How to develop an ETF trading system that works

Technically speaking, a multi-asset 1/N equities portfolio with uncorrelated assets and periodic re-balancing is “system trading”. It’s just a set of rules or a methodology that one follows mechanically to make investment adjustments with the typical goal of  increasing investment returns and decreasing the variability of the returns. But usually the term “system trading” refers to more complex, and typically computerized, trading algorithms. And that’s what I want to talk about: sophisticated systems which require some mathematical programming skills to implement.

Parameter estimation error

The biggest problem associated with system trading  is called “curve fitting” or “over fitting”. Trading systems typically consist of a model or a set of rules which have a number of free parameters. These parameters are usually estimated using historical data. If there are too many parameters and/or too little historical data, the model will read too much into the historical data and will be inaccurate on new data – sometimes extremely inaccurate. And this problem isn’t unique to just highly sophisticated models with lots of parameters. It can occur with even the simplest models.

When you get the itch to optimize a trading system’s parameters, think about this example:

For example, pretend it’s January of the year 2000, and we want to build a simple asset allocation portfolio, which we will periodically re-balance, consisting of two low correlation assets: stocks and bonds. We have only one parameter to estimate: the proportion of our portfolio invested in stocks.  We pull up 20 years of historical data and, using some trial and error, we estimate that the optimal value of our parameter is around 0.9 or 90%. It’s easy to see why: from 1980 to 2000, stocks pretty much monotonically increased in value – greatly outperforming bonds. Confident that we have a robust portfolio based on twenty years of historical data, and likely to return 30 or 40% this year, we put nearly all our funds into stocks. Two and a half years later, our portfolio will have lost some 40% of its value in the dot com crash.

What happened? Simple. We over-fit a model with only one parameter even though we used twenty years of data. Imagine what could happen if we used a sophisticated model with 5 parameters fit to 10 years of data. We could lose some real money.

The failure of the model on new data was caused by something called “parameter estimation error”. We estimated our parameter based on limited historical data which turned out to have no predictive value for what was coming. We would have been better off assuming that we couldn’t predict the future and used the naive 1/N rule, or 50% stocks and 50% bonds. Unfortunately, if we had back tested such a system in January 2000, we would have been unimpressed by the results. The strategy of buy and hold, which is what most people compare their trading strategies to, would have greatly outperformed our naive strategy. Any investment advisor using such a 50% bonds strategy back in 2000 probably would have been considered a loser who missed the bull market and wouldn’t admit it. Perhaps at this point you have more appreciation for advisors who focus on absolute returns rather than relative returns.

How to tell if a system is vulnerable to estimation errors

If you are contemplating buying, building or subscribing to a trading system, the only way to really know if it’s vulnerable is to understand the model it was built on, how sensitive the system is to parameter values and how they were chosen, how much and the quality of the historical data the system was tested on, and how it has performed on new, previously unseen data since it was built. The best case is a system that has very few, naively chosen, parameters to which it is insensitive to, and tested over a wide variety of economic and profit cycles, crashes, manias, etc, before and after it was developed.

The developers of solid, non-optimized (non-trivial) systems have a number of problems: 1) if they reveal enough information to assure their more sophisticated customers that their system is robust, they practically give the strategy away, 2) non-optimized system performance will always be worse than a curve-fit system, putting them at a marketing disadvantage because, 3) the amount of historical data available is limited, and 4) it may take many years to demonstrate, with any certainty, that a system performs as well on unseen data as it did in back-testing, and 5) customers tend to ignore boring, non-optimized systems and go after shiny new systems that bolt upwards right out of the gate.

Even if you do get access to all this information, you still need to have enough knowledge to properly assess the system and to ask intelligent questions.

Example of a system with a minimum of estimation error

As an illustrative example, I will introduce you to a multi-asset portfolio system that adjusts its allocations weekly and is based a the four asset 1/N portfolio (using short term treasuries, long term government bonds, stocks, and gold) but use a little bit of Machine Learning to tweak the allocations slightly to follow the trends.

But only a little. If stocks are in a strong trend upwards, I want to be slightly over exposed to them. If gold trends monotonically down in the future, I want my portfolio to be slightly underweight gold.

