Build a Bear?

Imagine every adult has 10% of their savings invested in “the global stock market”, and that each of them also invests 2% of their income in the stock market. The entire market consists of 10 stocks, and there is a known upside and downside for each stock.  It is a binary setup, and each stock is either going to move to its upside price or its downside price. Importantly, and fortunately, there is a known probability of upside and downside for each of them.  In other words, we know expected returns (for both the portfolio, and the market).

Imagine these four scenarios, in progression:

• For firm-specific, truly idiosyncratic reasons, the known upside and downside and probabilities for just one security change for the worse, in other words, expected returns for that single name deteriorate.  

           Easy question:  What happens to that stock?

           Less easy question: What happens to the other nine names in the stock market?

• Then, for macroeconomic reasons, the known upside and downside and probabilities for all securities worsen, and they each change in exactly the same proportions.  In other words, expected returns for all ten names deteriorate equally.  

           Easy question: What happens to the stock market?‍

• Subsequently, every citizen decides to stop investing more in the stock market. The 2% of income goes to 0%.

            Easy question: Do expected returns change?

            Less easy question: What happens to the stock market?‍

• Thereafter, every citizen decides to “raise cash” and reduce his or her investment savings from 10% to 5%.

           Easy question: Do expected returns change?

            Less easy question: What happens to the stock market then?

           Hard question: Where is the “cash” to buy the securities coming from if everyone is simultaneously cutting exposure?

Then imagine there is every other citizen, and then there is you.  You are independent.  You’re a free-thinker.  You don’t have to follow-suit, but you can if you want to.  So when the other global citizens decide to stop investing more, or when the others decide to simultaneously raise cash, how will you behave?  How should you behave?

Then imagine that the upsides and downsides actually aren’t known, and that the probabilities of each aren’t either.  Do you know how to play this game?.