Imagine, for a moment, that you're an investor who has been doing their homework in choosing the next stock in which you'll invest. You've narrowed your options down to two stocks, where you will one invest in one. One of the two stocks is a growth stock, which is to say that your returns will be totally determined by how its price changes over time. The other stock you're thinking about buying is a value stock, whose stock price could also grow, but which also will pay you dividends.

Which stock will you choose?

To answer that question, you will need to make some judgments about how each stock is valued. That can be as easy as calculating its Price-to-Earnings Ratio (P/E), but a word of warning. What you care about is the future, because that's where your returns will be. How can you factor in how much the companies behind each stock will grow in the future? And in the case of the value stock that also will pay you a dividend, how can you factor those future returns into your valuation assessment?

Quantamental Trader reviewed how legendary trader Peter Lynch did that when selecting the stocks in which he invested:

The Foundation: From P/E to PEG

Traditionally, the Price-to-Earnings (P/E) ratio has been a fundamental metric for valuing stocks. It relates the current stock price to its earnings per share (EPS). However, the P/E ratio alone often lacks context because it ignores the company’s expected growth. For example, a high P/E might be justified for a rapidly growing firm, while a low P/E might indicate undervaluation or fundamental problems.

The PEG ratio addresses this by dividing the P/E ratio by the company’s projected EPS growth rate (G):

PEG = Price-to-Earnings Ratio / EPS Growth Rate

A PEG ratio around 1 is generally considered fair value, less than 1 implies undervaluation, and above 1 overvaluation—though these are rules of thumb.

Peter Lynch recognized this metric’s usefulness but also noted its limitations.

The Innovation: Why PEGY?

The PEG ratio, while helpful, ignores dividends. Mature companies often grow earnings slowly but pay dividends consistently, returning value to shareholders. The PEG ratio tends to unfairly penalize these slower-growers because their growth rate is lower, making PEG higher even though their total return could be attractive when dividends are included.

To correct this, Lynch introduced the PEGY ratio, which incorporates dividend yield (DY) alongside expected earnings growth:

PEG = Price-to-Earnings Ratio / (EPS Growth Rate + Dividend Yield)

By summing the earnings growth rate and dividend yield, PEGY reflects the total expected return—growth plus income—and better accounts for companies at different stages: fast-growing firms with little dividend, and mature firms with steady dividends.

We've built the following tool to do the PEGY ratio math, but first, here's some data from two stocks we researched on Seeking Alpha. Both stocks are beneficiaries of the AI boom of recent years. One is a growth stock in the technology sector that pays a very small dividend, the other is a value stock in the energy sector that pays a substantial dividend. Here are their respective valuation metrics, which we sampled after the close of trading on Friday, 15 August 2025:

If you use a site like Seeking Alpha to look up this data, after searching for a specific company, you'll find the P/E Ratio (TTM) under the stock's "Valuation" section, the EPS Diluted Growth (YoY) under the "Growth" section, and the Dividend Yield (TTM) under the "Dividends" + "Dividend Yield (TTM)" section. This data is backwards-looking, which has the advantage of being relatively fixed and which can be used with the assumption that the near future will be similar to the recent past. Alternatively, you could substitute the FWD version of this data, provided you recognize expectations for the future are subject to change with little notice....

Here's the tool. If you're accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool.

The default data in the tool is for the growth stock, which finds it has a PEG of 2.45 and a PEGY of 2.35. Substituting the data for the value stock in the tool, we find it has a PEG of 1.93 and a PEGY of 1.39. Quantamental Trader provides the following guidance for how to interpret these results in comparing the two stocks:

Interpreting PEGY

• PEGY < 1: The stock may be undervalued relative to its combined growth and income potential.
• PEGY ≈ 1: The stock is fairly valued.
• PEGY > 1: The stock might be overvalued.

According to this interpretation, both stocks would be considered to be overvalued. The value stock however is closer to being fairly valued according to the PEGY measure.

That's not to say the growth stock won't provide the kind of return you might be hoping for, but it is important to recognize there is a greater risk associated with investing in it. The PEGY valuation tool gives you the means to quantify what that relative risk looks like - just plug in the numbers that matter for the stock you're evaluating.

Image credit: Microsoft Copilot Designer. Prompt: "Picture of an investor doing math to choose between a growth stock and a value stock". Just ignore the math and whatever the investor is doing with their lip and finger to balance the gravity-defying pencil as depicted.

The passage of President Trump's "One Big Beautiful Bill" into law wasn't pretty to watch, but for Americans who have been or will be born in the years from 2025 through 2028, it offered something very new. The law sets up a pilot program for children born during this period that gives them a new way to save, plus a $1,000 credit to get them started.

Called "Trump Accounts", the new investment builds on legislation proposed by Senator Ted Cruz earlier in 2025, which was rolled into the "big beautiful bill". Here's NerdWallet's excellent summary of the basics for the new accounts:

Who qualifies?

Not every kid can get a Trump Account. To be eligible for the $1,000 credit under the pilot program, children must:

• Be born between Jan. 1, 2025, and Dec. 31, 2028.
• Be a U.S. citizen.
• Have a Social Security number.

How do Trump Accounts work?

Getting started

Under the pilot program, the Treasury will set up accounts for qualifying kids if their parents haven’t already done so. Parents aren’t required to make an election.