But to do this I’ll need to add another asset to the portfolio which I am pretty confident will tend to go up in value during a crisis. I want to do this because over-weighting cash will not offset loses in the other asset classes during a financial panic as the system is essentially constrained to make only minor adjustments to the 1/N allocations. For this example the asset I’ll use is an inverse S&P 500 fund. This introduces a serous drag on this portfolio, essentially canceling out stocks, so I’ll simulate the use of leveraged (2x) long bond funds and stock index funds to overcome some of this friction. Secondly, I’ll need a specific technique to do the tweaking. For this I’ll use something called Direct Reinforcement Learning [1].

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Though Direct Reinforcement Learning requires a lot of parameters, methods exist which can reduce the effective number of parameters for this type of system. Instead of optimizing the parameter values, I’ll use the average of the recommendations of the system over a wide range of parameter values. For example, if I have three parameters, a, b, and c, and we give each a range of 0 to 1 and an increment of 0.1, then I could average the recommendation of the system over all 11³ combinations:  [0,0,0], [0.1,0,0], … [1,1,0.9], [1,1,1]. Hopefully the system will be relatively insensitive to some parameters and I can just use a representative value or just a few widely spaced values to approximate using the full range and save a great deal of computational time.

Most systems will inevitably perform much better over a tighter range, say, for example, from 0.2 to 0.4. But remember the curve fit example at the beginning of this article when you observe this and are tempted to tighten the range. The example would also have performed much better in back-testing at a tighter range, say 0.8 to 1.0, than it would over the full range of 0 to 1. (You’ll note in this particular case that averaging the recommendations over the full range from 0 to 1 is just the recommendation at the middle, 0.5).

The graphic below shows the back-testing results of this system (the black line). The foundation of the system, the 1/N base portfolio (aka the permanent portfolio), is the blue line. As you can see, except under exceptional circumstances, like the long bull market from 1997 to 2000, or the 2008 financial system crash, the system is pretty much tracks the permanent portfolio, which is supporting evidence that we haven’t tweaked it too much.

Click the graphic for a larger picture:

This system has an average yearly ROI of about 11%, a maximum (end of week) draw down of 9% and Sharpe ratio of about 1.3 over the period of September 1995 through the middle of April, 2012, based on weekly data. By comparison, the permanent portfolio has an average yearly ROI of about 8%, a maximum draw down of 18% and a Sharpe ratio of about 1.0.

Suggested Steps

1. If you haven’t had much programming experience, I suggest you use the programming language R. It’s free, relatively easy to learn and there are lots of free resources available on the web. Search for “programming R”.
2. Download the papers below and duplicate Fig. 2 in the second paper, which is a single artificial asset trend following exercise.
3. Duplicate Fig. 10 in the first paper, which is a portfolio with three artificial assets.
4. Modify your portfolio system to average over a wide range of parameter values if you haven’t already.
5. Replace the artificial assets with weekly data from the funds “VFINX”, “VUSTX”, “TWUSX”, “CEF”, and “RYURX”. These are easily downloaded from Yahoo finance. You’ll need to write a function to double the returns of the first two funds to simulate 2x leverage.
6. I used training periods ranging from 50 to 75 weeks, 10 epochs for training, regularization factors ranging from 0.1 to 0.5 and I averaged the results over a rho vs. eta matrix with values ranging from 0.01 to 0.1.  I used a softmax output with a=2 (see equation 5 in the first paper).
7. Feed the system with data up to the year 2000 and optimize the parameters to this data. Then test it on data from 2000 to present.
8. Determine how sensitive the system is to increasing transaction costs.
9. Try using other mutual funds or ETFs.
10. Try simulating the use of higher leverage (x3) funds. How much leverage can the system handle?
11. Check out other approaches, for example, this.

References

[1] J. Moody, et al, Performance Functions and Reinforcement Learning for Trading Systems and Portfolios, Journal of Forecasting, Volume 17, Pages 441-470, 1998 [pdf]

[2] J. Moody, M. Saffell, Learning to Trade via Direct Reinforcement, IEEE Transactions on Neural Networks, V. 12, No. 4, July 2001 [pdf]

If you are interested in purchasing an exchange traded note, better read the prospectus extremely carefully, or, better yet, hold off purchasing any for the time being:

From Invest with an Edge:

The industry has promulgated the idea that what makes ETFs and ETNs unique is their ability to create and redeem shares on demand through in-kind and cash exchanges with Authorized Participants.  I, and the majority of investors, believe this feature constitutes the soul of an ETF, makes it a unique vehicle, and provides investors with the confidence that these products will trade at prices close to their net asset values.

