The objective of this article is to describe the construction of a diversified portfolio of high dividend, higher risk ETFs with an overall low portfolio risk by paying close attention to the correlation coefficients between the individual ETFs.

Investors have for several years been chasing yield and accepting higher risk by buying the high yield varieties of corporate bonds and municipal bonds plus investing in other areas such as emerging market bonds, master limited partnerships, bank loans, and mortgage REITs. After a short review of just what is a correlation coefficient and how it is quite different than beta, alpha, standard deviation, and r^{2} (r squared), a low risk portfolio will be built using most of these investments.

Correlation coefficients between pairs of investments range from -1 to +1. A value of +1 implies that when one stock price increases, the other will increase an equal percent. A value of -1 implies that when one stock price increases, the other will decrease an equal percent. A value of zero implies no relationship between the two stocks.

For example, the S&P 500 Index should be highly correlated to the Dow Jones Industrial Index and indeed they have a three-year correlation of .98. It is well known that bonds are negatively correlated to stocks and, for example, the S&P 500 Index and the Vanguard Total Bond Index ETF (BND) have a negative three-year correlation of -.51. This is also verified by recent experience with risk-on days where stock prices go up and bonds sell off. Conversely, on risk-off days stocks sell off and bond prices go up.

The correlation coefficient will not help identify investments that have the potential for capital appreciation or high dividend payouts or both. However, once investments are identified that have high potential, the correlation coefficients between them will help identify what investments will zig while the others zag and, as a result, reduce the total volatility (risk) of a portfolio. The ideal situation is that the majority (or all) of the investments in a portfolio pay dividends and have capital gains over the long term but, while this is happening, the lack of correlation or negative correlation between the individual investments reduces the volatility of the portfolio (and you sleep better at night).

Investment Correlation Coefficients are the Rodney Dangerfield of Modern Portfolio Theory statistics. They get no respect. While there is much talk about an investment's beta, alpha, standard deviation, and maybe r-squared, there is little mention of the correlation coefficients between a pair of investments. Yes, some articles will suggest an investment that is "not highly correlated" with "the market" or "uncorrelated" with another stock. Still it is rare to see actual numbers published.

For those who need a review of Modern Portfolio Theory statistics beta, alpha, r-squared, and standard deviation, refer to the Morningstar Investing Glossary. The point here is that none of these MPT statistics describe how one individual investment is correlated or uncorrelated with another.

The MPT statistics (beta, alpha and r squared) are calculated using a least-squares regression of an investment's excess return over Treasury bills and the excess returns of the related benchmark index. This assumes a straight line or linear relationship that is unfortunately not always true. This disadvantage necessitates the use of r-squared to give a confidence level for beta and alpha. A low r-squared indicates that the calculated beta and alpha may be useless after all.

Beta may seem like a measure of correlation to the benchmark index, but it is only an indication of how an investment may magnify or underperform the movements of the benchmark based on history. No information is given about price movements in relation to other specific investments. Also, Beta is sometimes mistaken for a measure of volatility; however, standard deviation is the accepted indicator of an investment's volatility.

The standard deviation of an investment's price indicates statistically how much price variation from the average has occurred over time and is typically quoted as an annual percentage. Standard deviation is considered a measure of an investment's volatility or risk and a historically high value implies a higher risk going forward. For example if an investment has a historical average price appreciation of 15% and an annual standard deviation of 20%, then 68% of the time it can be expected to return 15% plus or minus one standard deviation or between 12% and 18%. Also, 95% of the time the investment would be within two standard deviations of its historical average price appreciation or between 9% and 21%. Of course, many factors affect an investment's price and a statistical calculation cannot predict future performance, but standard deviation has proven to be a good measure of risk over time.

Standard deviation and correlation can interact together in a way that can be used to produce a portfolio that yields dividends significantly higher than the lowest yielding component and simultaneously has a risk or standard deviation lower than most of the other components. It is significant that some of the portfolios components will zig when others zag thus smoothing out the value of the portfolio other time.

How can all of this be put to work building a portfolio? Table 1 below shows the correlation coefficients for representative ETFs in all of the categories listed at the beginning of this article. The SPDR S&P 500 ETF (SPY) is included only as a proxy for "the market". (Table 1 was produced using the Correlation Calculator located on my web site and historical stock price data from Yahoo Finance.