How do contributions and withdrawals work?

Trump Accounts come with some restrictions. Contributions made before the calendar year in which the beneficiary turns 18 are limited to $5,000 per year. Employers can contribute up to $2,500 to accounts, which won’t count as income for the parents or children.

Trump Account distributions aren’t allowed before the first day of the calendar year the child turns 18.

Contributions made after the child’s 18th year generally follow traditional IRA rules. The IRA contribution limit in 2025 is $7,000 for those under age 50. The money invested grows tax-deferred, and withdrawals are taxed as ordinary income.

There’s a 10% penalty for withdrawing money from an IRA before age 59-½, unless there’s a qualifying exception, such as homebuying, or paying for higher education expenses.

What about taxes?

Contributions made to Trump Accounts before the child’s 18th birth year must be made with after-tax dollars, which means no tax deduction for parents or employers, said Jacob Martin, a certified financial planner in Columbus, Ohio, in an email interview.

While the new Trump accounts aren't themselves necessarily better than existing types of investment accounts, they are aimed to benefit those Americans who stand to gain the most from the power of compounding over time:

The "proposal reflects a growing consensus: investing early in every child’s future is a smart and necessary step," said Marisa Calderon, president and chief executive of Prosperity Now, a national nonprofit organization focused on expanding economic opportunity for low-income families and communities in the United States....

"Research shows that lasting change comes from scale," Calderon said. "Deposits must grow over time and be available when they matter most, such as paying for college, starting a business, or buying a first home."

After 25 years, $1,000 invested in the S&P 500 would grow to approximately $10,835, for example. The average stock market return is about 10% per year for nearly the last century, as measured by the S&P 500 index.

We decided to put that last statement to the test. We have the tools to estimate how much any hypothetical investment in the S&P 500 in any month would be worth at the end of a given period of investing.

We put those tools to work to produce the following chart to show how much $1,000 invested at the average level of the S&P 500 was in any month from January 1955 onward, with the value of the investment shown as of May 2025 when Cruz' introduced his bill. Because the value of the investment grows by more than one order of magnitude over this 70+ year period, we're presenting the following chart showing that growth in logarithmic scale. If you prefer to see the data on a linear scale, we have you covered - just follow this link.

Some quick observations:

• Reinvesting dividends unlocks the power of compounding. In the 20 years from May 2005 to May 2025, an initial investment of $1,000 in the S&P 500 would grow to about $4,932 without dividend reinvestment. With dividend reinvestment, that value of that $1,000 grows to about $7,672.
• The longer the investment is held, the better it gets. At the very long investment horizon of 70 years, $1,000 invested in May 1955 would grow to about $154,546 without reinvesting dividends, but with dividend reinvestment, that $1,000 would have grown to almost $1,231,743 in May 2025.
• The peaks on the chart come from the initial investment being made when the S&P 500 had experienced a crash. By the same token, the troughs in the value of how much a $1,000 investment has grown comes from having been invested when the index itself had either peaked before crashing (such as in 2007) or was experiencing inflating bubble conditions (such as from April 1997 through August 2000).
• Investing just $1,000 once is nice, but making regular investments monthly over a long period of time can help smooth out the investment gains over time. Even if the size of those regular investments is much smaller than $1,000, the benefit of dollar-cost averaging can reduce the impact of the S&P 500's volatility.

There are several tools that use historic data where you can see how the value of money invested in the S&P 500 has changed over time. Here's a sampling:

• Investing Through Time (Political Calculations)
• Stock market returns since 1957 (OfficialData.org)
• S&P 500 Historical Return Calculator [With Dividends] (Of Dollars and Data)
• S&P 500 Historical Return Calculator (Don't Quit Your Day Job)

Each of these tools will deliver similar, but not necessarily the same results. These changes are often attributable to minor things like how a given month's estimated dividends are rounded, which can lead to notable differences when long periods are considered given the compounding math.

We're fans of both Nick Maggiulli's work at Of Dollars and Data and also PK's work at Don't Quit Your Day Job. We recommend exploring their sites and posts to where they've incorporated tools to explore investing and other topics!

Image credit: Photo of a little girl sitting on a couch holding money by Bermix Studio on Unsplash.

You never saw the market crash coming. When it came, it lasted longer than you would ever have expected. The damage it did seriously dented your retirement savings at the worst possible time for you. Now, your ability to live through your retirement years the way you planned is in jeopardy. What can you do?

Working out how to deal with a worst case scenario like this is among the least fun aspects of financial planning because it casts a gloomy shadow over all that you might have hoped you could do in retirement. Yet if you don't and the worst case scenario for you happens, you'll find out quickly how much more gloomy the experience can be. Thinking about how you might recover from that kind of hit while planning your retirement will at least give you a good sense of what you can do if you need to face that situation. There's comfort in knowing what things you can do.

Previously, we considered a scenario in which the worst case happened, but the two hypothetical investors experiencing it at different points of their retirement years never adapted their retirement spending plans to recover from it.

