Category: Periodic commentary

ETFMathGuy provides periodic commentary on risks and opportunities of investing in Exchange Traded Funds (ETFs), including recent market trends.

ETFMathGuy is a subscription based education service providing commission-free ETF optimal portfolios. We offer individual investors insights into building optimal portfolios.  Each month, we analyze hundreds of commission-free ETFs available to individual investors.  Then, we build optimal portfolios based on a variety of risk tolerances and current market conditions using a quantitative methodology.

We hope these periodic commentaries on ETFs help you improve your investment knowledge!

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Bond Markets Fell in February 2021

ETFMathGuy optimal portfolios are now available to free and premium subscribers. Please log-in to see them now. In this post, we discuss how the bond markets fell with rising interest rates this past month, and its effect on the stock market and our ETF portfolios.

Bond markets fell. What is happening with interest rates?

The recent reaction of the bond markets appears to be due to investors being less convinced that U.S. Government interest rates will remain low for the long-term. Based on recent Wall Street Journal reporting, demand for the 10-year U.S. Treasury note has been “tepid”. With lesser demand come lower prices to stimulate buying. And, when prices go down in a bond, its interest rate goes up. How so? One simple way to think about this relationship is from the bond seller’s perspective. If the demand for bonds goes up, the bond seller can set a lower fixed interest rate and still find a buyer. Conversely, the bond seller must provide higher fixed interest rates, thereby compensating the bond investor more, if demand is low. If all this sounds confusing, please take a look at the nice visual representation below.

The seesaw relationship between bond prices and interest rates. Source: Securities & Exchange Commission
The seesaw relationship between bond prices and interest rates. Source: Securities & Exchange Commission

Why is demand low for U.S. Government bonds?

The most obvious explanation for the low demand for bonds is the large amount of debt the U.S. Government is expected to sell to fund the ongoing stimulus efforts. One measurable effect of this stimulus is to continue to keep the U.S.’s debt-to-GDP ratio above 100%. Servicing this debt will slowly become more expensive as interest rates rise.

How did ETFMathGuy Premium Portfolios do in February 2021?

Our portfolios gave back some of their gains in January, in part due to the increased chance that interest rates may be on the rise, increasing corporate borrowing costs. The chart below shows the year-to-date returns of stocks, bonds, and ETFMathGuy premium portfolios held at Fidelity and Schwab. Notice how the low demand for bonds has reduced the total return for the iShares Core U.S. Aggregate Bond ETF (ticker: AGG).

Total returns for ETFMathGuy premium portfolios for January and Februrary, 2021

We hope this post provided you with some helpful perspectives on why the bond markets fell, and how the stock market, ETFs, and the overall economy are all dependent on one another.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Optimal Portfolio Updates for February 2021

ETFMathGuy optimal portfolios are now available to free and premium subscribers. Please log-in to see them now. In this post, we will discuss how the recent GameStop stock prices influenced these portfolios and our portfolio construction process.

Markets in 2021

The 2021 year in the ETF marketplace is already shaping up to be very interesting. The big news recently was the impact of stocks like GameStop’s 500% gain from Jan. 25 through Jan.29. Fortunately, most diversified ETFs saw little impact of this extreme price move. However, this rapid price gain did have a noticeable impact on two ETFs.

What ETFs were impacted most by GameStop?

According to this ETF.com article, two ETFs had their holdings in GameStop jump into double-digits weights. They were the Wedbush ETFMG Video Game Tech ETF (ticker: GAMR) and the SPDR S&P Retail ETF (ticker XRT). In the case of GAMR, this ETF has the largest weighting of GameStop, currently at 26%. Notice, in the image below, that this holding is more than 10-times larger than the next largest one.

Top 10 Holding for the Wedbush ETFMG Video Game Tech ETF (ticker: GAMR). Source: etfmg.com/funds/gamr
Top 10 Holding for the Wedbush ETFMG Video Game Tech ETF (ticker: GAMR). Source: etfmg.com/funds/gamr

Less extreme is the SPDR S&P Retail ETF (ticker: XRT), which currently holds 12% of its assets in GameStop. So, these two ETFs are not as diversified as one might expect.