However, investors are often not aware that it is even possible for this process to be broken.  Furthermore, there is not an easy way to determine if a given ETF or ETN has a broken creation/redemption process.  Investor perception is that ETFs and ETNs trade very close to their NAVs.  As a result, investors can be caught unaware when these broken ETFs and ETNs are trading at premiums as high as 1,000% or more, as was the case for the former ELEMENTS MLCX Gold Index ETN (GOE) back in 2009.

Read the entire article here.

And from the Intelligent Investor:

Or consider the Credit Suisse Long/Short Index ETN, which seeks to replicate the returns of certain hedge-fund strategies. The front page of the prospectus reports the ETN’s “annual investor fee” as 0.45%. Not until page 30 of the 84-page document can investors determine that they also will incur an “accrued holding rate” of 0.7% (adjusted quarterly) and an “accrued index adjustment factor” fee of 0.5%—implying a total annual cost of 1.65%, or more than triple the reported fee.

High management fees aren’t the only way these instruments can raise investors’ costs. According to XTF.com, eight ETNs were trading at premiums of 5% or more this week. In one extreme example, to buy $100 worth of assets at iPath Dow Jones-UBS Natural Gas ETN, you would have had to pay up to $196.

Read the entire article here.

Finally, according to Reuters, the FINRA is currently investigating ETNs:

A spokeswoman for the Financial Industry Regulatory Authority said on Thursday the regulator is “looking at the events and trading” activity surrounding a sharp plunge in the price of an exchange-traded note designed to track stock market volatility.

“We have a review under way looking at a host of issues relating to ETNs and other complex products,” the spokeswoman said.

Read the entire article here.

If you haven’t already, visit the previous page, Stock Investing for Beginners. This page, and the pages that follow it, will make a lot more sense.

Disciplined investing is easier if you believe the future is unpredictable.

If I put together an investment portfolio right after reading a book about how the S&P 500 could reach 5000 in the next few years, I’m very likely to seriously overweight emerging market equities (or whatever is hot at the moment), use leverage, and minimize my “safe” investments in such things as bonds and cash. If I read a book about the ominous increase in the federal budget deficit, the coming killer plague or super volcano explosion, I’m likely to heavily overweight gold and commodities. Even if I put my investment decisions into the hands of a professional, they will probably only act on my existing biases but bend them slightly to help themselves to higher fees.

If you want to put a stop to your investments getting jerked around by your emotions then adopt an investment strategy that makes no assumptions about the future, and keep reminding yourself that the future is unpredictable.

A Simple Portfolio using Stock and Bond Funds

The simplest example of a non-forecasting investment strategy is a 50% – 50% stocks and long bonds portfolio using the Vanguard 500 Index Investor mutual fund (VFINX), which tracks the Standard and Poor’s 500 index of large U.S. corporations [1], and the Vanguard Long Term Treasury mutual fund (VUSTX) which invests in 15 to 30 year maturity U.S. Treasury securities including bills, bonds and notes. [Similar ETFs are the SPDR S&P 500 Index fund (SPY) and the iShares Barclays 20+ Year Treasury Bond Index fund (TLT)].  U.S. Treasuries are considered to be relatively safe investments in the event of economic turmoil because the U.S. government can simply print money to back them up. [2] Both mutual funds can be purchased free of trading charges via a Vanguard account, and most retail brokerages offer similar products also without trading fees.

The two fund strategy is re-balanced every 3 months to keep the assets near the target allocations, although re-balancing every year wouldn’t change the results much and may have tax advantages. The chart below contrasts the performance of the S&P 500 with the two asset strategy over the time period of 1997 to 2012.

This simple strategy, which assumes no knowledge of what will happen in the future, and which uses only two low correlation assets [3], had an average return on investment (ROI) of 7.6% per year over a  roughly 15 year period from 1997 to 2011, while the long-only investment returned only 4.9%. And the volatility was dramatically reduced: the maximum draw-down was 25% versus a gut-wrenching 55% for the buy-and-hold strategy.

