Tag: personal finance

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Measuring cryptocurrency risk

Cryptocurrency risk is well known to be very high for many reasons. However, both individual and institutional investors continue to evaluate it as part of their investment portfolios. This post discusses recent cryptocurrency trends in a diversified portfolio and how the risks of this alternative investment compare to mainstream investments like stocks and bonds.

Volatility estimates

Volatility is one common way of assessing the risk of any investment. For the stock market, we provide a historical perspective, updated daily, to see how volatility changes over time for the stock market. But, how does this volatility compare to investments in cryptocurrency? The chart below shows a 3-month annualized volatility for the last several years of the stock market, measured with the ETF IVV, the bond market, measured by the ETF AGG, and the crypto market, measured by the Grayscale Bitcoin Trust  (GBTC). As this chart shows, bond volatility is the lowest, averaging between 3-4%. Stock volatility is higher, averaging between 15 – 20%. Cryptocurrency risk is about five times higher than stocks, with average volatility between 90-100%.

3-Month Annualized Volatility of the stock, bond, and cryptocurrency markets. Source: ETFMathGuy.com
3-Month annualized volatility of the stock, bond, and cryptocurrency markets. Source: ETFMathGuy.com

How much to allocate to cryptocurrency?

This recent WSJ article provided some guidance for individual investors interested in investing in cryptocurrency. While the answers to this question really depend on the individual’s risk tolerance, this article suggested between 1-2%. So, even if the value of the crypto investment hits $0, the investor limits their loss to this original investment amount. But, given the high levels of volatility, more frequent rebalancing may be prudent. Thus, if there is a substantial increase in the price of a crypto investment, the targeted 1-2% allocation would most likely require selling some of the crypto gains.

Unfortunately, selling short-term gains can be “expensive”, especially for those individual investors in a higher income tax bracket. In this case, the use of a Roth IRA may be the best approach. Why? An investor can realize Roth IRA gains tax-free if taken after age 59 1/2 from an account open for more than five years.

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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2020 Year In Review

Happy New Year from ETFMathGuy! In this post, we conduct a 2020 year in review of stock, bond and ETFMathGuy premium portfolios.

For many, 2020 was an unusual year in the investing world. And, investing in ETFs was no exception. In our first post of 2020, we discussed how we adapted to the new normal of nearly all ETFs trading commission free. That opened our portfolio construction process to consider over 2,000 ETFs. But, as we noted in another post from 2020, we immediately exclude any ETF with under $50 M in assets, which helps an investor avoid ETFs that may soon close, as well as larger bid-ask spreads when traded.

So, how did ETFMathGuy portfolios fare in 2020?

In short, we have been very satisfied with our ETFMathGuy premium portfolios. Our goal was to achieve returns similar to the S&P 500, but at lower risk. We established this goal based on rigorous backtesting all ETFs that were previously commission-free from Fidelity, or slightly less than 500 ETFs. However, in 2020, we expanded into all commission-free ETFs, and the returns from two real accounts at Fidelity appear below.

Total returns for stock market, bond market and two ETFMathGuy portfolios for 2020
Total returns for stock market, bond market and two ETFMathGuy portfolios for 2020

Clearly, we achieved our 1st goal of generating returns “at least as good” as the stock market, which we assume as the S&P 500. These returns were possible thanks to our model’s ability to dynamically adjust to market conditions. For subscribers with free memberships, you can see what these ETFs were by logging into your account, and browsing the 2020 portfolios through June 2020. For example, PALL and ARKK have been consistent components of our optimal portfolios. If you are a current premium subscribers, your January 2021 portfolios and rebalancing calculator are now available for your consideration.

But, what about risk in our 2020 year in review?

The pandemic of 2020 had a substantial impact on market risk. When measured monthly, stock market volatility was 25.8%. Examining the monthly returns for our ETFMathGuy portfolios, we observed an 18.1% and 19.4% and volatility for our moderate and aggressive portfolios, respectively. So, we also achieved our 2nd goal of keeping volatility lower than the stock market. We also revisited our calculation of Alpha and Beta. For the 12-monthly returns in 2020, we found Alpha = 2.48% and Beta = 0.49. Their p-values were 0.09 and 0.02, respectively for the ETFMathGuy aggressive portfolio.  Recall from this post that the smaller the p-values, the greater confidence we have that these are the correct values and have minimal estimation error. So, for those of you “seeking alpha”, these statistics indicate our portfolios likely produced “alpha” in 2020.

