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The CBOE Put-Call Ratio: A Useful Greed & Fear Contrarian Indicator? – A Statistical Analysis

Author: Robert C. Koch

Summary

  • On average, option traders lose about 80% of the time (Nithin Kamath, CEO Zerodha, July 4th, 2021). Thus, the put to call ratio is often used as contrarian indicator when reaching extreme levels.
  • In this article, we will analyze the effectiveness of the put-call ratio as contrarian indicator to exploit extreme levels of greed and fear within the option market.
  • To reduce the subjectivity of interpretation in the term “extreme greed and fear levels of the put-call ratio”, we apply descriptive statistics to derive precise thresholds to identify appropriate entry- and exit points.
  • Afterwards, we analyze these entry- and exit points based on their average forward-looking returns on the S&P 500 and test them for statistical significance.
  • Finally, we introduce a new way on how to improve the trading results by applying the z-score statistics to the put-call ratios.
  • The put-call ratio as well as its z-score normalization, show statistical significances in identifying attractive entry- and exit points.

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The Most Rewarding Portfolio Construction Techniques: An Unbiased Evaluation

Abstract

Our research paper, published and awarded as Editor’s Pick on Seeking Alpha, analyzes and compares ten modern portfolio construction techniques by applying an advanced Monte Carlo Simulation. This enables an unbiased view of the pros and cons of each single portfolio construction technique.

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Diversification: Failure Or Free Lunch During Market Turbulence?

Abstract

Our research paper, published on Seeking Alpha analyzes the stress correlation behavior of single stocks.

Content

Since Markowitz, portfolio diversification is one of the most recommended and well known investment strategies among the financial industry.

In general, diversification is an investment strategy which should reduce risk within a portfolio by investing in different securities. If a price of a security does not move in the same direction like other stocks within the portfolio, a price decrease in that stock can be offset by a price increase in a different stock. For that reason, the volatility (risk) of the entire portfolio is limited although the expected returns of each security and thus the expected return of the portfolio remain unchanged.

However, diversification is only suitable to reduce/eliminate unsystematic risk (company specific risks like losing the market leadership, lack of innovation etc.) while the systematic risk (changes in the macroeconomics factors) remains predominant and cannot be diversify away. For example, the European dept crisis is a good example of a systematic risk that affects the stock market while the lack of innovation by Research in Motion would be a good example for an unsystematic risk that an investor could face. Therefore the goal of diversification is to minimize the risks for which an investor is not expecting to be rewarded.

It is a widespread belief that correlation tends to increase among different asset classes (stocks, commodities etc.) during turbulent market conditions and that implies a reduction in the benefits arising from portfolio diversification. This is exactly the time when an investor depends on these benefits the most, to keep his portfolio stable.

Diversification can be considered at a number of levels. While diversification among different asset classes has attracted a lot of research, the focus of this article is on diversification within equities or to be more precise, within the entire stocks among the Dow Jones Industrial Average (NYSEARCA:DIA).

We investigate, if the correlations among stocks within the Dow Jones Industrial Average are increasing during the time they are facing turbulences.

The mathematical background for diversification is well known. When investors diversify among stocks that are not perfectly correlated (having a correlation coefficient “ρ” less than +1) the volatility of the portfolio will be less than the weighted sum of the volatilities of the individual securities. All other things being equal, the lower the correlation between the different stocks the greater the diversification benefits will be.

Table 1 contains following data:

  • The degree of correlation coefficient between each stock and an equally weighted index, where all stocks within the Dow Jones Industrial Average are given the same weights (Correlation To Average).
  • The average correlation coefficient between each stock when they are facing a down-turn (only those periods have been taken into account, where this particular stock has been in a draw down (Average Drawdown Correlation)).
  • The degree of correlation coefficient between each stock and the Dow Jones Industrial Average (Correlation To DJIA).
The degree of correlation coefficient between each stock and the Dow Jones Industrial Average

Table 1: The Degree of Correlation Coefficient Between Each Stock and an Equally Weighted Index.

Not surprisingly, stocks that show a high degree of correlation between them and the Dow Jones Industrial Average are also highly correlated to an equally weighted index, where all stocks within the Dow Jones Industrial Average are given the same weights. More importantly, their correlation coefficient tends to be higher in times other stocks within the DJIA are face a peak to valley event.

If we have a closer look at those five stocks that have the highest correlation coefficient, we can see that on average those stocks go down in more than 50 percent of the time, if any of all the other stocks within the Dow decreases. So in total, those stocks will decrease the benefits of diversification, especially in times of market turbulences.

The case is different, if we focus only on the top 5 stocks, in terms of a low correlation coefficient (green area). On average, those stocks tend to have an extremely low correlation coefficient in times other stocks are facing difficulties. In total, they fell in almost less than 45 percent of the time if any of all the other stocks within the DJI had decreased. So those stocks are increasing the benefits of diversification and therefore they minimize the risk within a portfolio significantly.

