business at Carta.

In the very beginning, we gave all our financial analysts a standard offer of $75,000 a year with a 0.02% equity stake.  The salary was low for tech but the opportunity was sexy. Come join us in building the engine that would value the entirety of the private market.

Henry Ward, CEO of Carta, had a company-wide policy to never negotiate on compensation with any candidate. He coined this the "First and Best offer" to combat the effects of adverse selection.

I remember we extended the standard offer to an exceptional candidate. She countered within a few days and asked for $100,000 with an increase in equity. At any other company, we would have worked to get to a middle ground. Had our team decided to meet her demands, she would likely be happy for a brief moment. Before long, she would ask herself, "Should I have asked for more?"

Like the jar of coins analogy, information asymmetry causes the candidate dissatisfaction. Without negotiating on an offer, there is no way for her to know the most a company is willing to pay for her role. Even successful negotiations do not provide the full information.

However, what we found out is that the adverse selection was multifaceted and could not be solved simply by offering the first and best. By extending the standard offer, we ended up optimizing for the mean.