Our statistics on 2020 monthly returns indicated that we likely produced "alpha" in our ETFMathGuy aggressive portfolios.
Our statistics on 2020 monthly returns indicated that we likely produced “alpha” in our ETFMathGuy aggressive portfolios.

Forecasting 2021?

We won’t venture a guess at what the markets have in store for investors in 2021. Frankly, there are many, many articles already written on this topic. Instead, we will continue to pursue our goal to construct ETF portfolios that meet or exceed returns like the S&P 500 with lower volatility. If you are interested in accessing the January 2021 premium portfolios, please consider upgrading your membership now at 2020 subscription prices. In the coming weeks, we plan to increase our subscription prices for the new year. Please contact us if you would like a free sample of our latest premium portfolio.

We hope you found this 2020 year in review educational!

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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Retirement taxes under Biden or Trump

With the U.S. presidential election less than three weeks away, now is a good time to consider how your retirement taxes may change. In this post, we highlight the differences in Biden Vs. Trump plans for retirees.

The 2020 Presidential Election may change your retirement tax planning.
The 2020 Presidential Election may change your retirement tax planning.
Note:  This post has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for, tax, legal or accounting advice. You should consult your own tax, legal and accounting advisors before engaging in any transaction.

Income Taxes in Retirement

Most retirees face some amount of income tax. Social security benefits, pensions, interest on CDs, and bond coupon payments are just a few sources of that can produce retirement income tax. Any voluntary withdrawals from and IRA or 401(k)s, or taking required minimum distributions (RMDs) can also trigger income tax.

The Tax Cut and Jobs Act of 2017 established the current seven income tax brackets, with the lowest at 10% and highest at 37%. Both candidates wish to keep these tax cuts in place, which currently plan to lapse after 2025. But, Biden wishes to alter it so that households making more than $400,000 would pay higher taxes by limiting the value of itemized deductions. He also proposes to increase the top tax rate from 37% to 39.6%. For household making less than $400,000, Biden hopes to increase the standard deduction. Doing so should decrease taxable income and, subsequently, decrease taxes owed.

Capital Gains Taxes in Retirement

Current U.S. tax law states that qualified dividends and long-term capital gains from investments held for more than one year are taxed at a lower rate. Excluding the net investment income tax, the maximum rate is 20%. Trump has suggested lowering this rate to 15%. Biden wishes to tax long-term capital gains at income tax rates for households with over $1,000,000 in taxable income. He also plans to eliminate the step-up in cost basis realized by retirees wishing to pass highly appreciated assets to their heirs.

The SECURE Act and your retirement objectives, by DiLellio and Kinsman (2020), Vol 23, Issue 2, The Graziadio Business Review

What doesn’t appear likely to change

There are several areas of retirement taxation that likely won’t change. For instance, I recently published a peer-reviewed article about the SECURE Act. This law passed with broad bipartisan support, delays the onset of RMDs for younger retirees and changes rules for inherited IRAs.

For now, we encourage you to seek out a retirement calculator, like ours at ETFMathGuy, and we wrote about recently, to see what current U.S. tax law means to your retirement plans. We will update our calculator as tax law for retirement income changes.

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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Finding your Optimal Retirement Income

We introduced a new feature to ETFMathGuy.com in 2019 to help current and future retirees plan for the future. We have now upgraded it to find optimal retirement income. Fortunately, the calculator still offers answers to the many commonly posed questions for those nearing or currently in retirement.

  • How long will my portfolio support my discretionary and non-discretionary expenses?
  • How much will my heir or favorite charitable organization receive?
  • What will my future tax liabilities look like?

This calculator models income tax, capital gains taxes and other important elements of U.S. tax law relevant to individuals and couples in retirement. However, this model does not represent tax advice, and is for educational purposes only.

Sequencing Withdrawals for Optimal Retirement Income

In the former version of our calculator, we only applied the so-called “Common Rule“. Using values for a hypothetical 60-year old couple with a 20 year retirement horizon, the figure below shows how the couple can achieve $150,000 of annual after-tax retirement income. Notice how this “married filing jointly” couple has a effective 0% income tax bracket, as labeled on the right of the figure, due to use of the standard deduction. In 2020, this value is $24,800. To re-create these results or create your own, please visit our our interactive retirement calculator.