The real benefit of this simple strategy is that it can protect the majority of our funds in the event of a catastrophic stock market plunge caused by a severe and unpredictable event such as a pandemic, a market bubble bust, the outbreak of war, or the default of a developing country. Such events aren’t just hypothetical possibilities; each has a very real probability of occurring and some happen on a regular basis historically.

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Simple Strategy Plus: Using a Concentrated Mutual Fund in place of an Index

In the above example, I used a low fee, no load mutual fund which tracks large capitalization U.S. firms. If we had used the same strategy but invested the stock half of our funds in a concentrated value mutual fund such as Oakmark Select I (OAKLX) back in 1997, we would have done better – primarily due to higher performance during the 2000 to 2002 time frame in this case.

Using the Simple Plus strategy, the ROI improves to 10.0% and the maximum draw down is roughly the same at 27.5%. In general, concentrated fund managers tend to outperform more broadly diversified ones, but it would be a good idea to diversify across a number of different managers. [4] The downside to using concentrated funds is that there will be times when they under perform the index and they are more vulnerable to individual stock price shocks and manipulations. [5] The point is that we aren’t limited to using only broad index funds and the better any of our investments performs the better our portfolio will perform.

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Why 50%-50%?

Wondering why I haven’t talked about other stocks and bonds portfolios, such as an “aggressive” 70% stocks and 30% bonds portfolio or the “efficient frontier”. The reason is that they perform worse than the 1/N naive diversification rule (in this case, 1/2 and 1/2) over long periods of time. A 70% stocks/30% bonds portfolio is assuming that stocks will outperform bonds in the future. How can anyone possibly know that? Researchers have found that the naive strategy typically has a higher performance out of sample and a lower turnover than the policies from “optimal” asset allocation strategies which use past returns to predict the optimal allocation for the future. [6]

From VisualNews.com: Click for a gigantic graphic.

Infographic by Visual News

Equities Should Be Considered as One Asset

Can different equity funds can be considered separate assets? Most equity assets are correlated these days, whether they are health care funds, energy stocks, small cap growth Latin America stocks, or whatever.  They didn’t used to be, but they almost all are now, with a few exceptions like natural gas. If you want to use multiple equity funds, the safest thing to do is to consider them to be equal sized pieces of a single equities asset. In pie chart form, this simple portfolio might look like this:

Or, in terms of actual, low expense, ETF funds:

Long government bonds: TLT  50%
Technology: XLK  10%
Emerging markets: VWO  10%
Growth: VUG  10%
Dividend growth: VIG  10%
Retail: XRT  10%

To demonstrate what can happen if a portfolio is over weighted with equities, consider a portfolio of equal parts Oakmark Select concentrated value fund (OAKLX), the Vanguard 500 Index Investor mutual fund (VFINX), and the Vanguard Long Term Treasury mutual fund (VUSTX). This portfolio outperforms the simple strategy in terms of returns, but it suffers a  huge draw down of almost 40% during the height of the financial crisis – exactly what we want to avoid.

 

For a more diversified examples, continue to the next page, Adding Gold to a Portfolio followed by The Talmud Portfolio and finally The Permanent Portfolio.

Related Posts

1. Stock Investing for Beginners
2. Adding Gold to a Portfolio
3. Example of a Talmud Portfolio
4. The Permanent Portfolio
5. Investing in Growth Stocks

References

[1] Standard and Poor’s S&P 500 Index

[2] B. Noeth, R. Sengupta, Flight to Safety and U.S. Treasury Securities, The Regional Economist, July 2010 [pdf]

[3] T. C. Chiang, J. Li, The Dynamic Correlation between Stock and Bond Returns: Evidence from the U.S. Market (March 17, 2009)

[4] J. Busse, C. Green, and K. Baks, Fund Managers Who Take Big Bets: Skilled or Overconfident, American Finance Association, 2007 Chicago Meetings Paper

[5] V. Misra, M. Lagi, Y. Bar-Yam, Evidence of market manipulation in the financial crisis, Cornell University Library

[6] V. DeMiguel, L. Garlappi, R. Uppal, How inefficient are simple asset-allocation strategies?, 2005 [pdf]

[7] HSBC Global Research, Risk on – Risk off, Fixing a broken investment process, April 2012 [pdf]