But what if they did? The analysts at Schwab's Center for Financial Research considered how two different hypothetical investors who started off with the same retirement plan might respond to the worst case scenario of a prolonged market crash at the beginning of their retirement years by changing the rate at which they withdrew money from their retirement accounts while the market recovered. One would withdraw just 2% of their retirement savings per year, while the other would withdraw 4% [1]. The following chart shows the results of this exercise:

Here's what they found:

A rebounding market should help them quickly make up lost ground, right? Unfortunately, not always—those continuing withdrawals can create a strong headwind, with more shares sold to support spending in a down market than would be the case when values are appreciating. But by dialing back his annual withdrawals to 2%, Investor 1 will be back where he started after roughly 11.5 consecutive years of 6% annual gains. With a 4% withdrawal rate, Investor 2 would have to have 28 straight years of 6% gains to fully recover.

Somewhat lost in this discussion is the bigger question of what are each investor's retirement savings for. Is it to preserve and grow the total value of their accumulated retirement savings throughout their entire retirement so that it can be passed on to their heirs? Or is it to provide reasonably sufficient funds to support their living expenses during retirement?

For example, let's say you went from having a million dollars in retirement savings when you started your retirement and dropped to around $650,000 after two years of a market crash. Withdrawing 2% annually could get your retirement account to fully recover after 11.5 years, but would mean pulling just $13,000 to support your retirement in that first year of recovery and similar amounts in future years. You could double that withdrawal rate to 4% and you can have $26,000 in that year, but that would mean an extra 16.5 years before your retirement account might reach $1 million again.

Which outcome matters more for you?

Previously on Political Calculations

• When Is the Worst Time for Your Retirement Savings to Take a Hit?
• What Can You Do If Your Retirement Savings Take a Big Hit?
• Will Your S&P 500 Investment Last In Retirement?
• Cashing Out of the S&P 500
• Can You Afford to Retire?
• How Much Do You Need to Save for Retirement?

Notes

[1] Here is Schwab's hypothetical investing scenario for the two investors recovering from a bit hit to their retirement savings:

The example is hypothetical and provided for illustrative purposes only. It is not intended to represent a specific investment product. Dividends and interest are assumed to have been reinvested, and the example does not reflect the effects of taxes or fees. Both portfolios start with $1,000,000. Both portfolios experience 15% declines in years one and two, while both hypothetical investors also withdraw $50,000 per year. Starting in year three, both portfolios grow 6% per year. Investor 1 withdraws 2% per year. Investor 2 withdraws 4% per year.

Image credit: Recovery Chalkboard by Nick Youngson. Creative Commons CC BY-SA 3.0 at Picpedia.org.

Imagine you've made it to retirement and all that means. No more day job. The extra time to do the things you previously could only do while you were on vacation. Not that you necessarily would pass all your retirement doing those kinds of things, but if you wanted to, you certainly could do a lot more of them than you could when you were working.

There is a catch. Your retirement savings have to last as long as you do after you stop working. That means they will have to weather through things like the stock market's volatility. Volatility that could potentially deliver a hit to your retirement savings.

There's no telling when such a hit to your financial security in retirement might happen, but if you live long enough, chances are you will experience that kind of drama. If you were to take that kind of hit, when do you think it would be best for you to handle it? Early in your retirement when you might have more time to recover from it? Or later?

In other words, when is the worst time to take a hit to your retirement savings and your plans for how you'll live when you're retired?

Analysts at Charles Schwab's Center for Financial Research took on that question. Their answer is visually presented in the following chart for hypothetical investors who start their retirements with the same amount of savings and the same plan of taking $50,000 annual withdrawals that escalate by 2% a year for inflation all throughout their retirement.

The difference between the two scenarios for Investor 1 and Investor 2 is the timing for when their retirement savings takes a big hit. Investor 1 experiences a -15% annual return during each of the first two years of their retirement, while Investor 2 has to deal with the same magnitude hit in their tenth and eleventh year of retirement. Their investments otherwise perform similarly [1].

As the chart reveals, Investor 1 runs out of money in Year 18 of their retirement. Investor 2 however still has quite a lot of their retirement savings left at the same point of time. It is far worse to experience a major hit early in retirement.

Of course, that assumes that neither hypothetical investors ever changes how much they withdraw each year from their retirement savings after taking the big hits they do, which is a different topic for a different day. For now, the important thing is to know that being able to sustain a big hit to your retirement investments in the first two years of your retirement savings is something for which you can and should plan. Remember, the worst case scenario is your retirement savings get knocked down right after you retire. If you don't experience that kind of event until you're well into retirement, you won't have the same risk of your retirement savings running out of money while you need them.

Schwab's Rob Williams offers a suggestion for how to handle the worst case scenario:

One approach is to maintain a short-term reserve of low-risk liquid investments that you can use to cover your expenses while you avoid tapping your stocks.

Rob recommended keeping a year's worth of expenses after accounting for other income sources including Social Security, if applicable, in cash investments and another two to four years' worth of expenses in high-quality short-term bonds or short-term bond funds. This allocation can be included as part of your retirement portfolio. A portfolio in retirement can include a personalized mix of cash, cash investments, short-term and other types of bonds or bond funds, and stocks. With an allocation to cash, cash investments, and short-term bonds in place, you may feel more comfortable about having a decent chunk of stocks on hand that can generate growth later.

There are a lot of ways allocate funds to function as a relatively safe reserve and there's not by any means a one-size fits all way to do it. Setting up such a stormy weather reserve as part of your retirement plan can give you a better ability to handle a major market downturn by helping you avoid having to otherwise deplete your retirement accounts too quickly to pay your living expenses in retirement.