Table 1. Correlation Coefficients

Given SPY will be excluded, the focus will be on the bond and high yield ETFs in the seven columns to the right of SPY. Table 2 below will be used to categorize the correlation of the ETF pairs and to interpret these results. Note that out of the 21 correlation coefficients between these ETF pairs, none are highly positive, only five are moderately positive, seven are low positive, and nine have no correlation.

Table 2. Significance of Correlation Coefficients

Significance | Correlation Coefficient |

Highly Positive | +.85 to +1.00 |

Moderately Positive | +.60 to +.85 |

Low Positive | +.30 to +.60 |

None | +.30 to -.30 |

Low Negative | -.30 to -.60 |

Moderately Negative | -.60 to -.85 |

Highly Negative | -.85 to -1.00 |

It is rare, but not impossible to find investment correlations that are low negative and even more difficult to find correlations that are moderately or highly negative unless one of the investments, for example, is an inverse ETF designed to move in the opposite direction of some index or commodity through the use of derivatives.

We could analyze many scenarios here, but remember the goal is a portfolio that, to the extent possible, is not correlated to "the market" as represented by SPY. In Table 1 CFT, HYD, and PCY have the lowest correlation coefficient to SPY and will be selected first. CFT and HYD are also major contributors to little or no correlation with the other potential portfolio members given their abundance of low and negative numbers. Now add to this the stocks with the standout highest yields from Table 3 below i.e. REM and JNK.

Table 3. Dividend Yield (Source: Yahoo Finance)

Stock Name | Stock Symbol | Dividend Yield | |

iShares Barclays Credit Bond | (CFT) | 3.48% | |

SPDR Barclays High Yield Bond | (JNK) | 6.89% | |

Market Vectors Hi Yield Muni | (HYD) | 4.97% | |

PowerShares Emerging Markets | (PCY) | 4.73% | |

JPMorgan Alerian MLP ETN | (AMJ) | 4.90% | |

PowerShares Senior Loan | (BKLN) | 4.93% | |

iShares FTSE NAREIT mREIT | (REM) | 11.55% |

The test portfolio consists of CFT, JNK, HYD, PCY, and REM. Table 4 is the result of an off-line spreadsheet that back tests a portfolio's performance for three years by varying the portfolio allocations in column 2. It calculates the portfolio yield at the bottom of column 3 and the 3-year standard deviation of the portfolio at the bottom of column 4. What-if scenarios are then run using Microsoft Excel Solver on the spreadsheet to refine the results. (I plan to have a version of this spreadsheet on my web site in a couple of weeks.)

Table 4. Portfolio Allocations

Symbol | Portfolio Allocation | Dividend Yield | 3-Year Standard Deviation |

CFT | 24.94% | 3.48% | 4.33% |

JNK | 14.55% | 6.89% | 9.56% |

HYD | 26.97% | 4.97% | 6.05% |

PCY | 15.91% | 4.73% | 7.16% |

REM | 17.64% | 11.55% | 14.64% |

Portfolio | 100.00% | 6.00% | 5.01% |

For brevity I have not shown the very first result where the spreadsheet was only asked to maximize dividend yield divided by standard deviation. This ratio is similar to a Sharpe Ratio and has the effect of forcing yield up and keeping standard deviation down when the ratio is maximized. The initial result was a yield of 5.42% and a standard deviation of 4.19%; however, PCY and JNK were frozen out of the portfolio at an allocation of zero and 5% respectively. Most notable was the portfolio standard deviation that was less than that of any component of the portfolio!

Remembering that humans make the decisions about what may be a good investment and wanting a little more yield, Table 4 is the result of asking the spreadsheet to produce a portfolio that maximizes the ratio of yield divided by standard deviation, consists of more equal allocations of all five ETFs, and yields a minimum of 6%. Again, notice that the portfolio standard deviation (i.e. risk) is still less than that of four out of the five portfolio stocks and is significantly less that the standard deviation of the highest contributors to yield, REM and JNK. Plus the yield is 6%!

This portfolio's correlation to SPY is .62 which is borderline between low positive and moderately positive. It is possible that this could be lowered by doing some additional tweaking to the portfolio allocation or by changing one or more of the ETFs. Just remember that those negative correlations can be hard to find and can be particularly difficult to get when dealing with a diverse portfolio.

This example should make it clear that these types of higher yield, lower risk, and diversified portfolios can be easily constructed by paying attention to correlation coefficients and standard deviation while doing a little number crunching with tools that are available.

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