Did these ETFs impact the ETFMathGuy portfolios?

The short answer to this question is “no”, because of our portfolio construction process begins with a curated list of ETFs. For this month, we chose to intentionally exclude GAMR due to the excessive level of risk associated with holding large amounts of GameStop stock. Fortunately, there were still many ETFs to pick from to build our optimal portfolios, creating plenty of other opportunity for gains. And, gains for 2021 have been good so far. Below is an image showing total returns for stocks (ticker: IVV), bonds (ticker: AGG) and our three premium portfolios invested in real brokerage accounts at Schwab and Fidelity.

Total returns for ETFMathGuy premium portfolios in January, 2021
Total returns for ETFMathGuy premium portfolios in January, 2021

We were happy to see these returns in January, which continues the strong returns from 2020. Please watch for future posts where we will continue our discussion on ETFs, the economy and tax-efficient retirement income.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Concentrated exposure with thematic ETFs

In our recent post about thematic ETFs, we discussed the growth of so-called “thematic ETFs”. These are ETFs that follow a theme. One of our favorite writers at the WSJ is Jason Zweig, and he also wrote about these ETFs recently. Today, they represent some of the market’s hottest funds by using concentrated exposure.

“Often called thematic ETFs, these funds cut across industries, trying to capitalize on ideas like alternative energy, cloud computing or 3-D printing. Others buy stocks that could benefit as more people work from home, demand gender or racial diversity, or lavish money on their pets.”

Jason Zweig, The Intelligent Investor, Wall Street Journal, January 15, 2021

More Concentrated Exposure

By concentrating on a particular theme, like solar power, robotics or industrial innovation, many of these funds can have very high returns. For example, the Invesco Solar ETF (ticker: TAN) had a 234% return in 2020. Similarly, the ARK Innovation ETF (ticker: ARKK) returned 153%. Of course, these returns didn’t come without their own risks. The volatility of these two thematic ETFs were 55% and 49%, respectively. As a basis of comparison, our typical benchmark for stocks is the iShares Core S&P 500 ETF (ticker: IVV) and bonds is the iShares Core Total US Bond ETF (ticker: AGG). The 2020 return of these ETFs appears below at 18.4% and 7.5%, respectively. Also, note their lower volatility than the thematic ETFs mentioned here.

Risk and Return of Three popular thematic ETFs in 2020. Source: etfreplay.com/charts.aspx
Risk and return of three popular thematic ETFs and two broad-based ETFs in 2020. Source: etfreplay.com/charts.aspx

Higher expenses in thematic ETFs

Expense ratios are often much higher in thematic ETFs than broad-market ETFs like those that track the S&P 500. For instance, the three thematic ETFs from above have expense ratios of 0.69%, 0.95% and 0.75% according to ETF.com. In contrast, our stock and bond benchmark ETFs (tickers IVV and AGG) have expense ratios of 0.04% and 0.06%. So, investors must pay a premium to get unique exposure to these themes. And, until a thematic ETF grows sufficiently, the bid-ask spread on them could be much larger, further degrading returns when they are bought and sold frequently. Nevertheless, we found in 2020 that thematic ETFs, when built into a diversified portfolio, can both manage risk and boost returns.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Trading fractional shares of ETFs

Fractional shares are that latest innovation now available to individual investors. But, like many technical advances, there are upsides and downsides to it. In this post, we discuss this innovation in the context of Exchange Traded Funds (ETFs).

pexels-photo-164527.jpeg
Photo by Pixabay on Pexels.com

Opportunities with fractional shares

One of our favorite writers is Jason Zweig, who recently wrote about fractional shares in the WSJ. His article was largely discussing how high priced stocks, like Alphabet and Amazon, trade at over $1,000 per share. Prior to trading fractional shares, there was no way to have direct ownership of these company stocks if you were investing a few hundred dollars. Or, if you had enough for a few shares, you were unable to diversify across a larger group of these high priced stocks. So, your investment could be more susceptible to market volatility.