How to invest in the stock market like a professional

Unfortunately, we humans are subject to emotional responses that can result in some spectacular investment misadventures. It turns out there is a part of our brain that detects and directs us to avoid danger, and another, separate region, that recognizes and pursues opportunities.  In other words, fear and greed control centers. Unfortunately, these control centers don’t talk to each other and, because of the speed at which they react, they don’t negotiate or take prisoners either. These dueling controllers cause us to sell during a scary market drop and then turn around and buy aggressively when the markets rise dramatically.  [1] In the good old days, investment advisers could ignore the phone to help panicky investors ride out a market crisis, but today the same technology that gives us instant access to our investments makes it easy for us to act impulsively on these fear and greed emotions.

Cognitive Biases

We are also subject to behaviors called cognitive biases which are patterns of poor judgment. It’s possible that these behaviors led to a greater chance of survival or reproductive success in our ancestors or maybe our brains just can’t physically process some types of data very well, but they are not helpful to us as investors.

Wikipedia maintains a disturbingly long list of these patterns of poor judgment. Here’s just a few:

1. The Bias blind spot is the tendency not to be aware of or compensate for cognitive biases.
2. The Bandwagon effect  or herd mentality is the tendency to follow the crowd. This causes investors to buy into bubbles when they are near the top and to sell after everyone else has sold on the way down.
3. A Confirmation bias is the tendency to seek out conformational information or interpret information in such a way that it confirms what we thought we already knew. This bias tends to lead to overconfidence.
4. Loss aversion is the tendency for people to strongly prefer avoiding losses to obtaining gains. This can cause investors to sell off their best performing investments to buy more of their worst performing investments hoping to recoup their losses.
5. Outcome bias is the tendency to judge a decision by its outcome instead of on the quality of the decision when it was made.

On top of the emotional impulses and cognitive biases that can cause us invest poorly, there are other decision blind spots which can undermine what appear to be carefully thought out investment strategies.

The Observation Selection Bias

When we mistakenly focus only success stories, we risk overestimating historical investment performance. For example, many beginning investors invest in penny stocks (i.e., stocks that sell for less than a dollar) believing that they will make more money on the winners than they can lose on the losers. After all, the losers can only go down to zero but there is no limit to how far the winners can go up.  However, they are almost always basing this assumption on tests with stock data that has a survivorship bias. [2]

In other words, they have selected what they assumed was a random sample of penny stocks from 5 or 10 years in the past that survived until the present, and concluded that they could have made a considerable amount of money.  Unfortunately, there was no way to have known at the time the selection was made that the stocks selected would survive 5 or 10 years into the future.

Unfortunately, this observation selection effect undermines decisions on a large scale every day. Everyone knows that, over long periods of time, stocks have outperformed bonds.  This is the basis for the investing strategy known as buy-and-hold. An observation selection effect bias is at least partly responsible for this apparent superiority of stocks. Although most historical stock data favors owning stocks, the data is typically from the American and British exchanges, which have been unusually stable. If we examine all stock exchanges, we see that wars, political upheavals, and currency collapses have actually destroyed quite a few of them. From 1921 to 1996, while U.S. equities returned about 5 percent, all other equities from 39 different markets had returns of only about 1.5 percent. [3]

Moreover, if we look at a longer time frame, the unusual stability of the American and British stock exchanges is even more dramatic. Examining financial crises going back eight centuries, researchers have observed that serial defaults (i.e., a succession of defaults, one after the other) are actually the norm for developing countries, and these defaults can and have led to financial crises worldwide repeatedly. Although one or two decade long lulls between defaults were not uncommon, each lull was always followed by a new wave. [4] In fact, market crashes have described by some researchers as “a hearty perennial” due to the regularity of their occurrence over long time periods. [5]

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The Data Mining Bias

Also known as data-snooping, a data mining bias occurs when an investigator proposes a hypothesis after noticing a correlation in historical data instead of postulating a hypothesis first and then testing it on unseen historical data. Typical tests of statistical significance assume that the data has not been seen prior to the test. If this is not the case, a model may appear to be strongly supported by the data when, in fact, it is just a chance correlation and it doesn’t hold up on new data. [6] In developing a trading or investing strategy, a developer will always have previously examined historical data or, if using their own experience, they will have already noticed some correlation they want to take advantage of. When they test their strategy on historical data, the strategy is likely to do well, but, going forward, the correlation probably won’t hold up. [2]