Common Rule withdrawal sequencing leading to a $1,203,938.01 inheritance. optimal retirement income
Common Rule withdrawal sequencing leading to a $1,203,938.01 inheritance.

While the “Common Rule” is widely adopted by financial planners and major discount brokers like Fidelity and Vanguard, it is known to sub-optimal. Why? This rule typically produces very little tax burden in the earlier years of retirement, unless they are triggered by Required Minimum Distributions (RMDs). Consequently, later retirement years can see very high income tax to maintain retirement income at acceptable levels. This rule also doesn’t take advantage of the step-up in cost basis realized by the retiree’s heirs.

Optimizing Retirement Income Withdrawal Decisions

The latest version of the retirement income calculator can now optimize withdrawal decisions using an “Optimal Rule“. So, using the same values for the calculator as our previous hypothetical couple, their heir’s inheritance increases by 13.7%, or $165,000. If their heir is a qualifying charitable organization, the inheritance increases by  $335,343.94 or 26.1%. We encourage you to try out your own scenarios to see how you can improve your retirement withdrawal decisions.

Optimal Rule withdrawal sequencing leading to a $1,368,938.05 inheritance, a 13.7% increase. optimal retirement income
Optimal Rule withdrawal sequencing leading to a $1,368,938.05 inheritance, a 13.7% increase.

Plans for the Future

We have plenty of other plans for our retirement calculator. For instance, delaying social security, including tax-free municipal bond interest, and assessing the benefits of a Roth conversion are just a few. If you have any thoughts of what you would like to see, please send us your feedback!

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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S&P 500 down about 20% in the First Quarter of 2020

It was a difficult year so far for many investors. The total return of the iShares Core S&P 500 ETF (ticker: IVV) was -12.1% for the month of March. The total return of IVV in the first quarter 2020 was -19.6%. Such large losses often shake investor confidence. Also, the math is against you now. To recover from the 20% loss, a investor needs a 25% gain. If losses hit 40%, then an investor needs a 67% return to get back to where they started. And, if losses reach 50%, an investor needs a 100% return, or double their money, to recover all their losses. This is the unfortunate math behind compounded gains and losses.

The recovering from a large market loss can be challenging due to the effect of compounding
Recovering from a large market loss can be challenging due to the effect of compounding

How did the ETFMathGuy portfolios do in First Quarter 2020?

Using my account balances at the end of March, I measured my investment returns for the first quarter. For the Moderate Portfolio in my taxable account, my first quarter return was -5.0%. My Roth IRA used the Aggressive Portfolio and had a first quarter return of -2.1%. These returns far exceeded the S&P 500 in this first quarter. So, we are pleased with these results, which were supported by the backtesting we used to tune our optimization methodology.

Total Returns for the First Quarter Using Taxable and IRA Accounts
Total Returns for the First Quarter Using Taxable and IRA Accounts

Why is there such a large difference between the moderate and aggressive portfolios? The biggest driver was the moderate portfolio’s exposure to the municipal bond market. The aggressive portfolio did not include municipal bond ETFs, since it operated within an IRA. Please, look for yourself at the premium portfolios that produced these returns, which are now available to all free subscribers.

Measuring Volatility

We’ve added a new feature to the ETFMathGuy site to track the daily stock market volatility. Using the first ETF ever created, the SPDR S&P 500 ETF Trust, we developed an average of one, two and three month annualized volatility. At the end of this week, volatility was 70.6%, which is well above its median value of about 13% over the last 20 years.

Current stock market volatility hasn't been seen since the financial crisis of 2008.
Current stock market volatility hasn’t been seen since the financial crisis of 2008. Click this image to see the latest volatility, updated daily.

The last time volatility reached this level was the 2008 financial crisis. Then, volatility peaked at 77.8% on November 24, 2008.

In our next post, we will discuss using volatility to potentially detect market trends. Before then, you may want to read this article on on tips for investors in volatile markets.

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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Diversification and February 2020 returns

The stock market experienced a significant drop in the month of February 2020. But, the bond market had a positive total return for the month. In this post, we discuss the benefits of a diversified portfolio during times of market stress, like seen in the February 2020 returns.