Fractional trading has changed this. Whether you are trading with Robinhood, Fidelity, or many other discount brokers now offering fractional trading, access to high priced stocks is now possible. These brokers also permit fractional shares of ETFs. However, ETFs often contain hundreds, or even thousands, of underlying securities. Also, the ETF issuers generally don’t want to prevent access to their shares. Consequently, ETF share prices are typically in the tens to hundreds of dollars per share. For small account owners, fractional ownership of ETFs is more about investing every last dollar and cent. For stocks, fractional ownership is providing access.

Risks and limitations of fractional ownership

We looked at some of the details of fractional trading at Robinhood and Fidelity brokerages. The most obvious limitation is that these types of trades must be done from a mobile device. And, the Robinhood app appears to provide various “nudges” to encourage trading more frequently. Nevertheless, we think that fractional ownership, when used correctly, can provide individuals with better access to a wider variety of investments at a younger age.

You can’t invest without trading, but you can trade without investing.

Jason Zweig, The Intelligent Investor, WSJ, December 4, 2020

We think this quote says it all. We wish you and yours a safe and enjoyable holiday season!

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What are Model Portfolios?

Yesterday’s Wall Street Journal had a very interesting article about model portfolios. So, what are these, and why should an individual investor care about them?

A Wall Street Trend

This WSJ article stated that the use of model portfolios is a growing trend, since it helps take the emotion out of investing. So, these portfolios are based on scientific observations and analysis, rather than an investor’s “instincts” or emotional reaction to current market conditions. A growing number of financial advisors are embracing their use too.

Model portfolios take some of the human emotion out of investing. They provide the comfort of science.

Andrew Guillette, Research Director at Broadridge. source: WSJ, December 4, 2020

Thus, these model portfolios are ones that can “dynamically shift the funds it invests in as markets change”. We are advocates of this approach using commission-free ETFs. Our free and premium portfolios do exactly that, as we update them each month based on current market conditions. Please log in to see these portfolios now, which include the latest market shifts through Friday, December 4th. Premium subscribers also have access to a handy web calculator to assist in rebalancing their portfolio.

How have model portfolios performed this year?

Unfortunately, little is published about model portfolio performance. But, we report our model’s performance for ETFMathGuy portfolios on a regular basis. The image below shows the total returns from January through end of November from our investments at our Fidelity brokerage account.

Total returns from January through November of Stocks, Bonds and ETFMathGuy Portfolios

What about risk?

The performance over the last 11 months look very promising, suggesting a scientific approach to rebalancing an ETF portfolio can perform well in volatile markets. But, how much risk did we take with these investments? Using the monthly returns that led to the total returns shown above, the volatility of the stock market (ticker: IVV) was 26.9%. However, the volatility of the moderate risk ETFMathGuy portfolio was only 18.2%. Not surprisingly, the aggressive risk ETFMathGuy portfolio had a higher volatility of 19.0%, as expected for a portfolio seeking more risk. So, these portfolios continue to outperform the stock market, while also taking less risk as measured by volatility.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.

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Thematic ETFs continue to grow

Thematic ETFs continue to grow in popularity. But, how is this type of ETF different from the broad-based ETFs, like those that track the S&P 500? In this post, we discuss several points to consider when investing in thematic ETFs.

What is an ETF “theme”?

ETF themes can come from nearly anywhere in the investment world. As discussed in this recent WSJ article, themes are often found to hopefully align with “beliefs or interests” that investors may have. In the U.S., assets invested in thematic ETFs have doubled in the past three years. However, there have been quite a few closures along the way too. Closures are typically due to the ETF’s expense ratio failing to produce sufficient revenue to match the expense of running the ETF. This WSJ article suggests that ETFs without $50M in assets after three years are most vulnerable.

We agree. In fact, the initial evaluation of the ETFs we use in our portfolio construction process discards ETFs that haven’t existed for several years or have less than $50M under management. Our approach helps avoid the many issues associated with ETF closures.