Passive Investing Strategies

The average investor needs a fundamentally sound, non-biased investing strategy that they can commit to stick with even when their control centers are attempting mutiny. Strategies based on the unusual stability and performance of the U.S. and British markets (for example, long term buy-and-hold) are not supported by the aggregate of stock data from all markets over long time periods. Strategies based on fitting models to historical data such as “stock picking” or mechanical trading systems are prone to data mining biases which, in some cases, make them worse than doing nothing. As a result, the strategy used by passive investors (investors who are not frequently churning their investments) is called asset allocation, which relies on diversification among uncorrelated assets and rebalancing to generate returns rather than attempting to predict future prices.

To understand asset allocation, it is helpful to understand the sources of risk in a portfolio because, in the end, it will be desirable to spread our risk out over all of these buckets. There are typically said to be four, somewhat uncorrelated, market risk factors that determine the typical portfolio’s risk: [7]

1.)   Equity risk is the risk that stock prices will drop.

2.)   Interest rate risk is the risk that interest rates will change against you.

3.)   Currency risk is the risk that foreign exchange rates will change against you.

4.)   Commodity risk is the risk that commodity prices will change.

The Classical Mean Variance Diversification Theory

Harry Markowitz mathematically formalized the observation that if you combine a number of assets that aren’t correlated you can reduce your portfolio risk. [8] From this he defined an optimal portfolio, in terms of risk to reward at a given level of reward, called the mean-variance portfolio. The mean-variance portfolio for a particular investor will depend on the investors risk tolerance and the historical returns and variance of returns for each asset in the portfolio. An example of an asset combination is the stocks and bonds portfolio which is typically recommended by investment advisors for retail investors. By adjusting the ratio of stocks to bonds (for example, 70% stocks with 30% bonds or 50% stocks and 50% bonds) one can adjust the amount of risk (sometimes referred to as variability of returns or volatility) of a portfolio and the risk can sometimes be reduced dramatically for only a small performance penalty.

Before continuing, I should mention that studies have shown that somewhere around 90% of the variability of portfolio returns is determined by asset allocation. [9] The variability of returns should not be confused with portfolio’s average returns. Average returns are almost entirely dependent on the asset allocation because portfolio managers, on average, don’t beat the market. [10]  Typically, an asset allocation that has made more money in the past will also have had a higher volatility.

Portfolio Rebalancing

When uncorrelated assets are combined in a portfolio, the ratio of each asset to the total tends to drift as some assets will almost certainly outperform others and alter the risk characteristics of the portfolio. To maintain their risk protection, the investor will need to periodically sell off some of the outperforming assets to buy more of the underperforming assets. Unfortunately, Markowitz didn’t specifically address how to do this. One study examined the effect of different rebalancing schemes on a 50% stocks and 50% bonds portfolio and found that monthly rebalancing was slightly better than quarterly and only a tiny bit better than yearly over the 1968 to 1991 time period. Rebalancing based on thresholds (for example, any one equity exceeds +/- 5% of its target) were roughly equivalent to quarterly rebalancing. [11] A theoretical study found that periodic and threshold rebalancing strategies perform similarly as long as they are performed more frequently than every two years or have tolerance thresholds less than 10% (for a two asset portfolio anyway). [12] So, while rebalancing is needed in order to keep a portfolio’s risk/reward balance intact, the exact methodology does not appear to be critical.

Under some conditions rebalancing significantly increases returns beyond the geometric mean of the individual asset returns in a portfolio. This “rebalancing bonus” is most pronounced for assets that are volatile and negatively correlated. When highly volatile and weakly correlated assets are present in a portfolio, it may be more beneficial to use a threshold strategy to capture this bonus. [13]

Adding Gold to a Portfolio

Many investors include some gold in their portfolios, although typically no more than 10-15%, as a means of increasing the diversification of their holdings or as a safe haven (i.e., to add diversification in times of extreme market stress). Gold is also thought of as a hedge against inflation and currency fluctuations. As the dollar goes down in value relative to other currencies, or inflation increases, the price of gold (in dollars) tends to go up. Additionally, gold may add some protection to stock holdings against black swan events (infrequent, unexpected, negative market events such as market crashes, currency devaluations, wars or natural disasters) albeit only for a limited time historically (so investors should consider rebalancing within a few weeks of the event). [14] The addition of gold to a stocks and bonds portfolio has historically increased returns and reduced risk. [15]