Notes

[1] Here's the fine print from Schwab's hypothetical investing scenario for the two investors:

The example is hypothetical and provided for illustrative purposes only. It is not intended to represent a specific investment product. Dividends and interest are assumed to have been reinvested, and the example does not reflect the effects of taxes or fees. Both hypothetical investors had a starting balance of $1 million, took an initial withdrawal of $50,000, and increased withdrawals 2% annually to account for inflation. Investor 1's portfolio assumes a negative 15% return for the first two years and a 6% return for years 3 – 18. Investor 2's portfolio assumes a 6% return for the first nine years, a negative 15% return for years 10 and 11, and a 6% return for years 12 – 18.

Image credit: Worst Case Scenario Chalkboard by Nick Youngson. Creative Commons CC BY-SA 3.0 at Picpedia.org.

The Chief Executive Office, or CEO, of a business comes with a lot of responsibility. For better or worse, CEOs are the faces of the companies they lead. They not only set the direction for what the company does and will do, they also function as its main representative, both to the public and to the company's owners.

For publicly-traded companies, the owners are shareholders. Shareholders can be anyone from people who liked the company's prospects and bought a handful of shares of its stock to the institutions that manage multi-billion dollar retirement funds for millions of people who buy thousands of shares for the same reason. Shareholders have a vital interest in the success of the business because the future value of their investments depend upon it.

So what then are investors supposed to make of the situation when the CEO of a company in which they have staked their future starts prioritizing partisan politics in their public communications? Especially when that activity suggests they're not putting the shareholders' interests in the success and growth of the business first and foremost in their role as CEO?

Or to get straight to the bottom line, are politically partisan CEOs good for stock prices?

A new working paper by William Cassidy and Elisabeth Kempf of the Harvard Business School strongly indicates the answer is no. Political CEOs are not good for stock prices.

The way they came to that conclusion is pretty novel. They focused on corporate Twitter posts made during the period from 2012 through 2022, using natural language analysis to determine which contained partisan political content. They then looked at how various firms' stock prices behaved in the 10 days before a partisan tweet was issued with how they behaved in the 10 days after. The following figure from the paper shows what they found:

Cassidy and Kempf describe what the panels of the chart illustrate:

Figure 6, Panel A plots the average cumulative abnormal return around partisan tweets. On the day of the tweet itself, the average stock return is close to zero. However, a noticeable decline in the stock price occurs over the ten days following the average partisan tweet, reaching approximately –20 basis points (bps) on event day +10, statistically significant at the 5% level. When we extend the post-event window to 30 days after the tweet, we find that stock prices continue to decline until about 13 trading days after the tweet before leveling off, reaching a CAR of almost negative 30 bps (see Internet Appendix Figure IA.11). In other words, the full stock-price impact takes time to materialize, consistent with the delayed stock-price impact of legislation documented in previous work (e.g., Cohen et al. (2013)). We do not observe a significant trend in the stock price prior to the tweet event.

In Panel B of Figure 6, we separate tweets into those whose partisan slant is more versus less surprising given the company’s past tweet history. Specifically, we compute a tweet’s partisan-slant surprise as the absolute difference between the tweet’s P SI-value and the average P SI-value of the company’s tweets in the 36 months prior to the event. Tweets with a high surprise are those in the top quartile of partisan-slant surprises across all partisan tweets in a given calendar month. All other tweets are considered “low surprise.” Consistent with the news content of partisan-slant surprises being higher, we observe a stronger decline in the stock price in the high-surprise subsample.

The period from 2012 through 2022 saw a sharp rise in partisan tweets made by CEOs of U.S. corporations starting in 2017, particularly in support of policies associated with the left-leaning portion of the political spectrum in the U.S., which greatly outnumbered conservative-leaning tweets. Their results indicate that shift in CEO and corporate communications in favor of partisan politics hurt stock prices.

If you think about it, that makes a lot of sense. Whenever corporate leaders like CEOs turn their attention away from their chief fiduciary duties in running their businesses, it diminishes the outlook for their business' prospects. To put it into sports terms, it signals they're taking their eyes off the ball, which is not good for investors.

That's the best case scenario. A focus on partisan politics can also provide a distraction away from poor business performance, which in the very worse case scenarios, tries to cover up a series of bad decisions that actively hurt both the business and the interests of investors.

Here are Cassidy and Kempf's main conclusions, in which they also identify the main driver behind the shift in CEO and corporate communication practices:

This paper provides one of the first large-scale empirical analyses of partisan corporate speech, using a novel measure based on natural language processing of corporate social media communication. We use this measure to establish three key stylized facts. First, partisan corporate speech has increased significantly over the past decade, with a particularly sharp rise after 2017. Second, this increase has been disproportionately driven by Democratic-leaning statements, a trend that spans industries, geographies, and firms led by both Democratic and Republican CEOs. Third, partisan corporate statements are, on average, followed by negative abnormal stock returns, with significant heterogeneity depending on the political alignment of the firm’s investor base.

To explain these patterns, we explore potential drivers of the rise in Democratic-sounding speech. While employee and consumer preferences may play a role, we also find novel empirical support for an investor-demand channel. The surge in Democratic corporate speech coincides with the rapid expansion of sustainable investing, and firms with high BlackRock ownership exhibit a particularly strong shift toward Democratic language following Larry Fink’s 2019 letter to CEOs, which urged CEOs to engage more in contentious social and political debates. Our theoretical model formalizes this mechanism, demonstrating how shifts in investors’ nonpecuniary preferences can lead firms to adopt partisan positions, even when doing so negatively impacts stock prices.

