Basic Investment Math - note #2

In this note I provide an introduction to some of the basics of portfolio management. The word diversification within a portfolio is used to describe the strategy of owning more than one asset. The touted benefit of diversification is reduced risk. While diversification is beneficial, too much diversification may be no different than owning the market which may not be as effective as owing a representative index that would provide similar risk and returns at a lower cost. Owning a variety of stocks with similar risk and return characteristics (e.g. in the same or related industry) may provide little diversification benefit. Also, diversification does not insulate investors from mundane or severe market volatility which occurred during the 2008 financial crises for example. Beyond a certain point, a portfolio with x number of positions does not benefit from x+1, x+2 positions as the benefits of incremental diversification diminishes.

So instead of being singularly focused on diversification I have been simultaneously focused on portfolio covariance, correlation and standard deviation. In statistical terms covariance measures the degree of movement between two variables relative to their mean over time. In portfolio construction we are typically talking about rates of returns in investments and how they move together (or not) over time. Positive covariance describes returns for two assets that move in the same direction relative to their mean returns. Negative covariance indicates rates of returns for two assets move in opposite directions relative to their means. In portfolio terminology the term correlation means correlation coefficient which is a standardized measure of covariance that indicates the strength of the covariance of the assets in question. In the context of portfolio management standard deviation is a term that encompasses the previous terms. More specifically, the standard deviation of a portfolio encompasses the variances in returns for individual assets and the covariance between assets in the portfolio. In practical terms I have applied the concepts described here to determine at the margin, what type of assets to add to a portfolio. Ideally I strive to add assets with low or negative covariances and correlations. I also attempt to simultaneously manage two or more strategies with low or negative correlations within my portfolio at the same time (e.g. value investing over multi-year holding periods and arbitrage). (1)

Depending upon my circumstances at any given time I may not formally calculate the statistical measures described above day-to-day but follow an approach in line with these statistical measures based on my knowledge of specific assets (namely stocks). In stocks and bonds for example I typically hold positions in different companies, industries and countries that have minimum or negative correlations. I also attempt to think carefully about contagion risk and not so obvious economic linkages between specific investments. Finally I invest in securities where I believe long term value is not reflected in the current day price. Patience is the primary attribute here that may allow me to at times, look past shorter term correlation and standard deviation relationships to some degree, in order to focus on long term relationships in my effort to pursue long-term returns.

'(1) Note: there are many sources of information regarding covariances, correlation and standard deviation. For the discussion here my primary source of  information was "Investment Analysis and Portfolio Management," sixth edition by Frank Reilly and Keith C. Brown., pages 104 - 105 and 265 - 267.

Basic Investment Math - note #1

In this note, I describe some basic underlying mathematical principles that dictate investment strategies/ results which influence my portfolio construction and security selection.

One of, if not, the most important concepts in investing is the concept of compounding. A basic mathematical principal regarding compounding is the rule of 72, which is the approximate number of years an investment or portfolio will double at a given compound rate of return. For example, if an investor achieves an 8% annual rate of return his/her investment would double in value in approximately 9 years. An investor who achieves a 10% annual return would double his/her funds in just over 7 years, etc. 

Real life in the markets is far messier than the math presented here as desired returns may or may not be available, may involve too much risk and may not be positive or smooth during an investment horizon. Besides overall macro and market conditions, portfolio construction itself will influence the future value of the portfolio over an investment horizon. At the risk of over generalization, for sake of discussion, I assume higher returns involve higher risk. The interplay between return and risk is a key concept. The basic math of risk and return suggests that steady portfolio returns with lower volatility mathematically tend to result in higher returns over time than portfolios designed for higher returns that have higher volatility bounded by the fact that portfolio construction involves attempting to achieve that the optimal combination of risk and reward given various parameters.