Opportunities of Thematic ETFs

The obvious attraction of these ETFs is their opportunity to make more “concentrated” investments in companies within its theme. For example, investors interested in companies involved in automation could buy the ROBO Global Robotics and Automation Index ETF (ticker: ROBO). Or, if an investor wishes to make investments in solar companies, they can buy the Invesco Solar ETF (ticker: TAN). The image below shows the top ten holdings of this solar ETF.

Top 10 Holdings of the Invesco Solar ETF. Source: ETF.com
Top 10 Holdings of the Invesco Solar ETF. Source: ETF.com

However, theme-based ETFs also lack diversification inherent in broad-based ETFs like iShares Core S&P 500 ETF (ticker IVV). And, they are typically are less liquid. For instance, the average bid-ask spread of the Invesco Solar ETF was 0.11%. The iShares Core S&P 500 ETF bid-ask spread was much lower, at 0.01%, according to ETF.com.

Risks and Rewards of Thematic ETFs

Having more concentrated holdings than a broad-based index usually means higher risk. The chart below shows how the risk, measured by volatility, for the automation and solar ETFs compare to the S&P 500 ETF over the last three years. Clearly, these thematic ETFs exhibited greater risk. For the solar ETF, this higher risk level was compensated by a higher total return. However, the automation ETF’s higher risk levels didn’t produce returns higher than the S&P 500, lagging it by about 1% a year.

Three-year risk and return of the Invesco Solar ETF, ROBO Global Robotics and Automation Index ETF and the iShares Core S&P 500 ETF. source: www.etfreplay.com
Three-year risk and return of the Invesco Solar ETF, ROBO Global Robotics and Automation Index ETF and the iShares Core S&P 500 ETF. source: www.etfreplay.com
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Market uncertainty prior to next week’s election

The stock market, measured by the S&P 500, lost about 2.5% in October. But, earlier in the month, the stock market was up over 5%. The chart below shows the roller coaster ride for two ETFs that track the stock and bond markets: iShares Core S&P 500 ETF (ticker IVV), Vanguard Total Bond Market ETF (ticker: BND) So, what’s going on with this market volatility?

Stock and bond returns in October, 2020. Source: finance.yahoo.com

Markets don’t like uncertainty

There are many opinions to describe what caused the financial markets to move like they did in October 2020. We think that the combination of the upcoming election and spike in coronavirus cases is adding to uncertainty. But, this uncertainty, as measured by stock market volatility, is still well below where it was earlier in the year. We used our daily volatility monitor in the plot below.

Stock market volatility as of October 30, 2020. Source: ETFMathGuy.com
Stock market volatility as of October 30, 2020. Source: ETFMathGuy.com

As this chart shows, volatility has crept a little higher in October. But, based on the long-term historical norm, this volatility is still slightly elevated in the 75% percentile. Of course, if you are a believer in efficient markets, then you simply don’t know what the future of the market will hold. In more positive news, the WSJ recently reported that the U.S. economy recovered significantly in the 3rd quarter of 2020. Consumer spending for online retail items continue to stay strong, while the travel sector still lags.

How about the ETFMathGuy portfolios and market uncertainty?

Thanks to wide diversification from over 2,000 ETFs we analyze each month, our portfolios continue to perform well. Consequently, the moderate risk portfolio lost 0.6% and the aggressive risk portfolio lost 0.5% in October. The year to date cumulative return of the ETFMathGuy aggressive risk portfolio appears below, along with the S&P 500 and Aggregate Bond Market total return.

ETFMathGuy year to date cumulative returns, versus the S&P 500 and Aggregate Bond Market returns.

Premium subscribers can now access the backtested portfolios for November 2020. Not a premium subscriber yet? Then, just visit the bottom of our “Join Us” page to upgrade your subscription and get immediate access!

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Market Volatility is Back?

Market volatility returned in September 2020. In this post, we discuss this recent surge in the context of long-term historical volatility. We also show how our ETFMathGuy portfolio performed, and elaborate on a source of that performance.

Market Volatility returned, but will it persist?