Since 2022, BlackRock's Larry Fink has systematically backed away from supporting the left-leaning "Environmental, Social, and corporate Governance" (ESG) standards he previously championed. It wasn't good for his influential company's investments. Or for the investors who own shares in the companies whose CEOs put politics ahead of running the business.

Reference

Cassidy, William, and Elisabeth Kempf. "Partisan Corporate Speech." Harvard Business School Working Paper, No. 05-056, May 2025. [PDF Document]. DOI: 10.2139/ssrn.5249915.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a group of investors attending a company's annual meeting who are horrified that the CEO is tweeting about politics".

Through August 2024, the cost of eating out at establishments that provide full service meals and snacks has risen 23% since January 2021.

In fact, when you go out to a restaurant today, it's not uncommon to see things like $16 dollar BLT sandwiches on the menu. How is it possible that two slices of toasted bread, a couple strips of bacon, several leaves of lettuce, and one or two tomato slices and some mayonnaise possibly cost so much?

The short answer is because of the inflation unleashed in early 2021. That inflation has driven up the costs of everything it takes to provide you as a customer with a BLT sandwich, including rents, utilities, and labor - it's not just the cost of food itself that has gone up.

Brian Will is a restaurant owner in the north Atlanta metropolitan area. In the following TikTok video, he lays out the percentages and costs of doing business that dictate why he has to charge for a BLT sandwich:

@dropoutmm Restaurant food is expensive #restaurantlife #foodcost #restaurantindustry #restaurant #businessowner #businesscoach ♬ original sound - The Dropout Multimillionaire

We thought the numbers he provided, including the average number of BLT sandwiches that his restaurant must sell per day just to break even, made for some interesting math. We've built the following tool to convert the numbers he throws out into the math behind them, but you're more than welcome to change the numbers to consider a multitude of other scenarios. If you're accessing this article on a site that republishes our RSS news feed, you may need to click through to our site to access a working version.

The default values are mostly those given by Will for his restaurant, which almost certainly involve some rounding. We tweaked the value of the unit cost of the food to roughly match what it would take for the restaurant to break even, assuming an average of 257 BLT sandwiches at $16 each per day. Of course, the restaurant's net income represents the income that Will and his partners earn through their ownership and management of the business. If they're just breaking even, with a net income of $0, they can't afford to be in business and the restaurant will shut down.

If they do have a positive net income, say from selling an average of 300 BLT sandwiches per day instead of just 257 to break even, they're going to have to pay income taxes on it, which is why we added that additional element to the tool.

There's one other aspect to consider as well. Today's inflated prices for BLT sandwiches and every other menu item on American restaurant menus are changing the way people eat, with fewer people willing to eat out because of the higher prices they would have to pay. The effect of inflation on supply and demand has a negative effect on the restaurant industry. If they could count on selling more sandwiches every day, they could sell them for a lower price, but the higher costs for everything that goes into making a sandwich to be served at a restaurant have made that marketing strategy much more risky.

If the risk of making the wrong decision in this real world scenario means going out of business, especially if you expect inflation to continue making everything more costly, could you as a business owner even afford to try?

Image credit: Photo by David Trinks on Unsplash.

When is the absolute worst time to take a hit to your retirement savings?

Almost by definition, it has to be after you've retired. If it happened before you were planning to retire, you would have the option to postpone your retirement date, giving yourself additional time to add to your retirement savings.

But that's not something you can do after you've retired. Certainly not easily. After you've retired, you can reasonably expect your working days are behind you.

So when after you've retired would be the the worst possible time to experience a sudden decline in the value of your retirement savings?

That question was answered by Schwab's investment analysts, who compared two specific scenarios. In the first scenario, an individual who retired experienced a negative 15% annual reduction in the value of their retirement accounts over a two year period, starting immediately after retiring. The second scenario considered the impact an identical reduction would have if it occurred some ten years into retirement, when presumably the retiree would have no real option to rejoin the ranks of the employed.

They created the following chart to visualize the relative impact of this hypothetical event:

Here are the assumptions behind the visual analysis:

• Both hypothetical investors started with $1 million in their retirement savings.
• Dividends and interest are reinvested.
• The effects of taxes and fees on the retirement savings values are not considered.
• The hypothetical investors withdrew $50,000 from their accounts in the first year, then increased their withdrawals by two percent a year to account for inflation.
• Outside of the 15% annualized reductions during the years of decline, the value of the hypothetical investments grow at an annualized rate of 6% a year.

The chart confirms the worst case scenario is the one when misfortune hits at the very beginning. A financial calamity that strikes then has the capability to permanently reduce your retirement nest egg, making it likely it will run out of funds while you're still alive.

Assuming you make no changes to how much you withdraw each year. Schwab's analysts explain why getting hit early in retirement can be so damaging:

At issue here is a phenomenon known as sequence-of-returns risk. "Sequence" refers to the fact that the order and timing of poor investment returns can have a big impact on how long your retirement savings last.

