Standard Deviation and Friends

Risk, as it is related to investing, is the measure of the potential for loss of capital and evaluating the amount of capital that may be lost.

Risk management is the investment discipline of creating efficient investment portfolios; portfolios that create the best opportunity for gain with the least amount of risk of loss of investment capital.

The measurement of investment risk is central to the issue of risk management. 

The standard of value for the measurement of investment risk should be what information and what action will have the most impact on investment risk?

The current, most popular risk measurement tools are Standard Deviation, Efficient Frontier, Beta, VaR, and Sharpe Ratio.

The universal assumption of these risk measurement tools is that investment history is the investment future; that investment history will repeat itself almost as reliably, as repeatedly, as regularly, as frequently, and as predictably as the rain fall in the rain forests of Brazil.

Standard Deviation is variously defined as the measure of the amount of variation in any group of numbers that make up an average, the variance around a mean, or the quantification of the variance of returns.

A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other.

If you looked at normally distributed data on a graph, it would look something like the illustrated "bell shaped" curve.

By definition, one standard deviation away from the mean in either direction on the horizontal axis (the red area on the graph below) accounts for somewhere around 68 percent of, for example, investment returns. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of investment returns. And three standard deviations (the red, green and blue areas) account for about 99 percent of investment returns.

If this curve were flatter and more spread out, the standard deviation would have to be larger in order to account for 68 percent of the investment returns. That's why the standard deviation can tell you how spread out the examples in a set are from the mean.

A sample of bonds typically has a small standard deviation because most of the returns are close to the average. 

Gold investments typically have a high standard deviation because there usually is a  wide range of investment returns for each investment that makes up the average. 

However, just because there may be a wide range of investment returns does not mean that a class of  investments has more risk than another class of investments which has a narrow range of investment returns.

The standard deviation for bonds versus gold investments could change in an instant due to changes in economic conditions with gold investments having a low standard deviation and bonds having a high standard deviation.

When gold investments seemed to be fundamentally and strategically valuable years ago, investors started buying gold investments and, as a result, individual investment returns became more similar in a buying frenzy that caused a general and almost equal price appreciation resulting in individual returns being closer to the average returns creating a low standard deviation and the appearance of low investment risk.

The results were that the level of investment comfort and the probability of investment outcomes were artificially created.

Bond and utility investment returns (perceived as low risk/low standard deviation investments) can easily have a high risk of performing poorly, gold (perceived as a high risk/high standard deviation investments) can perform very well and both can collapse at the same time though the first typically has a lower standard deviation than the latter.

Sudden increases in interest rates will affect different bond valuations and returns in many different ways depending on the type, quality, and maturity of the bonds held, thus creating a high standard deviation; however, there could be a low investment risk because of the bond investment strategy being used in a specific bond investment environment.

The worst case can be to conclude that, because a standard deviation is low, no action need be taken as valuations begin to fall.

As a risk management tool, standard deviation is nothing more than a numerical way to record and retrieve investment history.

Yesterday's standard deviation is not today's or tomorrow's standard deviation.

Therefore, yesterday's investment risk as defined by standard deviation is not today's or tomorrow's investment risk.

Standard deviation gives no insight into the actual investment performance determinant variables and, for this reason, is little more than comfort food for those who do not understand real investment risk and who are looking for information to justify their investment decisions, "But, the standard deviation was low when I bought this class of investments!"

Standard deviation has little more than investing entertainment value for a quarterly review with a client or at a cocktail party; "We are on the efficient frontier with classes of investments that have low standard deviations and investments that have a low betas and high alphas, what could we possibly have to worry about?".

Volatility

'Investment volatility is a measure of investment risk!'

At best, investment volatility is a measure of theoretical investment risk, not actual investment risk.

For example, a random sample of Beta comparisons a few years back against the Dow Jones Industrial Average:

At that time the conservative investor would have been told to by GM because the Beta was low and, therefore, the investment risk was low and to avoid Google because to Beta was too high.

All three of the above represent theoretical investment risks based on an incorrect assumption that Beta measures investment risk.

As evidenced by the examples above — many more examples like them that are readily available — and in complete contradiction to the realities of the behaviors of investments as anyone who has spent more than a nanosecond in the financial markets would, should know.

The tragedy of this flawed investing concept is that you must not take the term Beta, translate its derivation to your liking, and apply your misunderstanding of it and an investors unfamiliarity with it to use as a basis for current investment selection and future investment price behavior.

Probability

'Probability can be calculated in the financial markets.'

Well, probability does not exist in the financial markets.

Numbers, math, equations, and probability are the discovery, the explaining, the unfolding of apparent chaos, to demonstrate and to prove the order and connection of underlying cause and effect variable relationships in an effort to understand the present and to predict the future with some degree of accuracy.