A big economic shock

Market returns for the the month of February 2020 were significantly impacted by the corona virus outbreak affecting the global economy. The S&P 500 index ETF (ticker: IVV) lost 8.5% in the month, but the iShares Core U.S. Aggregate Bond ETF (ticker: AGG) gained 1.6%. The stock market appears to be pricing in reduced earnings growth, due to the virus outbreak. Consequently, stock market sellers have rotated their investments into the bond market. Increased demand for bonds is driving up prices, and consequently returns, from bond investments.

The graphic below shows the total returns for the stock market, bond market, and two other portfolios for February, 2020.

Stock, bond and other portfolio returns in February 2020

Using a diversified portfolio and February 2020 returns

In hindsight, the bond market offered a higher return in February 2020. But, exclusively investing in bonds eliminates the possibility of the significant upside potential of the stock market, such as the 31.3% of the stock market in 2019.

One approach to managing risk while realizing some additional return is to invest in a 50% stock and 50% bond portfolio. For February 2020, this would have led to a 3.4% loss. However, wider diversification beyond the mainstream stock and bond markets offered a more substantial benefit. Specifically, the ETFMathGuy’s moderate risk portfolio (shown in a previous post) appears below. It returned 0.1% in February 2020, and was designed to match the volatility of the 50% stock and 50% bond portfolio.

The January ETFMathGuy moderate risk portfolio for taxable accounts.

The additional return comes from our optimal portfolio construction. ETFMathGuy portfolios diversify across other asset and sub-asset classes beyond stocks and bonds using a quantitative methodology. For instance, the portfolio above contains municipal bonds, commodity and tech sector exposure, among others. This diversified exposure has been very favorable to returns so far in 2020. But, market conditions are very dynamic. So, if you are looking for ideas on how to improve your portfolio’s diversification, please check out our current free and premium portfolios, constructed using the latest market data.

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2019 ETF Returns

Where will the global economy take us in 2020? To consider this question, we thought it would be helpful to review 2019 ETF returns. So, we devoted this post to highlight the 2019 returns among the major ETF categories.

So many ETFs to pick from…

In 2019, there were over 2,000 ETFs available to investors. Unfortunately, thinly traded and limited return history ETFs represented many of these. Thus, to focus on only the most major asset classes represented by ETFs, we chose to only review the 59 ETFs currently managed by Vanguard. Then, we broke the list into two obvious groups.

  1. Equity or stock-based ETFs
  2. Fixed income or bond-based ETFs

Equity ETF Returns

Vanguard offered 41 equity-based ETFs in 2019. Including dividends, the image below sorts their total returns for 2019.

Total Returns of Vanguard's Equity ETFs in 2019
Total Returns of Vanguard’s Equity ETFs in 2019

As this image clearly shows, our benchmark S&P 500 index ETF had a total return of 31.4%, making for an excellent year. In fact, it was the best annual return for this ETF since its inception in 2010.

But, there were other broad-based equity ETFs that did even better. The best performing one was focused on information technology. Other top performers included growth ETFs distributed across, small-cap, mid-cap and mega cap indices. And, a newer investment trend we’ve written about before also emerged as a leader: Environmental, Social and Corporate Governance (ESG) in the U.S.

Returns from Information Technology Firms led the markets in 2019
Returns from Information Technology Firms led the markets in 2019

On the other end of the return spectrum, the energy sector lagged the S&P 500 by the greatest amount. Other noteworthy groups of ETFs tracked by Vanguard that also lagged the S&P 500 were as follows.

  1. Value and dividend-oriented ETFs
  2. International, both developed countries and emerging markets
  3. Many industry sectors (real estate, industrials, consumer discretionary and staples, utilities, materials health care)

Fixed Income ETF Returns

Fixed income ETFs also had a very good year in 2019. Using the total bond market ETF as a benchmark, fixed income ETFs returned 8.8%

Total Returns of Vanguard's Fixed Income ETFs in 2019
Total Returns of Vanguard’s Fixed Income ETFs in 2019

The leaders in the bond market in 2019 were those that held riskier bonds, like those from corporations vs. the U.S. government. Fixed income ETFs with longer maturities also led the bond markets in 2019.