After all, a retirement portfolio generally isn't just a lump of cash in a savings account that you draw inexorably down to zero. It also includes a mix of investments that can provide both income and growth over time. Ideally, the growth will replenish at least a portion of what you take out, making your withdrawals more sustainable over the length of the retirement you've envisioned.

However, a major drop in the early years of retirement can scramble this picture. When you tap into your portfolio as it's losing value, you have to sell more investments to raise a set amount of cash. Not only does that drain your savings more quickly, but it also leaves you with fewer assets that can generate growth and returns during potential future recoveries.

In contrast, if a decline occurs later in your retirement, you may not need your portfolio to last as long or continue growing to fund a long retirement, so you may be in much better shape to fund withdrawals.

Please do click through to read the whole article, because Schwab's analysts also discuss the steps that can be taken after financial disaster strikes to mitigate its impact. We will take their ideas and others on in future discussions.

If you spend any time working with the math of finance, you'll eventually encounter the Rule of 72. What is the Rule of 72? It is, quite simply, one of the most useful tools you can use to quickly approximate how long it will take to double your money in an investment that compounds annually. All you need is to take the percentage rate of return for your investment and divide it into the number 72. The result you get will be a good estimate of how many years it will take for the value of your investment to double.

Best of all, it's math you can do in your head. Which compared to the math formula you would need to use to get an exact answer otherwise, is lightning fast. Even if you were to use a calculator to do the exact math.

Sal Khan has a short video explainer describing the Rule of 72 that picks up after he uses the exact formula. What makes this video stand out from others is he goes the extra mile to answer the question of how good the Rule of 72 is at approximating the exact answer across a range of common rates of return that matter to investors.

Because the video picks up the discussion from examples of compounding interest, it might help to take a step back and start from the basic future value formula, which looks something like this for an investment that compounds annually:

Future Value = Present Value * (1 + Rate of Return)^{Time in Years}

Since we want to find out how long it takes the value of the investment to double, we'll set "Future Value" to be equal to 2 times the "Present Value"

2*Present Value = Present Value * (1 + Rate of Return)^{Time in Years}

At this point, since we now have "Present Value" on both sides of the equation, we can simplify the equation by dividing both sides by it. Doing that gives us the following result:

2 = (1 + Rate of Return)^{Time in Years}

From here, if we want to solve this equation for "Time in Years", we'll need to deploy the magic of logarithms. Which for us, starts with taking the natural logarithm (ln) of both sizes of the equation:

ln(2) = ln[(1 + Rate of Return)^{Time in Years}]

In this next step, we'll apply the power law of logarithms to transform the exponent math into simple multiplication on the right hand side of the equation:

ln(2) = Time in Years * ln(1 + Rate of Return)

We're almost there. We'll next solve for "Time in Years" by dividing both sides of the equation by ln(1 + Rate of Return). Here's the result:

ln(2)/ln(1 + Rate of Return) = Time in Years

In the final step, we'll swap the left and right hand side of the equation to make it easier to read by putting it into a more standard format:

Time in Years = ln(2)/ln(1 + Rate of Return)

To use this formula, the Rate of Return has to be written in a decimal format. For example, a rate of return of 6% would be written as 0.06 in the formula. And from here, you would be doing the same math Sal Khan was doing in the video, which we'll leave as an exercise for you if you really want to do it.

But why does the Rule of 72 work to closely approximate the exact result you get from the logarithm math we just showed? Steve Fiorino takes the explanation to the next level:

It may not be apparent at first glance how this exact equation is able to bring us to the rule of 72. For it to become clearer, input ln(2) into a calculator. It's an irrational number, but when you put it into the calculator by itself it will give you a number that it equals: 0.69314718056.

Or, phrased in another way, 69.3%.

That's how you get the rule of 69.3, but unless you're a math whiz who somehow memorized multiples of 69.3 it's still pretty difficult to do the equation. Thus, 70 and 72, which have more numbers that divide cleanly into them while still giving close approximations, became popular.

The Rule of 72 became the most popular version of this application because it has more whole number divisors that produce whole number results.

Perhaps more remarkably, the Rule of 72 for approximating the time it takes an investment to double in value predates the invention of logarithms! Here's WesBanco's description of its earliest use:

The Rule of 72 was first introduced in the late fifteenth century by the Franciscan friar and Italian mathematician Luca Pacioli. A contemporary of Leonardo da Vinci, Pacioli is considered by many to be the father of accounting. The Rule of 72 was introduced in his book Summa de arithmetica, geometria, proportioni et proportionalita, published in 1494 for use as a textbook for schools in what is now northern Italy.

Here's a link to Pacioli's 1494 book. Meanwhile, logarithms as we know them today weren't invented until John Napier developed them over a century later, publishing them in his 1614 book Mirifici logarithmorum canonis descriptio.

For what it's worth, the origin of the Rule of 72 can be attributed to earlier, unknown mathematicians who built it on a foundation of much older math that dates back centuries earlier, who recognized they could apply it to solve practical, real-world problems. However, it wasn't until after logarithms were invented that mathematicians could demonstrate why it works as well as it does.

Image credit: A number (72) of white letters on a black surface photo by iridial on Unsplash.

If you invested $100 at the beginning of 1970, how much would it be worth at the beginning of 2024?