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The Talmud or 1/N Portfolio

The Talmud is a record of rabbinic discussions or debates on a wide number of topics, one of them being an asset allocation strategy recorded around 1500 years ago which is known as the 1/3 rule, or, more generally, as the 1/N rule for N assets. [16] The original asset classes suggested were land, business interests and reserve funds (probably meaning coins). A modern version of the 1/N portfolio which has been reportedly used successfully holds real estate investment trusts, stocks and U.S. bonds. [17] In spite of it’s seemingly naïve nature, the 1/N rule has been found to outperform sophisticated mean variance strategies on the majority of real data sets studied, especially when N is small. [18]  The reason for this may be that the strategy doesn’t assume that past return volatility predicts future volatility, unlike the mean-variance method which tries to predict the best allocation using historical prices. The mean-variance method also assumes that returns follow a gaussian distribution – when we know for a fact that they don’t.

The Permanent Portfolio

The permanent portfolio, first published by Harry Browne [19], is a specific 1/N portfolio which builds on the stocks/bonds/gold portfolio by adding cash as a forth component. Basically, the underlying theory is that one should hold four equally weighted assets – gold, cash, stocks, and bonds- which tend to move in different directions during different stages of the four economic cycles: inflation, deflation, prosperity and recession. During times of inflation, gold tends to do well, during deflation bonds tend to do well, during times of prosperity stocks soar, and during recessions, cash is best. This portfolio has returned about as much as the overall stock market in terms of returns in the 1974 to 2008 time frame but with dramatically lower volatility,[20] [21] perhaps due to the remarkably low correlations of  its components. [22] The strategy certainly worked well recently for Icelanders – whose country defaulted on its debt in 2008 – by returning a profit of 28% while the Icelandic stock market suffered a 90% loss.[23]

Diversification Beyond the Permanent Portfolio

There are numerous other real assets that can be used to diversify a mean-variance or 1/N portfolio beyond the assets previously mentioned. Examples of real assets are art, antiques, rare coins, land, and commodities such as oil, timber, rice, industrial metals, livestock, etc. [24] Because of the difficulty of buying and selling small amounts of many of these assets, they are typically only used by very wealthy investors. Beginning investors should be wary of commodity exchange traded funds (aka ETFs) because they may not track the underlying commodity futures prices very well, [25] and there is an unfortunate history of price manipulation of some of the underlying assets. [26]

Conviction Stocks

Many sophisticated investors also hold what I call conviction stocks. A conviction stock is one that you have high expectations for in the long run for a good reason. You may have some (legal) insider information (you may work for the company or work for a supplier, for example) or you may have done research and have concluded that the company’s prospects are potentially spectacular. Best case, the price of the stock will be driven primarily by something other than the general market and will thereby add some additional diversification to your portfolio. Most advisors would probably recommend that no more than 10 to 15% of a portfolio should be in conviction or employer stocks because the risk will begin to dominate the potential rewards beyond that.

Which investment strategy is best?

The “best” strategy depends on the investor. How much risk the investor is willing to take, how much money they have to invest, and how well the investor can control their emotions during tough times, among other things, determine which strategy is the best. And most people don’t even know how much risk they can stomach until that day of wild swings arrives.

The best investors probably aren’t as much smart as they are disciplined.

The problem with unconventional portfolios like The Talmud and the Permanent Portfolio is that most investors will bolt after a couple of years of underperforming the market – which is certain to happen.  [22] Non-conventional portfolios are probably utilized primarily by wealthy investors whose advisers have taken the time to thoroughly educate them and who are willing to accept sub-market returns for years in exchange for the likelihood of preserving their wealth when the inevitable financial crisis erupts. [17] 

Should you get an investment advisor?

Small investors who are self-educated and disciplined can also easily take advantage of the portfolio strategies on this page without an advisor.  Investment advisers have been found to, on average, push investors into funds that benefit the advisor, not the client. [27]  And even if they see a crisis coming, they may not be able to warn you: [28] 

 Bernstein, the chief strategist, has actually been bearish for much of the past decade. Given his recent disposition toward market pessimism, I asked him why he didn’t tell Merrill’s clients to dump their equities seven months ago. “I said it as best as I could within reasonable professional standards,” he said. “I’m not going to yell ‘Sell, sell, sell!’ I’m not going to go out and be irresponsible.”

