Remember the story of the apple falling on Issac Newton's head? Whether or not this actually transpired, Newton is credited with developing classical physics. Newtonian mechanics let us understand the movement of the planets and stars. It helps us calculate the trajectory of a cannonball. It's used to design buildings, bridges, and automobiles. We can make sure trains, and lots of other things in our lives, stay "on track". One of the important characteristics of Newtonian physics is exact predictability.
Stand in a certain place, throw a football with a specific velocity, angle, and rotational speed, and physics will let us calculate a very precise location of the football at a particular time in the future. We can even know whether the laces will be up or down at that millisecond. Neil Armstrong could not have taken his "giant leap" without such precision.
We live much of our lives in a world dominated by Newtonian ideas. Our concept of cause and effect ("for each action there is an equal and opposite reaction") is easily understood because we watch causes result in effects on a daily basis. If something works well, we try do more of what caused it. If something turns out badly, we look for the "root cause" in order to eliminate it next time. Newton's mechanics say that we can make accurate predictions about a specific outcome.
But statistics is completely different. Studies have shown that statistical concepts are difficult for our human brains to understand. As easily as we can intuitively grasp falling apples and flying footballs, our heuristics cause all kinds of inaccuracies when applied to statistics (think Powerball).
Gobbledygook warning! A Gaussian distribution (also known as a normal distribution) is a continuous probability distribution function often used in science when the specific distribution of a random variable is not known. It lets us compute the probability of certain random events happening. Central limit theorem uses a Gaussian distribution to conclude that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, they become normally distributed when the number of observations is sufficiently large. In simple language, Gauss tells us that we can't know very much about a specific statistical outcome, but we can make some reasonable predictions about large numbers of outcomes.
Normal distributions and the central limit theorem have allowed us to deal with risk. Life insurance is an obvious example. Designing structures to withstand high winds and earthquakes is another. Casinos and weather forecasters are equally dependent on statistics. Modern portfolio theory and investment risk management also rely on statistics and assumed distributions of random variables.
We also draw many cultural references from statistics. "Reversion to the mean" is a simple way of understanding central limit theorem. We say things like "If at first you don't succeed, try try again!" and understand that even Babe Ruth doesn't hit a home run every at bat.
But the investment implication of these assumptions isn't as easily understood. If investment returns are random statistical variables (and we have to model them with such assumptions even though we know those assumptions aren't exactly correct), then it implies lots of difficult concepts. For example, getting either excited or discouraged about how are our investments are doing doesn't make much sense (since any given day, week, or year is modeled as an independent random event). Only when "the number of observations is sufficiently large" do outcomes warrant scrutiny. The math says that we need a very long period of time (as much as 11-17 years) to determine with reasonable certainty if a given investment strategy "worked".
We have to deal with this difficult reality and we do so by diversifying our portfolios, using proper risk management, and designing our strategies to take advantage of the expected eventual long-term reversion to the mean. Statistics is why we invest in multiple different asset classes at all times. It is why we talk at length up front about what risk profile to use for a certain investor's portfolio (this risk level setting the size of likely periodic losses). We use valuation methods to estimate whether assets classes are more statistically likely to be undervalued or overvalued at a particular period of time.
Most importantly, we have to be patient and understand that investing doesn't work like most of the rest of our life works. A bad outcome could result from a good decision (and often does!). A great outcome one month doesn't imply much at all about what is likely to happen the following month. For these reasons, many of the most successful long term investors simply pick a reasonable strategy, put their account deposits on auto-pilot, and then think about their account balances very little for years. For the rest of us, that just can't resist checking in on balances and performance from time to time, it is good to keep the Gaussian (and not Newtonian) nature of our investments in mind.
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Due to differences in actual account allocations, account opening date, timing of cash flow in or out of the account, rebalancing frequency, and various other transaction-based or market factors, a client’s actual return may be materially different than those portrayed in the model results. The reader should not assume that any investments in sectors and markets identified or described were or will be profitable. Investing entails risks, including possible loss of principal. The use of tools cannot guarantee performance. Past performance is no guarantee of future results. The information provided may contain projections or other forward-looking statements regarding future events, targets, or expectations, and is only current as of the date indicated. There is no assurance that such events or targets will be achieved and may be significantly different than that shown here. The information presented, including statements concerning financial market trends, is based on current market conditions, which will fluctuate and may be superseded by subsequent market events or for other reasons. The charts depicted within this presentation are for illustrative purposes only and are not indicative of future performance. The data do not reflect the material differences between stocks, bonds, bills, and inflation, such as fees (including sales and management fees), expenses or tax consequences.