Earlier this year, we developed an app to automatically measure stock market volatility. This app updates daily, and the figure below shows the latest result.

Stock Market Volatility was 19.7% on Friday, slightly above its long-term historical norm.
Stock Market Volatility was 19.7% on Friday, slightly above its long-term historical norm.

We also provided a table showing the distribution of long-term historical volatility, as observed over more than 20 years. Current volatility is 19.7% as of October 2nd, which corresponds to the upper limit of the third-quartile. So, while market volatility returned, it is still well below the volatility seen in early 2020.

Market Performance through the 3rd Quarter

The higher volatility occurring in September did indeed correspond to a loss in the stock and bond markets. The stock market lost 3.7% and the bond market lost 0.1%, based on the ETFs with ticker symbols IVV and AGG. The year to date return of these stock and bond index ETFs were 5.5% and 6.7%, respectively, including dividends. The year to date return of the ETFMathGuy Aggressive Risk Portfolio was 20.8%. This return is the result of trades conducted in a brokerage account at Fidelity Investments, and so includes the bid-ask spread.

Stock and Bond Market YTD Returns compared to the ETFMathGuy Aggressive Risk Portfolio
Stock and Bond Market YTD Returns compared to the ETFMathGuy Aggressive Risk Portfolio

Premium subscribers now have access to the October 2020 premium portfolios, as well as a handy rebalancing calculator. Free subscribers are welcome to log in to review older premium portfolios through May 2020, or upgrade their account to enable premium access.

Sources of Excess Performance

One ETF that our portfolios have consistently included throughout this year is the Aberdeen Standard Physical Palladium Shares ETF (ticker: PALL). Its 12 month return and volatility appear below next to the S&P 500 ETF (ticker IVV).

The Palladium ETF has higher volatility than the S&P 500, but also has a higher return over the last 12 months. Source: www.ETFreplay.com
The Palladium ETF has higher volatility than the S&P 500, but also has a higher return over the last 12 months. Source: www.ETFreplay.com

Examining these results for PALL confirms the expectation that higher risk can lead to a higher return. Our optimal portfolio construction process creates a portfolio that, along with PALL, finds other ETFs that maximize expected return. This process also keeps the portfolio’s expected risk between the stock and bond markets. Additionally, we backtested this process over a full market cycle. We hope you will consider upgrading your subscription to gain insights into a wider variety of ETFs that appear in our efficient portfolios.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.

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Can minimum volatility ETFs consistently perform well?

Last weekend, there was a fascinating article about minimum volatility ETFs. It was written by one of my favorite Wall Street Journal columnists, Jason Zweig. In this article, he shared a lot of wisdom, which I will highlight more here.

What is a minimum volatility ETF?

One of the most common ways to measure risk in an ETF is to track its volatility. So, investing in a minimum volatility ETF may make sense for investors seeking to reduce risk. One of the largest low volatility ETFs is the iShares MSCI USA Min Vol Factor ETF (ticker: USMV), with over $30B in assets. The chart below shows it performance since its inception in October 2011, which generally lagged the S&P 500 (ticker: IVV). However, its volatility was noticably lower.

Risk and Return of a large minimum volatility ETF compared to the S&P 500 . Source: www.ETFReplay.com
Risk and Return of a large minimum volatility ETF compared to the S&P 500 . Source: www.ETFReplay.com

Why did this ETF produce lower risk and lower return?

This ETF is able to lower risk through the use of optimization, much like the ETFMathGuy portfolios. However, we don’t limit our optimal portfolios to equities like minimum volatility ETFs. We consider bonds, commodities and other alternative investments too. ETFMathGuy also uses backtesting that includes transaction costs to build portfolios to maximize returns.

The fund’s index uses an optimization algorithm to build a “minimum variance” portfolio—one that considers correlation between stocks—rather than simply holding a basket of low-vol stocks…

USMV Factset Analytics Insight (https://www.etf.com/USMV)

So, this ETF consists of stocks which typically emphasize lower volatility sectors like financial, utilities and real estate. These sectors are often termed “value”, rather than “growth” investments, in part due their issuance of dividends. Consequently, optimization to produce a minimum volatility ETF removes some market risk, generating a beta of 0.87. But, as we can see in the economic cycle from 2011 – 2020, the return also lagged the market.

