Hi Guys,
Your responses to my earlier posting on a portfolio composed of a small number of Balanced mutual fund holdings were awesome. Your excitement is infectious.
That submittal was organized to illustrate the potential benefits from such a simple approach; it was not intended to suggest that the products selected for illustrative purposes were anywhere near optimum. They are not.
Your enthusiastic replies nudged me to explore the balanced holdings strategy a little bit more deeply. So I expanded the matrix of candidate actively managed balanced mutual funds from 3 to 12, a dirty dozen. As a benchmark for comparative purposes, I retained the 50/50 equity/bond Index mix to represent a passively managed portfolio.
The funds I selected for this expanded study came from Board member suggestions, from the Morningstar preferred lists, from investment newsletters, and from the three major fund families, Fidelity, T. Rowe Price, and Vanguard.
Since the study is limited to only a dozen actively managed funds, any claims to optimization would be arrogant and misleading. But it surely is a move in that direction.
The Permanent portfolio (PRPFX), used as a third diversification ingredient, was retained in the current statistical analyses, but it really is not a balanced mutual fund with its precious metals and foreign money exchange components.
The actively managed balanced mutual funds included were: DODBX, VWINX, FBALX, FPURX, ACGIX, VWELX, NAINX, JABAX, RPBAX, BUFBX, and LOMMX. The PRPFX offering completes the dirty dozen group. The MFO website word limit does not permit a description of each fund symbol. Sorry.
The sometimes popular focused LOMMX fund managed by the eclectic and short-fused Ken Heebner was added since that fund was expected to have a low correlation with the other products. It did not fail in that regard.
Once again, annual returns from the most recent 15-year period was chosen for analysis because it recorded both upward and downward directed markets. The data were collected from the Morningstar and Yahoo Financial websites. All analyses were performed on the StatView computer code.
A summary of that analysis was prepared. It included average annual returns, fund volatility as measured by standard deviation, and correlation coefficients inputs.
A few observations are pertinent after scanning that tabular summary.
Ten of the actively managed Balanced mutual funds outperformed the passively managed 50/50 equity/bond mix benchmark. The exceptions were the PRPFX and NAINX funds.
In general, the higher performing Balanced funds had the higher volatility and thus a higher likelihood of a negative return in any given year assuming a Bell curve returns distribution. Among those funds examined, Heebner’s LOMMX offering recorded the highest volatility of 19.3 % on an annual basis.
The Permanent portfolio entry displayed a very low correlation with candidate companion Balanced funds. That’s expected because of its holdings (gold, silver, REITs, Swiss Francs) that are an integral part of that portfolio’s design. Hence, PRPFX is an excellent diversifier choice to lower your composite portfolio volatility.
The original 3-fund grouping, the team of DODBX, VWINX, and PRPFX, was not too shabby a cohort from both a returns and a risk perspective. It yielded a 7.94 % annual average return with a 8.76 % standard deviation. Its compound annual return for the 15-year period was 7.58 %.
For the expanded candidate Balanced fund field, the Janus product (JABAX) seems to be a horse of a different color, especially with respect to its lower correlations with other Balanced fund entries, and, its near best-of-field annual returns. It is an excellent suggestion for candidate inclusion from one of our talented Board members.
A number of the funds have a disappointingly high correlation coefficient with one another. If diversification is the goal, buyer beware.
If both diversification and above-average returns are equally weighted goals, a 2-holding portfolio pair of JABAX and DODBX is attractive. The 15-year average annual returns for this pair was 9.73 % with a standard deviation of 12.36 %.
If lower volatility (fewer negative years) is a primary objective, and some sacrifice of returns is acceptable, the Balanced fund pairing of JABAX with VWINX appears to be a respectable compromise. That pairing delivered a 8.87 % annual average return over the study period with a standard deviation of only 11.93 %.
