Not long ago I used to teach investment management courses to Master’s students (MBAs and MS Finance types). A core aspect of my course was so-called modern portfolio theory. We did a lot of math and problem-sets to make it feel like we were doing something useful. But I can summarize the core muscle movements of portfolio theory in 3 slides.
Slide 1: The Math Works.Why do academics love diversification? Well, they love the math. Let’s explain… Let’s say you walk up to someone on the street and say the following:
“Hey, I have 1000 assets for you: Each assets has a 10% expected return, but these assets are insanely volatile. Also, all these bets are structurally uncorrelated with anything in the world.”That sounds OK in theory, but do who wants to own a bunch of incredible risky assets? Nobody! But wait, what if someone with a PhD told you that this offering has no risk and is essentially a guaranteed 10% return! Say what? How can a bunch of “insanely volatile” assets create a guaranteed 10% return? Well, math can help explain how this works. An old course slide… Pooling uncorrelated bets lead to no risk as the number of bets goes to infinity. Magic! Many of us in finance now generally understand this concept (even if we don’t know the math). Of course, some smart people have gotten in trouble for relying on this concept. But before we get to the “why” on how blindly following the diversification math can get you in trouble, we’ll attempt to make the concept even clearer via a picture.
Slide 2: Diversification Works…Let’s “prove” the math with a picture. We’ll have our spreadsheet conducts a 1000 simulations. In each simulation run, a portfolio system can do the following:
- Take 1 bet
- Take 10 bets
- Take 100 bets
- All bets are uncorrelated. 1
- Each bet has a 10% mean and a 20% standard deviation (roughly equivalent to owning the S&P 500 stock market bet).