 Next: Investment Portfolio Examples

Related Posts

1. Investment Portfolio Examples
2. Effect of Adding Gold to a Portfolio
3. Example of a Talmud Portfolio
4. The Permanent Portfolio
5. Adding Growth Stocks to a Portfolio

Recommended

R. Gibson, Asset Allocation, 4th Ed, McGraw-Hill; 4th edition (December 20, 2007)

W. Bernstein, The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk, McGraw-Hill; 1st edition (September 22, 2000)

References

[1] D. Lenick, K. Jordan, Financial Intelligence: How to Make Smart, Values-Based Decisions with Your Money and Your Life, FPA Press, April 21, 2010

[2] R. Kan, G. Kirikos, Biases in Evaluating Trading Strategies, Nov. 1995 [pdf]

[3] P. Jorion, W. Goetzmann , A Century of Global Stock Markets, Yale School of Management Working Paper No. F-55, 1996

[4] C. Reinhart, K. Rogoff,  This Time Is Different: Eight Centuries of Financial Folly, Princeton University Press; 1st Edition (September 11, 2009)

[5] C. Kindleberger, R. Aliber, Manias, Panics and Crashes: A History of Financial Crises, Sixth Edition, Wiley, 5th edition (October 4, 2005)

[6] J. Ioannidis, Why Most Published Research Findings Are False, PLoS Medicine 2(8) 2005

[7] Wikipedia Market Risk

[8] Markowitz, H.M.,  Portfolio Selection, The Journal of Finance, 7 (1): 77–91, March 1952

[9] G. Brinson, B. Singer, G. Beebower, Determinants of Portfolio Performance II: An Update, Financial Analysts Journal, May/Jun 1991; 47, 3

[10] R. Ibbotson, The Importance of Asset Allocation, Financial Analysts Journal, Vol 66, No. 2

[11] Robert D. Arnott and Robert M. Lovell, Rebalancing: Why? When? How Often?, The Journal of Investing 2, No. 1 (Spring 1993): 5.

[12] Y. Si, The Benefits of Portfolio Rebalancing and How They Can be Achieved, Feb. 27, 2009 [pdf]

[13] W. Bernstein, The Rebalancing Bonus: Theory and Practice, efficientfrontier.com website

[14] D. Baur, B. Lucey, Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold, The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, 05

[15]  iShares.com Gold Benefits Calculator

[16] R. Duchin, H. Levy, Markowitz Versus the Talmudic Portfolio Diversification Strategies, The Journal of Portfolio Management Winter 2009, Vol 35, No. 2, pp 71-74

[17] J. Grote, The Talmud Strategy: A couple rely on ancient principles to build a thoroughly modern clientele , Financial Planning, Sept. 1, 2001

[18] J. Tu, G. Zhou, Markowitz Meets Talmud: A Combination of Sophisticated and Naïve Diversification Strategies, April, 2009

[19] H. Browne, Fail-Safe Investing: Lifelong Financial Security in 30 Minutes, St. Martin’s Press, 2001

[20] G. Considine, What Investors Should Fear in the Permanent Portfolio, Advisor Perspectives website  March 22, 2011

[21] Crawling Road blog, December 22, 2008

[22] W. Bernstein,  Wild About Harry , efficientfrontier.com website 2010

[23] European Permanent Portfolio blog, June 16, 2010

[24] Real Assets and Inflation Hedge Investing, E. O’Donnell, NEPC, LLC [pdf]

[25] P. Robison, A. Loder & A. Bjerga, ETFs Imperil Investors as Contango, Pre-Roll Conspire, bloomberg.com, Jul 22, 2010

[26] W. Cohan, A Conspiracy With a Silver Lining, The New York Times, March 2, 2011

[27] S. Mullainathan, M. Noeth, A. Schoar, The Market for Financial Advice: An Audit Study, NBER Working Paper No. 17929, Issued in March 2012

[28] J. Goldberg, Why I Fired My Broker, The Atlantic, May 2009