Tag: portfolio

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Retirement tax alpha and optimal retirement drawdowns

Tax alpha refers to the additional rate of return generated by making tax-efficient investment decisions. For retirees, we provide an optimal retirement income calculator that models the U.S. tax code and determines an optimal drawdown strategy. Here, we discuss a recent upgrade to this calculator that quantifies your potential retirement tax alpha using an optimal drawdown strategy.

retirement tax alpha and your optimal retirement income strategy
Retirement tax alpha and your optimal retirement income strategy
Photo by Nataliya Vaitkevich on Pexels.com

What is alpha?

In the investment world, the return not captured by the movement in the broad market is alpha. Thus, for many investors, it means a risk-less return. In fact, we’ve even talked about it before in the context of CAPM and its counterpart, beta. Alpha and beta provide portfolio statistics important for consideration by any investor.

What is tax alpha?

Tax alpha is a relatively new term and may differ based on the source. We like the following definition.

If “alpha” is the return generated by an advisor’s skill in picking and managing investments, then “tax alpha” protects that return and generates a boost by making sure that taxes don’t eat away more of a client’s wealth than absolutely necessary.”

Source: https://www.atstax.com/p/what-is-tax-alpha

What about in retirement?

In retirement, tax alpha focuses on tax-efficient drawdowns. In addition, the industry standard for retirement income drawdowns from taxable, tax-deferred, and tax-exempt accounts is the Common Rule. The image below shows a summary of the default case used in our optimal calculator, which compares its results with those from the Common Rule.

Summary of Optimal Retirement Calculator. Source: https://app.etfmathguy.com/

This last line (line 4) indicates the value of tax-alpha of 0.57%. That is, a retiree would need to generate pre-tax returns 0.57% higher using the Common Rule to generate the same after-tax inheritance for their heirs. Therefore, by making optimal drawdown decisions in retirement, a retiree can expect to increase their investment returns using the Common Rule. Interested in seeing the details of this example or inputting your own assumptions for retirement? If so, please try our free online calculator.

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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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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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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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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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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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.
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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.