Recent performance of minimum volatility

This year’s pandemic has certainly affected the stock market in significant ways. Investments favored by minimum volatility ETFs (financials, utilities, and real estate) have been significantly impacted by coronavirus lockdowns. However, technology has done very well, as remote work has increased the demand for technology systems and services. Unfortunately, technology is typically more of a “growth” investment. So, minimum volatility ETFs often limit their exposure to growth stocks to reduce volatility. In the ETFMathGuy portfolios, technology has been a noticeable portion this year, and has led to encouraging year-to-date returns and performance statistics.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
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Alpha and Beta Portfolio Statistics

In this post, we will be diving deeper into two commonly used portfolio statistics. These terms are Alpha and Beta, are based on a statistical method called “Regression“, and are used in the Capital Asset Pricing Model (CAPM). They are calculated by fitting a “line” to a set of points.

“…alpha is the return on an investment that is not a result of general movement in the greater market”.

Description of “Alpha” from the Capital Asset Pricing Model (CAPM). Source: Investopedia

“Beta effectively describes the activity of a security’s returns as it responds to swings in the market”

Description of “Beta” from the Capital Asset Pricing Model (CAPM). Source: Investopedia

If we define the market as the S&P 500, then Beta is an indication on how sensitive a portfolio is to S&P 500 returns. Alpha indicates how returns occur independent of the S&P 500. The term Alpha is so important, that it has even spawned its own website. And, why not? It represents the return obtained without exposing an investor to (stock) market risk.

An Example of CAPM

To better illustrate how Alpha and Beta are determined, consider the last 8 months of returns for the the following data sets:

  1. ETFMathGuy Aggressive Portfolio Returns
  2. S&P 500 total returns (ticker: IVV) to represent the market
  3. Short-term U.S. Treasury bill returns (ticker: SHV) to represent the risk free rate

Since CAPM is based on the concept of “excess returns”, which are returns above the risk-free rate, we can visualize this relationship in a scatterplot. The horizontal axis is the “Market Returns – Risk Free Rate”, and the vertical axis is the return of our “ETFMathGuy Aggressive Risk Portfolio Returns – Risk Free Rate”.

The Capital Asset Pricing Model (CAPM) applied to 8 months of returns of ETFMathGuy Portfolios
The Capital Asset Pricing Model (CAPM) applied to 8 months of returns of ETFMathGuy Portfolios

These results look promising, with a value of Beta = 0.37 and Alpha = 2.1%. However, 8 observations are small, so analysts typically look to see if these values are “significantly different” than 0. Or, put another way, what is the chance that these value were obtained by skill, rather than luck?

Assessing Luck vs. Skill

More data or evidence is always helpful in supporting any claim using statistics. For the example we show above, we are claiming that Alpha and Beta are non-zero values. Using some fundamentals from statistics, we can determine p-values for our Alpha and Beta calculation above as 29% and 15%, respectively. (Yes, p-value is another statistical term.) These p-values are fairly easy to interpret. In this case, 29% is the probability that Alpha = 2.1% is due to random chance, and the 15% is the probability that Beta= 0.37 is due to random chance. Put another way, we can say that Alpha = 2.1% and Beta = 0.37, but there is a chance (29% and 15%) that, in fact, we are wrong and that these value should be zero. So, the smaller the p-values, the greater confidence we have that these are the correct values and have minimal estimation error.

So What?

These results show that the ETFMathGuy Aggressive Portfolio is generating positive Alpha, and isn’t overly sensitive to the market. However, more data is needed to provide stronger evidence that these results are not simply due to luck. We hope you will continue to check back to see how the ETFMathGuy portfolios perform for the rest of 2020. And, for those who are premium subscribers, the September portfolios are now available, which includes a new calculator at the bottom of the page to further aid in portfolio re-balancing decisions.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.