To prove those numbers, we have constructed two different portfolios:

  • Top 5 Stocks Portfolio: an permanently equally weighted portfolio with the best stocks in terms of low average drawdown correlation
  • Bottom 5 Stocks Portfolio: an permanently equally weighted portfolio with the worst stocks in terms of low average drawdown correlation
  • For both, there is no allowance for transaction costs or brokerage fees

Table 2 presents the results of our back tests from 2001/06/15 until 2012/06/01 on the two portfolios described previously. The first and second column tests the proposed Top 5- and Bottom 5 Stocks portfolio. The third column represents a buy and hold strategy on the Dow Jones Industrial Average.

Performance Ratios of the 2 Portfolios

Table 2: Performance Ratios of the 2 Portfolios

The Top 5 Portfolio has an annualized return of 5.5% while a buy and hold has only generated an annualized rate of return of 1.2%. More importantly, on a risk-adjusted basis (Sharpe Ratio), the Top 5 Portfolio is strongly outperforming the buy and hold.

Historical Performance

Chart 1: Historical Performance

If we have a closer look on the diversification benefits (reducing risk during turbulent market conditions), we can see that those stocks that have the lowest average draw down correlation, have also shown significant lower draw-downs in the past. The maximum draw down for the Top 5 Portfolio was only 37.9 percent compared to 70.1 percent for the Bottom 5 Portfolio. In total, the Top 5 Portfolio was reaching a new high after 716 days compared to 1115 days for the Bottom 5 Portfolio. The Dow Jones Industrial Average is still trading below its high from 2007.

Largest Drawdowns Top 5 Stocks

Table 3: Largest Drawdowns Top 5 Stocks

Largest Drawdowns Bottom 5 Stocks (with Highest Drawdown Correlation)

Table 4: Largest Drawdowns Bottom 5 Stocks (with Highest Drawdown Correlation)

Largest Drawdowns Dow Jones Industrial Average

Table 5: Largest Drawdowns Dow Jones Industrial Average

The Bottom Line

Diversification does not eliminate systematic risk. No investment strategy does. However, a well diversified stock portfolio reduces the risk within a portfolio significantly. Even in times the market faces turbulent conditions, diversification helps to reduce draw-downs considerably. In our study we have found no proof that stocks have a higher correlation coefficient to other stocks in times they facing draw downs. In general, diversification is not just about investing money in different kind of stocks; it’s about the idea of investing in low-correlated securities, able to utilize the full benefits from this well proven strategy. The basic principle is working as long as investors do understand what diversification is all about.

Note: This research publication was published on Seeking Alpha in July 2012.

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The Most Diversified Inflation-Proof Retirement Portfolio

Abstract

  • Inflation is always and everywhere a monetary phenomenon.
  • Investors will need an inflation-proof portfolio, since a heavy loaded bond portfolio won’t be the perfect hedge in a low interest-rate environment.
  • For conservative investors at or near retirement, inflation can be the biggest threat, since many of them have converted much of their portfolio into bonds.

Content

As a result of the global financial crisis, elevated levels of sovereign debt and extremely expansive monetary policies by all major central banks around the world have led to growing concerns about inflation among the investment community. Since 2008, central banks are keeping interest rates low by providing massive liquidity into their economies, whereas the probability of high inflation rates in the future has increased significantly.

Milton Friedman, a well known economist, stated once that “Inflation is always and everywhere a monetary phenomenon.” On Monday (4th March 2014), the five year US inflation expectations rose to their highest level in seven months, as investors are seeking insurance against the prospect that a recovering economy will stoke price pressures.

Basically, inflation is an increase in prices since there is too much money for fewer goods around. However, right now this is not an immediate problem, since the output gap of the U.S. has still a lot room for improvement and unemployment remains elevated, and therefore, the current inflation expectations remain quite low for the time being. Nevertheless, inflation will become a huge issue sooner or later; at the latest, when the economy is getting back on track.

Moreover, if this is the case, interest rates will rise too, and fixed income investors will suffer the most, as bond prices will decline and inflation will wipe out all the earned interest and principal. Even Warren Buffet said recently in an interview that low interest rates and inflation should dissuade investors from buying bonds and other holdings tied to currencies.

In addition, for conservative investors at or near retirement, inflation can be the biggest threat, since at this stage, many of them have converted much of their portfolio into fixed income to protect capital. As a consequence, investors will be in the need of an inflation-proof portfolio, since a heavy loaded bond portfolio won’t be the perfect hedge for such a scenario. Diversifying a portfolio’s income stream with investments that are less affected by inflation is the only way to fight the upcoming inflation threats. Moreover, investors at or near retirement are in the need of a more or less low risk/volatility portfolio that should generate stable returns.