The answer to that question depends on how you invested that $100. Would you buy gold? What about stocks or corporate bonds? Would you play it safe and go for Treasury bonds? Or maybe buy some real estate? How about if you found an investment that would keep up with inflation? What would $100 worth of 1970's dollars be worth after all that time?

Visual Capitalist's Dorothy Neufeld considered each of these options and charted the results. Here they are:

These results are based on data collected by NYU's Aswath Damodaran, which is a tremendous resource. Unless you have your own personal Wayback Machine, or are the beneficiary of some really savvy investing by someone who decided to put $100 to work in an investment in 1970 rather than spend it on 1970's consumer goods, the results shown in the chart are as close as you'll get to the answer to the question we asked at the beginning.

Here's Neufeld's discussion of the results she obtained by hypothetically investing $100 in 1970 through the end of 2023:

As we can see, a $100 investment in the S&P 500 (including reinvested dividends) in 1970 would be worth an impressive $22,419 in 2023.

Not only were U.S. stocks the top performing major asset class, they outpaced other investments by a wide margin. Consider how a $100 investment in corporate bonds would have grown to $7,775 over the period, or 65% lower than an investment in the S&P 500.

When it comes to gold, a $100 investment would have been worth $5,545 by 2023. During the 1970s and 2000s, gold boomed amid bouts of inflation and a falling U.S. dollar. By comparison, the S&P 500 saw much lower returns over these decades.

Real estate, another safe haven asset, grew on average 5.5% annually since 1970, with the highest gains seen in the decade through 2020. It’s worth noting that these numbers are from the Case-Shiller Home Price Index, which is based on purely price changes over time.

Given that real estate is a unique asset class, this doesn’t necessarily illustrate the returns that homeowners actually receive, factoring in leverage, property taxes, insurance, and other expenses. From this price perspective, a $100 investment would have grown to just $1,542 by 2023 due to slower price growth through the 1980s and 2000s weighing on overall gains.

The result for "cash" is the result of investing $100 in 3-month U.S. Treasury bills and continuously rolling the investment over all this time to keep up with inflation. If you had really kept it as cash and say stuck a $100 bill in a library book that you didn't open again until the beginning of 2024, we're afraid that $100 bill from 1970 will only go as far as $100 in 2024's dollars would if you went out and spent it.

But what if you decided to take that $100 and restart the experiment for real in 2024? How would you invest $100 today? What do you think your investment will be worth in, oh say, 2078?

We're in the midst of one of the great stock market stories of all time. The soaring stock price of Nvidia (NASDAQ: NVDA) to become the most valuable company on Earth in the middle of 2024, as measured by its market capitalization, is one that market historians will study for ages.

In terms of recent market history, the rise of NVDA is most similar to the Apple (NASDAQ: AAPL) dividend speculation bubble of early 2012. During that event, the stock price of Apple soared in the early months of 2012 as speculation built Apple would soon re-initiate a regular dividend for its shareholders, powering the rise of the S&P 500 (Index: SPX) as the component weighting of Apple stock within the index inflated as investors piled into the stock, peaking in March 2012.

That speculative bubble went on to dissipate during the next several months, through a phenomenon we call the conveyance effect. After Apple announced its plans to resume paying dividends to its shareholding owners, many stockholders sold their shares while Apple's stock prices was still buoyed by the speculation that caused it to rise. But instead of pocketing their profits, they reinvested them in other companies that make up the S&P 500 index.

In doing so, much of those gains were conveyed to the rest of the S&P 500, even though Apple's stock price and component weighting within the index fell during the deflation phase of that bubble event.

In 2024, the rationale behind the speculative investing in NVDA's stock is different, as speculation in the stock has been fueled by the potential of artificial intelligence technology to reshape the information sector of the economy. The resulting rise in NVDA's market capitalization can be seen in the following interactive chart. [If you're accessing this article on a site that republishes our RSS news feed, you may need to click through to our site or to access a working version of the chart.

Since NVDA's market cap peaked on 20 June 2024, we've seen signs the conveyance effect is kicking in. Here's Capital Spectator's James Picerno arguing now is the time for investors to "rebalance" their portfolios, though he doesn't specifically cite the run-up in NVDA's market valuation:

By nearly any measure you cite, US equities are enjoying a stellar run. Despite numerous global risks, investor sentiment for American shares is resilient. The question, as always, is when is it timely to take some of the winnings and redeploy to other assets classes?

There are countless ways to engage in opportunistic portfolio rebalancing analytics, but a good way to start is by profiling performance. For US equities, the case for tamping down expectations looks persuasive. To the extent that expected return evolves inversely with trailing performance, recent history provides a baseline for thinking about risk.

Meanwhile, the view that the bear-market for bonds is over is attracting more attention. The future’s uncertain as always, of course, but one can argue that the foundation is in place for a round of portfolio rebalancing.

Then again, at least one Wall Street trading desk did specifically cite the run-up in technology stocks like NVDA as a reason to take profits and reinvest elsewhere:

Goldman's trading desk summed up the market theme perfectly today: "sell tech and buy everything else"...

Then again, they've already been doing that for at least a couple of months. The question now is how many more investors will adopt the strategy now that NVDA has achieved its lofty valuation?

