# Quantifying Risk: Volatility and Drawdown

Traditional financial theory has relied heavily on standard deviation or variance (the square of standard deviation) to quantify historic risk. Markowitz mean-variance optimization and the Sharpe ratio are two such examples under the umbrella of modern portfolio theory that reference variance or standard deviation as a proxy for risk in their formulation. However, there are some concerns with using these risk metrics that should be considered.

# The Black Swan

I consider myself a child of the Global Financial Crisis (a.k.a. The Great Recession). As I wrote about in my introduction I started my career in early 2008, just as the US housing market was unwinding and shortly before financial markets imploded. To those not familiar with financial markets this sort of event would appear to be a rarity–a one-in-a-billion (I’m embellishing) sort of event. Looking back at financial history, however, paints a very different picture. Severe market movements, both positive and negative, have occurred with greater frequency than I (or most others) realize.

# The Mythical Rebalancing Bonus-Part 2

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

# The Mythical Rebalancing Bonus-Part 1

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.

# Defining Risk Part 2

For part 1 see Defining Risk

Just over a month ago I wrote on the subject of risk with an attempt to define what risk really is (at least for me). I ended the article by defining that risk was anything that stood in the way of accomplishing an objective. A recent correspondence with a reader made me rethink how my definition was presented. The subject of risk is often discussed in a negative or derisive manner. It is something we seek to avoid or banish from our lives. My definition clearly falls into this category. However, there may be another side to risk that I failed to see in my previous post. Consider the following definition of risk from Apple Computer’s former CFO Peter Oppenheimer

The degree to which an outcome varies from expectation. [1]