In other words, when comparing risk/reward characteristics over an investment horizon, portfolios losses are difficult to overcome. In the table below I illustrate four scenarios with each producing different returns at varying amounts of volatility. In each scenario I start with $100 and stay invested for 5 years. In scenario 1 I achieve varying but positive returns in all 5 years. The 5 year compound average growth rate (CAGR) of 12.2% is the highest of the four scenarios. In scenarios 2 through 4 I assume negative returns in the models to show that the CAGR is lower than scenario 1 in each of the alternative scenarios. In scenario 2, I model only one slightly negative year (with the other 4 year returns unchanged) which results in a lower CAGR. In scenarios 3 and 4 I assume a series of higher returns combined with one and two losing years. Scenario 4 which includes two losing years produces the lowest return with the highest volatility. This is the worst case result of the four models. 

Real life in the markets is far more complex than the math presented here. Outright losses are possible and common. Concepts that are important here include: (1) judging your ability as an investor to produce returns at a given level of risk; (2) the risk/return constraints/requirements of the portfolio in question; and (3) other holding period factors that come into play. Please see the table below for a summary of results. In real life numerous scenarios beyond these four exist. 

In the table below PV is the present value of the portfolio, ARR is annual rate of return and CAGR is the annual compound average growth rate of the 5 year investment horizon. I have highlighted negative returns in red.

Scenario		PV	Year 1	Year 2	Year 3	Year 4	Year 5
1	ARR		10%	20%	7%	5%	20%
		100	110	132	141	148	178
	CAGR						12.2%
2	ARR		10%	20%	7%	-5%	20%
		100	110	132	141	134	161
	CAGR						10.0%
3	ARR		20%	20%	-20%	20%	20%
		100	120	144	115	138	166
	CAGR						10.7%
4	ARR		20%	-20%	20%	-20%	20%
		100	120	96	115	92	111
	CAGR						2.2%

"The Farther One Travels The Less One Knows"

The title is from the song, "The Inner Light" written by George Harrison of the Beatles.(1) The lyric reflected Harrison's nuanced view of Indian music. As we grow and mature we become aware of how much we do not know about a body of knowledge we are exposed to or are immersed in. Learning exposes us to the depths of our ignorance. (2)

We are all ignorant at some level even as a subject matter expert. In investing this is an unavoidable handicap and one that many individual investors are not aware of. The challenge in investing is that we can never completely know, understand or predict everything we would really need to know to clearly see the future we are investing in over time. So our results cannot be guaranteed. Ignorance is believing we know more than what we actually do. Ignorance in investing will ultimately lead to sub optimal results and over time take investors out of the game altogether. Investors in this category often blame outside forces for their poor results which is misguided. Mastery (i.e. maturity, development and experience) on the other hand allows investors to acknowledge this issue which may allow for development of techniques to better cope with this problem.

The lyrics made famous by Harrison and the Beatles are based on a Zen poem. The meaning of these lyrics are profound as beauty, joy, fulfillment and riches are found within each of us. If we hope to obtain these things, the more they will elude us as the world cannot give us what it does not contain. Where do you experience the universe as the calling in life should not be to gain more beauty, joy and riches, etc. When you discover what you are you will find that the universe is contained within you. You will find the the world is really inside of you and that the world outside of you is an illusion. (3)

Average and below average investors typically do not understand this so they are all too often focused on the opinions (predictions) of others, the outside world, markets, instruments, the economy and indexes, etc. that they have no control over. This type of focus and framing results in sub par results over time. Masters are instead focused within themselves in a way where they are not relying on outside forces to drive their investment process and approach. The pursuit of riches in investing typically leads to the opposite result because it is an outcome focus that leads to poor processes which ultimately results in poor results.

In summary, success or failure in the markets over time for an investor will be dictated from what lies within the investor instead of outside factors such as the economy, markets, investment vehicle performance (i.e. movements in asset prices) and a myriad of other outside factors. This is often not understood or acknowledged by investors focused on external factors which results in their depths of their ignorance not being exposed.

