Hi Guys,
Yesterday, MFO participant Hogan asked a pertinent portfolio construction question that deserves special attention, and therefore a standalone listing on the MFO site instead of a quickly buried reply.
Specifically, Hogan solicited help to identify a portfolio “diversifier on a down US equity day”. Many MFO members proffered excellent candidates. The purpose of my post is not to offer a fish, but rather to instruct on how to fish.
Hogan framed his question in terms of a single day; of course he is referring to diversification over an extended period. Unless you are a day trader, a single days performance is really noise and not a reliable signal.
Accordingly, at the root of Hogan’s query, we are now talking statistics and probabilities. Specifically, we are referring to correlation coefficients and how to calculate them.
Don’t panic. These days you need not do the calculation yourself. There are many websites that will not only do the calculation, but will also do the heavy lifting of securing all the data inputs required to complete the analysis. I will list one such user friendly site a little later.
First, for the benefit of the neophyte investor, a definition of correlation coefficient is needed because it appears in the formal mathematical equation that describes a portfolio’s volatility (standard deviation). When applied to a portfolio, correlation coefficient measures the price movement togetherness of two investment products. Its scale goes from plus One (perfect togetherness) to Zero (completely random behavior between the two holdings) to minus One (totally out-of-synch performance).
It is significant to record that correlation coefficients are not static; they dynamically change over time because of complex market interactions.
It is also significant to note that one primary goal in portfolio diversification is to minimize its volatility while simultaneously maintaining average annual returns. Over the years, portfolio volatility works to erode end wealth; cumulatively, it is a negative factor. This goal is partially achieved by incorporating investment products that have low correlation coefficient values, preferably negative values if you can find these rare opportunities. Low correlation coefficient pairs are the secret to proper portfolio diversification.
Enough theory, here is the Link to a site that provides a number of financial tools, particularly an easy to use correlation coefficient calculator:
http://buyupside.com/calculators/stockcorrelationinput.phpThe simple inputs can handle stocks, mutual funds, and ETFs. The historical data sets are automatically extracted from Yahoo! Finance. Please observe that the analysis can employ daily, weekly, or monthly data as a user option. This choice will make a difference in the computed correlation coefficient.
To illustrate, I did a few calculations using Hogan’s PIMCO Global Bond—Unhedged fund (PGBDX) and Vanguard’s S&P 500 Index fund (VFINX)) as an equity market proxy.
Using daily data for the three months ending yesterday, the PGBDX holding is a superior diversifier with a -0.638 correlation coefficient. Congratulations Hogan.
For the three months preceding the current three month period, the correlation coefficient was -0.926. That’s even better. Things change often, often rapidly, and sometimes for the better.
For the one year period before the current date, the correlation coefficient was -0.0397 using daily data inputs. That’s very much like a random behavior between the two units being examined. It is a given that statistical market data constantly evolves.
Let’s examine how data entry frequency alters this last finding. For the last year, using weekly pricing inputs, the correlation between the S&P 500 market proxy and the PIMCO product was -0.158. So the price series interval does make an impact, as expected.
If you use the referenced calculator, remember to select an interval that is consistent with your anticipated holding period. Short holding periods need the daily data; long-term holders should use the weekly option. Do not use the monthly data sets since the statistical accuracy will degrade because of an input paucity.
This stuff is great fun and just might enhance your portfolio performance. Diversification is a tool that you control and can be deployed to great advantage. In the investment universe, it is indeed a rare nearly free lunch. Just do it even if you are somewhat statistically challenged. You need not be an expert auto mechanic to be a winning race driver.
I hope you add the correlation coefficient calculator to your toolbox.
Thank you Hogan for inspiring this submittal.
Best Regards.
Comments
Joe
Hi Joe,
Thank you for reading my post, and a hardy hoorah for using the referenced website to compute a negative fixed income product pair correlation correlation for diversification purposes.
The correlation coefficient calculator is a great tool. A few years ago this same calculation would take hours as data were recovered and arduously transported to a statistical analysis computer package. Errors were rampant. Today, we complete this same task, error-free, with a couple of keystrokes.
Your search to identify this risk mitigating entry in the fixed income arena demonstrates some considerable intuition on your part. Congratulations. Many MFO members consistently amaze me with their research skills and their market-wise acumen.
But a word of caution is warranted here. Your analysis examined the relative performance between the two bond products for one month. That surely utilizes the freshest data set, but it might also introduce what the behavioral researchers call the “Recency bias” by ignoring earlier historical relationships.
Also, a statistician might challenge your findings because of the very short data series that you employed in your analysis. The extensiveness of a data set needed to get meaningful statistical results is often a subject of debate, especially if the likelihood odds of the projected event are nearly even, and the measurement errors and accuracy are unknown.
Both these criticisms are partially addressed by using the same correlation coefficient calculator for several and longer timeframes. These additional calculations allow you to examine trends and the persistence of the correlation coefficient. These all add to a fuller understanding and are easily done for your candidate EVBIX diversifier versus your reference IEF study. A little parametric analysis works wonders when exploring options before a decision.
For example, for the three month period ending today, and using the daily pricing series option, the correlation coefficient is a plus 0.140 for your comparative pair. For the YTD timeframe, the value is 0.298. Using the weekly pricing option, the correlation coefficient is 0.241. Although the expanded timeframe has changed the sign of the correlation, EVBIX still appears to offer significant diversification benefits.
One issue with the weekly-based analysis is that the number of data entries is reduced to 17 pricing points. A statistical wonk might not be comfortable with the paucity of data points in that particular analysis. The number of numbers matter.
The YTD results are very representative of historical relationships. Context matters. In the investment marketplace, there is a strong pull towards a reversion-to-the-mean. The marketplace does not tolerate outliers.
I especially thank you for using the calculator so quickly. I rank that as the best reward I can receive for my documentation efforts.
Best Wishes.
https://www.google.com/finance?q=NYSEARCA:UUP&ed=us&ei=2kW6UeC5DIibrAH2dQ
Hi Ron,
I do not directly do currency exchanges, although I do own international mutual funds that hedge the dollar. Also I do not own pure Gold funds, although I do have funds who own gold and other hard assets. So I am definitely not an expert in these arenas.
However, you might consider using a short-term government bond product as a surrogate for the US dollar. I have no idea how valid the bond fund will serve as a proxy for the dollar.
Regardless, I used the referenced correlation calculator to explore the relationship. I used First Eagle Gold (SGGDX) as a representative of gold products; I used Vanguard Short Term Treasury fund (VFISX) as the US dollar proxy.
To examine timeframe sensitivity, I did the analyses for 1 month, 3 months, YTD, 1-year, and 3-year time periods.
Indeed, these two holdings provide considerable diversification.
For the 3 month, YTD, 1-year, and 3-year timeframes, the correlation coefficients were 0.0552, -0.273, -0.395, and -0.419. The results were based on daily pricing. The two holdings have moved in opposite directions except for the most recent 3-month period in which these funds behaved in almost a random manner.
For the most recent 1-month period, the correlation again turned negative at a -0.350 level. Keep in mind that for this brief period, only 22 data points entered the calculation, so the results might not be too statistically meaningful.
I hope this post helps to expand your approach for appropriate surrogates for the comparison you seek. I’m sure you can be much more productive than I am in doing your search. Good luck.
Best Wishes.
With that, the YTD daily correlation of GLD and UUP is -0.6178 and the 5 year monthly r^2 is -0.77. So overall a very good diversifier between the two.
However the real diversifier out of them for the S&P 500 over the past 5 years would be UUP with a -0.7515 whereas gold had an r^2 of 0.7652.