The lowest correlation calculated was between the LOMMX and the VWINX products. They had a correlation coefficient of 0.23. An equally weighed portfolio of these two offerings generated an average annual return of 8.45 % with a with a still high standard deviation of 11.17 % for the study timeframe because of the LOMMX volatility. The low correlation coefficient between these two entities reduces volatility a little below the JABAX/VWINX option, but also sacrifices a little return based on the historical performance record. You get to choose your own poison.
End wealth is ultimately determined by compound annual return, and not average annual return. Portfolio volatility subtracts from average annual return when converting annual results to a compound final figure. For the three cases considered, the JABAX/DODBX mix produced a compound yield of 9.03 %, whereas the JABAX/VWINX 2-holding portfolio generated a 8.22 % compound annual return. The LOMMX/VWINX array delivered a 7.87 % compound return.
The Modern Portfolio Theory (MPT) tradeoff between risk and reward is evident when contrasting the JABAX/DODBX against the JABAX/VWINX options. These results also demonstrate that the LOMMX/VWINX candidate portfolio is not on the Efficient Frontier line; it falls below that line. Therefore, MPT suggests that the LOMMX/VWINX combination is not an effective portfolio.
If you want to do your own analysis, I append the equations that allow converting individual mutual fund performance data sets into a 2-holding composite portfolio. Note the coupling effects of correlation coefficient on a portfolio’s overall volatility, and the impact that volatility has in reducing average annual returns into a compound annual return framework.
Portfolio Return = W1 X R1 + W2 X R2
Portfolio Volatility (std dev) = Square root of {(W1 X V1)(W1 X V1) + (W2 X V2)(W2 X V2) + 2 X CC X W1 X W2 X V1 X V2}
Compound Return = R – 0.5 X V X V/ (1 – R)
With W being the portfolio weight fraction, R being the annual average return, V being the volatility or standard deviation, and CC being the correlation coefficient. For the 2-holding portfolio, the added numbers (1 or 2) to the symbols equate to the two separate holdings.
I hope you find these formulas helpful. Sorry about the mathematics, but it is necessary once correlation coefficients are introduced into the discussion.
One further point is deserving of some attention. The data collection frequency and period should be selected to be compatible with your expected trading frequency. A day trader needs minute-by-minute inputs.
These data reflect annual returns. That frequency of data collection is consistent with a portfolio that has an annual turnover rate of perhaps 10% or less. If you trade more often, monthly or quarterly data collection would be more appropriate and more time demanding.
I hope you find this submittal useful. I advocate no special portfolio strategy or specific holdings. Those decisions are yours, and yours alone. Good luck and good hunting.
Comments
Because of my perceived issue with limited space on the MFO website, I elected t forgo defining by name the Balanced mutual funds that I included in my reported survey.
For completeness and your convenience, I now correct that omission. Here are the 12 outfits that I assembled for my study, along with their current Expense Ratio (ER) as reported by Morningstar. Expenses always matter, sometimes costs matter greatly.
The presented order of my Dirty Dozen is consistent with the postings submitted earlier, and has no other implications.
DODBX = Dodge & Cox Balanced ER = 0.53 %
VWINX = Vanguard Wellesley Income ER = 0.28 %
PRPFX = Permanent Portfolio ER = 0.77
FBALX = Fidelity Balanced ER = 0.61 %
FPURX = Fidelity Puritan ER = 0.61 %
ACGIX = Invesco Van Kampen Growth and Income A ER = 0.74 %
VWELX = Vanguard Wellington ER = 0.30 %
NAINX = Virtus Tactical Allocation A ER = 1.33 %
JABAX = Janus Balanced T ER = 0.82 %
RPBAX = T. Rowe Price Balanced ER = 0.64 %
BUFBX = Buffalo Balanced ER = 1.03 %
LOMMX = CGM Mutual ER = 1.08 %
As I stated in my companion posting, I really do not take an advocacy position with any of these exceptional mutual fund offerings. They all do yeomen work within their category.