(1) From "Concert for George," 2002 and genius.com/The-beatles-the-inner-light-lyrics, the song lyrics are:

The Inner Light
The Beatles

(Verse 1)
Without going out of my door
I can know all things on Earth
Without Looking out of my window
I could know the ways of Heaven

(Chorus)
The farther one travels
The less one knows
The less one really knows

(Verse 2)
Without going out of your door
You can know all things on Earth
Without looking out of your window
You could know the ways of Heaven

(Chorus)

(Outro)
Arrive without traveling
See without looking
Do all without doing

(2) Adapted from genius.com/The Beatles "Inner Light" lyrics.
(3) Adapted from from a synopsis from the blog, blog.light-up-your-life.com/web_log/2011/01/the-further-one-travels-the-less-one-knows.html.

Background and Introduction - December 2014

I am a former national public accounting firm CPA who has been an individual and professional investor since the 1970’s. I worked as a stockbroker from 1987 to 1992 in both the U.S. and Hong Kong. I also traded stocks in a family office hedge fund from 2002 to 2007 followed by a stint as an independent financial analyst to institutional investors between 2008 and 2012. I bought my first stocks in high school and college in the 1970’s. My first stock holdings consisted of two companies known as Pogo Producing Company (an oil E&P company) and Beatrice Foods (a large food processing company). I made these bets based on my view of the oil market and prospects for Beatrice. I lost money on both bets. All-in-all not a great start as an investor. As a CPA I audited public and private companies in a variety of industries for approximately eight years and also held titles such as Controller and CFO in private industry. I have been fortunate to have audited and worked for several successful companies as well as a few that have failed. I learned from both but realistically have learned more from the failures than the successes. Along the way I have traveled to conduct business in 16 countries located in Asia, Europe, the Caribbean and Central America. My career, to say the least, has been eclectic.

I learned accounting in college as an accounting major but was also serious student in economics, finance and history. As a public accountant I learned how to prepare and read financial statements of companies of varying sizes and complexity in a multitude of industries. In the late 1980’s I read an investment book about Warren Buffett titled “The Midas Touch,” by John Train. The book was my introduction to Warren Buffett. As a result of the book, Buffett became a major figure in my investment thinking and remains so today. For years I have followed Buffett, Charles Munger, Peter Lynch, Seth Klarman, Marty Whitman and John Maynard Keynes among a long list of professional investors who I admire and have learned from. I have also developed investing strategies based on the approaches of Buffett, Munger, Lynch, others and have at times mimicked their select holdings. I have also been bought out of companies by Buffett on more than one occasion in names such as Burlington Northern Railway and Heinz. I enhanced my technical investing skills by passing level 1 of the CFA exam and have also been a member of the CFA institute for about 10 years between 1999 and 2009. I do not know any of the gentlemen mentioned here but know a fair amount about their style as I have read countless books and articles about their lives, careers and approaches as investors.

My primary investment strategy has been to make long-term concentrated bets in stocks. My largest and longest term bets held over multi-year horizons have produced returns that have paid for my mistakes. Examples include Expeditors International - EXPD (1998 to 2007) and Costco -COST (2004 to present). I am a bottom up investor who is focused on finding current and future value in stocks and bonds, etc. I am attracted by what the public and other market participants often view as bad market or company news and general mayhem. I am not a market timer as I am not focused on predicting or worrying about the future direction of the economy or market. I am attracted by situations where a perceived gap exists between public market asset prices and current/future intrinsic value.