Conclusions on 2019 ETF returns

We hope you found this review of stock and bond ETF returns from 2019 helpful. Interested in using the Vanguard ETFs in a 2020 diversified portfolio? If so, please check out our Free Optimal Portfolios for 2020 for some ideas. Or, if you are seeking a diversified portfolio that analyzes over 2,000 ETFs (including those from Vanguard), please review our Premium Optimal Portfolios for 2020.

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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Making sense of ETF Liquidity

In my last post, I discussed ETF liquidity risk. After the post, a subscriber to ETFMathGuy asked me to talk more about this risk and how it relates to the wide variety of commission-free ETFs now available.

Bid-ask Spreads

Bid-ask spreads are an excellent way to measure liquidity. Less liquid ETFs generally have higher bid-ask spreads. But, the liquidity of the securities held by the ETF also affects bid-ask spreads. The image below shows the distribution of bid-ask spreads for Fidelity commission-free ETFs, which I updated from my April 2019 post.

Bid-ask spread of Fidelity Commission-Free ETFs, as of 9/22/2019. Source: ETF.com, Fidelity.com
Bid-ask spread of Fidelity Commission-Free ETFs, as of 9/22/2019. Source: ETF.com, Fidelity.com

Minimizing costs

As we see from these results, there is a wide variation of bid-ask spreads. So, about half have spreads under 0.1%, and about 80% under 0.3%. For ETFs traded commission-free, these spreads are likely the largest contributor to cost of ownership. To reduce this cost, an investor can either buy-and-hold for extended periods, or choose ETFs with lower bid-ask spreads. Investors should also avoid trading ETFs close to the market open and close. Higher volatility over a typical trading day can often occur close to the market’s open and close, and can produce higher bid-ask spreads.

What about ETF liquidity during high market volatility?

It is very likely that, during periods of high market volatility, bid-ask spreads will grow. This growth is simply the result of finding a balance between supply and demand. Or, in the case of ETFs, this balance occurs when an ETF seller finds a buyer. Remember that, due to liquidity risk, we can expect a return premium over risk-free investments. If market volatility is a concern, investors should seek lower volatility investments (e.g. bonds over stocks), and/or seek lower volatility in their portfolio through diversification.

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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September portfolios and year-to-date returns

The September 2019 optimal portfolios are now available to subscribers of ETFMathGuy. So, please log in and select your discount broker to see the effect of current market conditions on our optimal portfolios. In this post, we discuss the year-to-date returns of my personal account using the ETFMathGuy portfolios.

Year-to-date returns

Although there are still four months remaining in the year, I thought this would be a good time to talk about my year-to-date returns. I have personally been using the moderate risk level portfolios in my Fidelity brokerage account since the beginning of the year. Monthly returns, based on the balance in my account, appear below.

Monthly returns using commission-free Fidelity ETFs and the moderate ETFMathGuy risk level.
Monthly returns using commission-free Fidelity ETFs and the moderate ETFMathGuy risk level.

To better understand the returns in my account that maximizes return for a portfolio with volatility half-way between stocks and bonds, I created the next table. Here, you can see that the ETFMathGuy portfolio return so far in 2019 is 14.1%, with a monthly volatility of 2.1%. To one decimal place, the same volatility is seen if an investor had simply maintained a 50% stock and 50% bond fund, re-balanced each month. But, the 50/50 portfolio would have seen a return of only 13.7%

ETFMathGuy portfolio returns are higher than a 50/50 stock/bond portfolio, with the same volatility.
ETFMathGuy portfolio returns are higher than a 50/50 stock/bond portfolio, with the same volatility.

Key takeaways

The ETFMathGuy portfolios appear to be behaving as expected. That is, they have about the same amount of volatility as their benchmark. However, I realized an additional return of about 0.4% in my brokerage account. For a $100,000 portfolio, that is an additional gain of about $400. I will revisit my portfolio’s performance again at the end of the year, so please stay tuned!

The future of ETFMathGuy

For the near future, I will continue to provide the optimal portfolios without a fee. But, in the meantime, I decided to begin accepting donations, if you are so inclined. Please find the donate button at the bottom of the “Join Us” page. For your convenience, it also appears below.

Thanks for supporting ETFMathGuy!

Thank you all for your interest and support in 2019. I hope you all had a wonderful labor day weekend!

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.