The final decision is totally in your purview. The responsibility is also solely yours. I know you will choose prudently and wisely.
As renown economist and Nobel Laureate Milton Friedman is often quoted as saying, “The power to do good is also the power to do harm”. So be cautious and do your portfolio no harm.
Best Regards.
Thanks for your interest. There are no dumb questions.
The correlation coefficients measure the linear relationship between two data series. In this instance it is the relationship between the annual returns from the two Balanced funds that are being assessed.
The formal name for the correlation is the Pearson Correlation Coefficient.
Many websites define this statistical measure, provide the mathematical equation, allow you to input data sets that you wish to examine, and do the calculation.
The correlation always takes values between plus One and minus One. A value of One means perfect returns alignment; a value of minus One means that the returns are perfectly out of synchronization. A value of Zero means that the two data sets have no linear coupling to each other; they behave in a random way relative to each other. Values between these extremes indicate various levels of co-movement if positive, and countermovement if negative.
Historically, investment classes have correlation coefficients between 0.995 (for passively managed Index funds and their benchmark Index) and about -0.2 ( like gold and equity fund correlations). For example, the correlation between equities and bonds usually varies between 0.2 and 0.5.
The correlation coefficient is dynamic; it changes over time, and is also dependent on the data collection timeframe and frequency.
Here are two such sites:
http://pearsoncorrelation.com/
http://easycalculation.com/statistics/correlation.php
Good luck and good calculating. Prudent investors really do need to understand statistical concepts to tilt the odds of success more in their direction.
I hope this helps.
Best Wishes,
http://low-risk-investing.com/
Thank you for researching the calculation of correlation coefficients. I do it the old fashion way with a lot of error prone data entries and application of a statistical computer code.
If reliable, the Low Risk Investments Discovery Tool website that you uncovered will save me and other Forum members a considerable amount of time.
To verify the reliability of the Low Risk calculations, I compared computed results from three other websites for several mutual funds. The three alternate websites were Morningstar, WSJ/Lipper, and Yahoo Financial (powered by Morningstar so not an independent source). Here are some findings.
The standard deviation (volatility measure) values correlate tightly.
When adjusted for the number of data points used in the analyses, the correlation coefficients seem reliable compared to my earlier work. Some data set adjustments are needed. I used annual data over a 15-year timeframe; the most common data frequency is monthly data collected over 3 years. The correlation coefficients must be adjusted by the square root of the ratio of data points used in each analysis.
I am puzzled by the discrepancy in reported annual total returns. The Low Risk site consistently reports higher values contrasted to all other sources examined. Why?
Care must be exercised to assure that the annual returns are total in that they include both asset capital appreciation and reinvested dividends. These sites recognize that distinction. Also care must be exercised to distinguish between average annual returns and compound return. These outfits acknowledge that crucial difference.
Of course. in my labor intensive effort, I may have made a data entry error, but the sites are automatic and should be free of that issue.
I do not have a firm answer to the “why” question.
One possible speculation is that the Low Risk site calculates total return by computing additional shares at each distribution release, and then assumes that the final number of shares were active for the entire study period. That’s wrong and will overestimate returns. That’s a guess on my part.
So the correlation coefficients seem reliable for a 3-year period using monthly inputs. The annual return data is highly suspect.
I hope this helps.
Best Wishes,
I checked a few funds and results are not consistent.
at low-risk, VFINX
period 12/31/2006 to 3/31/2009
Portfolio Total Return: -40.9%
The above portfolio's total return was -40.9%, outperforming the S&P 500's return of -43.7%. The total return includes stock price appreciation and dividends.
Q1. Why is VFINX return better than VFINX?
Q2. Morningstar has total balance at $5906 for this period for VFINX, which should be around -31% total return, not -40% as above. However, OAKBX has ending balance of $8809, which matches low-risk site total return of -11.8%.
I had checked VGHCX over a few periods and the total returns matched.