The market crash of 1987 and the financial crises of 2008 and 2009 were two of the best opportunities during my investing lifetime to find value in the markets. At the time of the 1987 market crash I had been in my financial career as a stock broker for two months. A few weeks before the crash my large book of one client had bought a stock through me that dropped 50% during the crash. I did not see the crash coming so my client suffered significant unrealized losses. I managed to talk my only client into holding onto the stock bought through me that was a large position for him. Six to nine months later the stock recovered all of the losses incurred during the fall of 1987 and went on to produce a significant gain for him. The name of the company was Nordstrom who at the time operated (if my memory serves me correctly) about 2 to 3 stores in the U.S. This real life experience taught me lessons about markets, risk taking, emotion, and volatility, etc. that have stayed with me. At the time of the 2008/2009 crises I was an individual investor doing proprietary research for institutional investors. By the time of the crash I had been investing personally and professionally for ten to fifteen years. Long enough to have experienced plenty of volatility and success/failure. By this point in my career I had evolved from an analytical stock picker to someone who had a much stronger understanding of the emotions of Mr. Market as well as my emotional self. Trial + error and experience (at times painful) were the teachers here as the market found ways of exploiting weaknesses and flaws in my approach. What I learned came from experience and study. By the time the 2008 crises erupted and stocks, high yield debt and other asset classes had collapsed, I had developed a mental inventory of companies and instruments that I wanted to be invested in for several years but had not, due to valuation concerns. In the 2008 and 2009 crises I made a series significant bets in companies with strong balance sheets. I made additional bets during 2010 and became fully invested during 2011. What was attractive to me in this period was that stocks were trading at cheap valuations on depressed forward earnings expectations. Opportunities were aplenty in some of the greatest companies in the world. Much of the merchandise presented by Mr. Market appeared to be a positive asymmetric bet because of overall liquidity issues, contagion risks and fear that existed in investors who were focused on predicting the direction of the economy, market in the U.S. and world, the European debt crises and the Japanese tsunami disaster, among other factors.

More specifically speaking, I was a large cap stock and high yield debt buyer in the U.S. during the financial crises and stock buyer in Europe during the peak of the Greek debt crises plus Japan shortly after the tsunami. Value was available as stocks and high yield debt sold at incredible discounts to then current and longer term prospective value prospects in my then humble opinion as conditions were rough. Opportunities existed in great companies with competitive advantages, superb balance sheets, high return on invested capital business models that was combined with depressed forward earnings expectations. It was also apparent by hitting the streets and experiencing these companies firsthand as a customer and/or observer that their businesses were not falling apart. Companies, instruments and asset classes that I invested in were an eclectic group that included, Wal Mart, Coke, Colgate Palmolive, CVS, Microsoft, Berkshire Hathaway, Moody’s, IGT, gaming operators (MGM at the time it was on the verge of bankruptcy), Costco (during negative comps in 2008 and 2009), High Yield debt (2008 and 2009 at 20% to 30% yields), the S&P 500 index (SPY) when the U.S. government was threatened with shutdown, the Japanese index and Hitachi (in the days following the tsunami) and European stocks (Adidas and SAP) in the midst of the Euro debt crises, among others (call me a fox and not a hedge hog as many unique bottom up opportunities presented themselves). Many if not most of the individuals I spoke to left or stayed out of the stock market during this time as they were fearful of the economy, markets, politics, the Fed and central bank actions despite my best communication effort. I am a lousy salesman.

Economic conditions in the U.S. are better today than they were in 2008 and 2009 but overall market opportunities are fewer in my opinion. More people are excited about the market today than 2008. On the other hand, while not negative, I am less excited about the markets today than I was in 2008 as there is less overall value to be found. Despite this, I do remain invested. As usual, negative headlines and negative price movements can be found in places like energy and other spots in the U.S. that may or may not provide opportunities in the future. Chaos and current day problems can also be found around the world today that may/will create opportunities for folks willing to do research who have financial and emotional staying power over a horizon.

In future entries to this blog I will attempt to provide some investing wisdom, historical perspective and insight regarding present day conditions plus “how to” insight for individual investors, among other topics. Stay tuned. I wish you success!    

Costco Wholesale Corporation,"The beat goes on," March 2012

From time to time I make available published research. In March 2012, I published a research report on Costco (COST) that addressed market share and store penetration rates in the U.S. among other company and industry issues.

For a link to report go to:

http://www.slideshare.net/GreggCarlson1/costco-retail-industryanalysismar2012-24082713

Please contact me if you have any questions.