Math & Models

The Mythical Rebalancing Bonus-Part 2

~ Daniel Sotiroff

In Part 1 I showed that as investment time increased there was, at least historically, a smaller probability of realizing a rebalancing bonus in 60/40 stock/bond portfolios. There was a lot that I left unaddressed at the time and I felt a need to develop a better understanding of the mechanics of the rebalancing bonus. Why does it work in some instances, but not in others? In other words, more was needed to demonstrate what actually drives the rebalancing bonus. A good place to start is with the work of Harry Markowitz, which showed that portfolio performance–both return and volatility–was mathematically related to three characteristics of the constituent assets

  1. Correlation with other assets
  2. Volatility
  3. Rate of return

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The Mythical Rebalancing Bonus-Part 1

~ Daniel Sotiroff

Go to part 2

The rebalancing exercise that I performed with Shannon’s Demon implied that a premium may be obtained by rebalancing a portfolio of uncorrelated assets. These assets featured highly hypothetical performance with expected rates of return and volatility both well out-of-bounds of anything that’s likely to be seen in real world capital markets. The extreme nature of these make-believe stocks was used to illustrate what is possible.

Back to reality.

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Markowitz’s Portfolio Selection

~ Daniel Sotiroff

Harry Markowitz is often referred to as the father of Modern Portfolio Theory–a collection of mathematical models that quantify the behavior of assets and portfolios of assets. Harry’s work specifically addresses the latter and examines how assets may be combined to reduce volatility and (potentially) increase returns. I briefly alluded to Harry’s work in an earlier article on portfolio construction, but wanted to cover the major points in greater detail.

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Rebalancing With Shannon’s Demon

~ Daniel Sotiroff

Claude Shannon was a prolific individual when it came to mathematics and science. The former Bell Labs researcher and MIT professor helped develop a field of study known as information theory and played a major role in inventing the way that computers compute. He also had an interest in the stock market, and would hold occasional meetings at MIT on the topic of scientific investing. One such method he proposed required no knowledge of future market behavior–a strategy that was designed to profit from a completely random walk.

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The Rule of 72 And Skew

~ Daniel Sotiroff

I’m a big fan of simple things. The rule of 72, a quick calculation that computes how long it will take to double an investment, is probably as simple as they come. The formulation is fairly straightforward. The time required to double your money is equal to 72 divided by the rate of return

Years To Double Money = 72 / i

Where i is the expected rate of return. Obviously, lower rates mean more time is needed, and the relationship isn’t linear

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