In general, there are enough asset classes around which should provide a good hedge against an inflationary environment:

  • iShares Dow Jones Select Dividend Index (DVY): The DVY is invested in the 50 highest dividend yielding stocks listed in the S&P Composite 1500 Index which have increased dividends every year for at least 25 consecutive years. Dividend stocks represent a good opportunity for greater yield, and the potential for capital appreciation which can help to protect against inflation costs. According to a research conducted by Black Rock, stocks have historically outperformed bonds by an average of 4.9 percent in years with above-average inflation.
  • SPDR Dow Jones REIT (RWR): The RWR tracks the Dow Jones U.S. Select REIT Index which follows companies that operate commercial real estate properties across the country. Real Estate Investment Trusts (REIT) own and operate income-producing real estate. They are required to distribute at least 90 percent of their taxable income to shareholders annually in the form of dividends and in turn, they can deduct those dividends paid from their corporate taxable income. However, real estate investments provide a natural protection against inflation, as rents tend to increase when prices do.
  • PowerShares Dynamic Food & Beverage (PBJ): The PowerShares Dynamic Food & Beverage ETF is based on the Dynamic Food & Beverage Intellidex Index. The Dynamic Food & Beverage Intellidex Index is invested in US food and beverage companies that are principally engaged in the manufacture, sale or distribution of food and beverage products, agricultural products and products related to the development of new food technologies. Since inflation has a direct adverse impact on food prices, this ETF provides a good way to get exposure to that sector.
  • PowerShares DB Agriculture (DBA): The PowerShares DB Agriculture Fund (DBA) is based on the DBIQ Diversified Agriculture Index Excess Return. The index is a rules-based index composed of futures contracts on some of the most liquid and widely traded agricultural commodities. The Index is intended to reflect the performance of the agricultural sector. As already mentioned above, the agricultural sector provides a good hedge against a looming inflation environment.
  • Energy Select Sector SPDR (XLE): Companies in the energy sector can also provide other benefits like increased production or higher dividend payments as another source of return in addition to rising profit margins due to higher commodity prices. Investing in the common stocks of natural-resources producers is the easiest way to get on board.
  • SPDR Gold Shares (GLD): Gold is and always has been a perfect hedge for inflation, since it has fulfilled its role as a store of wealth for ages. It has been used as a form of exchange and currency and is has retained (increased) its value over time. If you think about the purchasing power of 1 dollar today with 20 years ago, this fact becomes even more evident.
  • iShares Barclays TIPS Bond (TIP): The iShares Barclays TIPS Bond is the largest exchange-traded fund for Treasury Inflation-Protected Securities. The TIP ETF combines the security of Treasuries with inflation protection in the form of Consumer Price Index-adjusted principal.

The main problem with the mentioned asset classes above is the fact that most of them are highly volatile/risky, and therefore, creating a conservative inflation-proof at or near retirement portfolio can be quite challenging.

Asset Classes and their average volatility and maximum loss

Table 1: Asset Classes and their average volatility and maximum loss

For that reason, we would like to highlight a conservative inflation-proof model portfolio which is regularly being updated on our website. The main target of the portfolio is to generate enhanced and stable returns above the average inflation rate and to minimize potential losses, even during times when the overall inflation expectations remain quite low. The “Inflation Proof Retirement Portfolio” is constructed by applying the so-called Maximum Diversification approach, which we have already reviewed extensively in previous Seeking Alpha articles. In general, the basic idea behind the maximum diversification approach is to construct a portfolio that maximizes the benefits from diversification.

First of all, diversification can be measured by the so-called diversification factor. This factor is the portfolio’s weighted average asset volatility to its actual volatility. The result of this calculation measures the essence of diversification. For a given set of assets, there is a long-only portfolio solution that maximizes the diversification factor. In other words, if the overall correlation coefficient of any underlying security increases, the less weighting it will receive, since its diversification benefits are decreasing. For that reason, the portfolio is balancing the risk of its underlying asset classes to minimize the overall portfolio volatility, as it is possible to put the maximum weight into each asset class whereas the overall portfolio risk (volatility) is not being increased at all. Theoretically, if the expected returns of the underlying asset classes are perfectly proportional to their total asset risk, there should be no other portfolio combination that can achieve a higher Sharpe Ratio.

As already mentioned above, the Inflation-Proof Retirement Portfolio has the following investment universe:

  • iShares Dow Jones Select Dividend Index (DVY)
  • SPDR Dow Jones REIT (RWR)
  • PowerShares Dynamic Food & Beverage (PBJ)
  • PowerShares DB Agriculture (DBA)
  • Energy Select Sector SPDR (XLE)
  • SPDR Gold Shares (GLD)
  • iShares Barclays TIPS Bond (TIP)

Apart from the iShares Barclays TIPS Bond (TIP), the investment universe of the Inflation Proof Retirement Portfolio solely consists of non-fixed-income investments. Furthermore, in our example, there is no allowance for transaction costs or brokerage fees. In order to minimize transaction costs, we rebalance the portfolio on a monthly basis.