From very simple mathematical matters to the very complex of landing a man on the moon, numbers of the orderly universe are precise and the outcomes are a certainty, or a near certainty, because they depend on finite, actual variable relationships as found in the universe but seldom experienced in the financial markets.

When 'Monte Carlo' dice are rolled, you know with 100% certainty that either a 1, 2, 3, 4, 5, or 6 will come up on each die, but you don't know which combination of numbers will come up on a particular roll of the dice.

The probabilities of different outcomes can be calculated by determining how many different ways the same total number can be rolled with the dice. There are more ways to roll a total of 7 than any other total number when rolling the two dice. Therefore, 7 has the greatest probability of being rolled. As the total number decreases down to the lowest total, 2, there are fewer and fewer ways to roll the total number. Therefore, if you need a seven or six to accomplish your goal the probability of success is greater than if you need a 3 or a 2.

Unlike the universe where there are underlying relationships and forces that are known, connected, predictable, and can be modeled for simulation, the financial markets' infinite, changing variables and sometimes and sometimes not associated ranges in an environment of randomness and chaos without rhythm and pattern and without underlying, mathematically explainable and predictable order make it impossible to accurately, consistently, and reliably model and simulate the behavior of the financial markets and the probability of future events.

Therefore, as one moves from predicting the probability of outcomes based on the roll of 'Monte Carlo' dice to predicting the probability of outcomes in the financial markets with 'Stock Market' dice, the probability of correctly predicting outcomes moves from possible to futile.

Modern Risk Measurement Equation Mystique

There is an ever increasing and unexplainable investing equation phenomenon; if what seems to be or is defined to be a cause and effect occurrence expressed as a mathematical equation, the equation must be valid, universally true, and has unique predictive powers.

'Einstein's theory of relativity seems to be valid:'

'Certainly If is valid and reflective of cause and effect variable relationships and is, therefore, predictive of behaviors in the universe, then surely the latest iteration of the Beta risk measurement equation below — much more complex, with many more variables than Einstein's equation — most certainly, must be valid.'

From:

Beta = [Cov(r, Km)] / [StdDev(Km)]2

To:

'Wow, look at this one. Just has to work!'

Regrettably, mathematicians concluded that since Einstein's simple math works in the universe to predict future events, it most certainly will work in the financial markets.

A few Albert Einstein mathematician wantabes, while ignoring the obvious structural and causality differences between the universe of nature and the universe of the financial markets, extracted the laws and concepts of Einstein's universe, so to speak, and attempted to superimpose them, in effect, onto the world of investing by confusing, comparing, and applying the concepts of immutable order, structure, relationships, causes, connections, correlations, effects, and rules (Newton's three Laws of Motion, for example) as found in the sciences and systems of the universe — and as explained with mathematics — with the chaos, incidences, coincidences, chances, correlations (none of which are causal; but, assumed in order to make Modern Portfolio Theory math work) and no rules as found in the artistry and complexity of investing and managing capital in the financial markets in an effort to predict investment outcomes; the ultimate 'non sequitur' of investing.

None of the above are measures of investment and investing skills; the actual determinant of individual investment and investment portfolio investing risks.

There is no theory — modern or otherwise — that can be ordained, no computer that can be programmed, no software that can be designed, no investing tool that can be contrived, and no equation that can be divined to quantify, evaluate, and predict the primary forces that drive the financial markets and investment prices; human consensus, mood, and behavior — intelligent and not, knowledgeable and not, reasoned and not, rational and not, and logical and not.

The true measure of investment and investing risks is a subjective one and cannot be predicted by any equation.

Modern Risk Measurement Popularity

The appeal of Modern Portfolio Theory risk metrics are that neither investing insight, nor investing foresight, nor investing judgment, nor investment selection and portfolio management skills and disciplines are required; just search historical investment databases based on past investment performance, retrieve investments based on past investment performance, sort investments based on past investment performance, plug data into risk metrics algorithms, pick investments based on past investment performance, then view, print, and present, and then hope that the investing past will somehow be the investing future.

If a portfolio underperforms and/or if individual investments do not meet performance exceptions, you have the perfect investing underperformance excuse already built in; 'It's not my fault we did not do well, Beta did this to us!'