If we have a look at the annualized volatility this portfolio utilized in the past, we can see that apart from 2008, where the financial crisis hit the markets, the portfolio volatility itself swung between 4 and 10 percent. The average volatility, in contrast, was around 8.5 percent, although we are mainly using high volatile asset classes (volatility of zero percent means that the ETF was not available during that time).

Annualized Volatilities

Chart 1: Annualized Volatilities

The allocation of the portfolio for January and February can be seen in the table below:

allocation of the portfolio for January and February

Table 2: Allocation of the Portfolio for January and February

Furthermore, we compared the portfolio with a common balanced portfolio, whereas 40 percent is weighted in the S&P 500 (IVV) and 60 percent is allocated in Long-Term Treasury Bonds (TLT).

Performance Overview of the Portfolio

Chart 2: Performance Overview of the Portfolio and the Benchmark

Due to its high diversification benefits, the portfolio almost achieved a Sharpe Ratio of 1, indicating that investors have received 1 percent performance for each unit of risk. This is mainly due to the fact that it is possible to put the maximum weight on each asset class without increasing the overall portfolio volatility.

To visualize this effect, we have plotted a ratio which measures how much risk-reduction in percent the portfolio utilizes through diversification. For example, if the portfolio’s weighted average asset volatility is 20 percent and the actual portfolio volatility itself is only 4 percent, the ratio reaches a score of 80 percent. This means that the portfolio only carries 20 percent of its initial risk.

In such an environment, nearly all underlying asset classes are perfectly uncorrelated to each other and, therefore a draw-down in any underlying asset class does not have a big impact on the overall portfolio performance. The case is different if the ratio drops near or even below 20 percent, indicating that most asset classes are highly correlated to each other. In such an environment, risk reduction through diversification is not working very well, since even a perfect diversified portfolio still carries 80 percent risk from its underlying asset classes. Such a fact is not really a big threat for a diversified portfolio, as long as the overall momentum of the underlying asset classes remains positive. Large draw-downs are only occurring if the ratio drops below or near 20 percent and if simultaneously all asset allocated classes are facing strong declines (e.g. 2008).

Risk Reduction Through Diversification

Chart 3: Risk Reduction Through Diversification

Another interesting fact is to look at the Callan periodic table of investment returns, where the yearly returns of each underlying asset classes and of the portfolio itself are plotted in descend ending order. There we can see that the portfolio is achieving quite attractive results, especially if we consider the fact that the historical annualized volatility of the portfolio was extremely low.

Periodic Table of Investment Returns

Chart 4: Periodic Table of Investment Returns

The Bottom Line

The portfolio is designed to generate stable returns during all predominant market conditions, even if the inflation expectations remain low. For that reason, such a portfolio is a perfect solution or complement investment for investors at or near retirement who are searching for a conservative inflation-proof investment which is not heavily loaded on bonds.

Note: This research publication was published on Seeking Alpha in March 2014.


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Risk Parity – Why Correlations & Classifications Can Be A Huge Stumbling Block!

Abstract

  • Despite the fact that the risk parity approach has some disadvantages over other risk based asset allocation strategies, if offers investors an attractive risk/return profile and has, therefore, clearly a competitive edge over traditional balanced portfolios.
  • Nevertheless, it can be quite dangerous to think that this strategy is a free lunch, since most risk parity funds/ETFs have not experienced a significant drawdown so far.
  • In our article, we review a hypothetical risk parity portfolio that consists of three risk balanced asset clusters (equity, commodity and fixed income), whereas within each bucket all single securities are also being weighted according to the risk parity approach.

Content

After a decade of extremely high macroeconomic uncertainties and increased volatility within the stock markets, investors have started to re-think their traditional asset allocation models that have often fallen short of expected returns/losses. For that reason, new risk-based portfolio construction techniques like “Risk Parity” have become extremely popular among researchers and investors. For example, the Invesco Balanced-Risk Allocation Fund (ABRIX) just recently passed USD 1.5 billion in size while the AQR Risk Parity (AQRIX) has swollen nearly to USD 1 billion. After such a success, even Global X has filed paperwork with the SEC for a “Global X Risk Parity ETF”.

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Modern Portfolio Theory 2.0 – The Most Diversified Portfolio

Abstract

Our research paper, published and awarded as Editor’s Pick on Seeking Alpha, reviews a portfolio construction technique called “Maximum Diversification,” which maximizes the asset class diversification within a portfolio. The article refers to the WSC All Weather Portfolio, which is regularly updated in our members area.

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