Risk Types

Systemic Risk

Fundamental Risk

Timing Risk

Best Measures of Investment and Investing Risks

Effective investment risk measurement and investment management must focus on the elements that actually cause and that actually affect investment and investing risks and returns rather than by perceived investment/investing variable coincidences:

• Investment Quality
  • Mature, established, emerging, unproven companies.
• Capital Allocation
  • Distribute capital to different investment sectors that have separate and distinct investment characteristics and that tend to behave differently as the financial markets change; cash, bonds, REITs, large capitalization equities, etc.
  • Distribute capital to many, several, a few, or single investment sectors.
• Investment Diversification
  • Many or a few investments in an investment sector.
  • Equal or unequal investment weighting for each investment within an investment sector.
• Investment Structure
  • Debt and/or Equity; lender and/or owner.
  • Equity and/or Derivatives; shareholder and/or gambler.
  • Bonds; secured and/or unsecured, insured and/or not insured, investment grade and/or junk.
  • REITs; equity and/or mortgage.
• Portfolio Management
  • Diversification.
  • Rebalance.
  • Reallocate.
• Price Management
  • Lump-sum purchase and/or dollar-cost-averaging.
  • Predetermined price limits to buy/accumulate and to sell/distribute.
• Portfolio Management Disciplines, Rules, and Procedures
  • Global
    • Investing Principles and Perspectives — Who you are, what you represent, how you conduct your business; what you need to know, do, have, use, and avoid to invest successfully; what, when, why, how, and what if..
    • Investment Selection Disciplines, Rules, and Procedures; for example, "A Simple Bond Plan".pdf
    • Investment Sectors — User adds to fit investment philosophy and style; such as categorized by broad investment classes such as bonds, equities, mutual funds, money managers, and user defined or by different economic or business investment sectors.
    • Investment Categories — As a subheading to Investment Sectors, user adds to fit investment philosophy and style; such as to categorize by different economic/business sectors or by specific types of bonds, mutual funds, money managers, and user defined investments.
    • Investment Quality — Match to investor's investment risk profile.
    • Investment Database — Potential and recommended investments.
    • Asset Allocation Matrixes — A central investment theme and variations on that investment theme to generate different asset allocations for different types of investors.
    • Asset Allocation — Match investor investment objectives with the appropriate types and numbers of weighted investment sectors and weighted underlying investments.
    • Investment Diversification — Match investor investment comfort zones and time horizons with the appropriate types and numbers of investment sectors and underlying investments by investment categories.
    • Model Portfolios — Suitable, hopefully timely investment sectors and investments by investment categories for different investment strategies.
    • Cash Investment Portfolios — Create unique investment portfolios that match investors with the correct investments.
    • Blended Investment Portfolios — Blend an investor's existing investments with a model portfolio to the extent and when desired to bring new investors under one investment umbrella and to update existing client's portfolios with current investments as opposed to having too many different investment portfolios and to many different investments in different investment portfolios that were intended for the same or outdated objective.
    • Rebalance Portfolios — Reset investment portfolios to original investment sector and investment weightings to maintain the initial structural integrity of investment portfolios.
  • Personal
• The Investment Past — Other than in passing, other than a reference point is irrelevant.
• Protect Capital — Regardless of the market conditions, always be in the investment present, on the investment defensive, and never excuse present portfolio cash value with future value hopes, explanations, and expectations.
• Primary Investments — Cash, bonds, equities, and real estate — Packaged products are never better than the investment integrity of the underlying investments.
• Interest Income & Dividends — All portfolios.
• Trading — Never, unless the client knows at least as much as I do.
• Alternative Asset Class Investments such as Hedge Funds, Private Equity, and Limited Partnerships — Often have lock-up provisions and other limitations on liquidity, difficult to value/price, no investment so good that it is worth losing liquidity.
• Liquidity — Must be a daily market, never sacrifice for apparent investment opportunity.
• Commodities — At no time to speculate, OK to hedge, and never unless the client knows more than I do.
• Money Managers & Mutual Funds — Second choice. Why have them do what I am supposed to be able to do.
• Bond Mutual Funds — Never. There is always a better, smarter way.
• Investment Firms' IPOs — In most cases, if you can get it, you do not want it.
• Modern Portfolio Theory — Investment diversion amusement.
• Companies — Quality, products, management, competitive, balance sheet, accounting, earnings, growth, research and development, entry, and use of debt. 
• Earnings — Realistic, maintainable, accurate, honest, and increasing.
• Margin* — Never leverage capital to buy more investments unless borrowed capital will be used only as a short-term source for cash needs outside the investment portfolio and where there is a clear and specific source of funds to eliminate margin in the short term.
• Sell Short* — If Warren Buffett can survive without shorting stocks, so can I; odds are bad going against the upward bias of the market, loss potential infinite.
• Options* — Never buy, never write covered, and never, ever naked. Well, OK, maybe "buy" every once-in-a-while!

Find skilled, patient, disciplined, forward-looking, vigilant, serving — not self-serving — investment management that seeks fundamentally sound core — not hybrid or derivatives — investments consistent with investors' investment profiles (risk/income/time), that wraps those investments in structurally sound and competitive investment portfolios, and that attempts to buy those investments and to sell those investments at the right time and all other 'imagineered' investment risk measurements fall by the wayside and I can tell you exactly what your investing risks are; close to, if not zero.