About the Chart

We calculated NVDA's approximate market cap by multiplying the index's market cap as of 30 June for each year from 2015 through 2023 as reported by Ycharts by the stock's component weight within the S&P as reported by SlickCharts and captured by the Wayback Machine at the following dates:

• 28 June 2015
• 4 July 2016
• 16 June 2017
• 20 June 2018
• 19 July 2019
• 22 June 2020
• 23 June 2021
• 27 June 2022
• 7 July 2023

This method should closely approximate NVDA's market capitalization at the mid-point of each year from 2015 through 2023, though the results are subject to error because of stock price changes between these dates and 30 June of these years. For 2024, we multiplied Slickchart's estimated market cap of $45.851 trillion by Slickchart's reported peak component weight for NVDA of 7.25% on 20 June 2024 to obtain the result presented in the chart.

Since that date, Nvidia's stock price has experienced considerable volatility, so the approximate value we've shown for 2024 may be quite different from where it will settle at the end of the month.

Disclaimer: Aside from long positions in funds that track the S&P 500 index, we don't hold any position of any kind in either NVDA or AAPL, which we find to be interesting because of their influence on the index.

Image credit: Microsoft Bing Image Creator. Prompt: "An artificial intelligence computer chip with the letters NVDA in the middle." We originally featured this image on 26 February 2024.

Are publicly-traded companies that incorporate practices favored by social and environmental issue advocates into their business models better for investors? Or rather, can you make more money by investing in these companies than in companies that place less emphasis on these issues?

These are not small questions. Whether it's your investment portfolion that may have thousands of dollars at stake or the entire global economy that boosts the money at stake up into the trillions, the answers matter.

Over a decade ago, Robert G. Eccles, Ioannis Ioannou, and George Serafeim provided the strongest academic endorsement of what has come to be known as Environmental, Social, Governance management policies, or ESG, for publicly-traded corporations. They claimed their research proved firms that had incorporated policies favored by environmental and social issue advocates into their governance structures, including in their business models and daily operations, financially outperformed firms that had not.

They described their approach and findings in the abstract of their 2014 paper.

We investigate the effect of corporate sustainability on organizational processes and performance. Using a matched sample of 180 US companies, we find that corporations that voluntarily adopted sustainabilitypolicies by 1993 – termed as High Sustainability companies – exhibit by 2009, distinct organizational processes compared to a matched sample of firms that adopted almost none of these policies – termed as Low Sustainability companies. We find that the boards of directors of these companies are more likely to be formally responsible for sustainability and top executive compensation incentives are more likely to be a function of sustainability metrics. Moreover, High Sustainability companies are more likely to have established processes for stakeholder engagement, to be more long-term oriented, and to exhibit higher measurement and disclosure of nonfinancial information. Finally, we provide evidence that High Sustainability companies significantly outperform their counterparts over the long-term, both in terms of stock market as well as accounting performance.

Here are the two figures they put forward to illustrate their claim that ESG-practicing firms had delivered better results for investors from 1992 through 2010:

Figure 1

Figure 2

Here is their discussion of what the two charts show (boldface emphasis ours):

Figure 1 (2) shows the cumulative stock market performance of value-weighted (equal-weighted) portfolios for the two groups. Both figures document that firms in the High Sustainability group significantly outperform firms in the Low Sustainability group. Investing $1 in the beginning of 1993 in a value-weighted (equal-weighted) portfolio of High Sustainability firms would have grown to $22.6 ($14.3) by the end of 2010. In contrast, investing $1 in the beginning of 1993 in a value-weighted (equal-weighted) portfolio of control firms would have only grown to $15.4 ($11.7) by the end of 2010. Table 7 presents estimates from a four-factor model that controls for the market, size, book-to-market, and momentum factors. We find that both portfolios exhibit statistically significant positive abnormal performance relative to the market. However, we note that this might be because for both samples we have chosen companies that survived and operated throughout the early 1990s and until the late 2000s.

The better performance of the firms in both samples compared to the rest of the market may be attributed, to a considerable extent, to this survivorship bias. However, the relative performance difference between the two groups is not affected by this bias since both groups are equally likely to have survived, by construction of our sample. Accordingly, we find that the annual abnormal performance is higher for the High Sustainability group compared to the Low Sustainability group by 4.8% (significant at less than 5% level) on a value-weighted base and by 2.3% (significant at less than 10% level) on an equal-weighted base.

Those are pretty impressive results. And given the stakes, it's no wonder why the paper has received considerable attention on both Wall Street and Capitol Hill, where its findings have influenced both investing strategies and public policy.

There is just one problem. When another economist finally got around to attempting to replicate Eccles, Ioannou, and Serafeim results, they found those results and their methods came up short on multiple levels.

In a newly published paper, Andrew King found he could not duplicate Eccles, Ioannou, and Serareim's findings with the information they published. King also found he could not obtain similar results by replicating their methods in a new study.

For our purposes, we'll focus on the findings that so-called "High Sustainability" (HS) firms delivered better investment returns than "Low Sustainability" (LS) firms. King ran 1,600 scenarios with 400 pairs of HS and LS portfolios to compare their returns. Here are those findings and charts (boldface emphasis ours):

For each of 1600 cases (400 draws X 4 caliper settings), I compared the difference in stock returns for the HS and LS portfolios using the same Fama French model employed by EIS. Figure 3a shows a graph of the performance difference of the two portfolios for each modeled case, sorted by the difference in portfolio performance – from largest positive difference to largest negative difference. The black line is the estimated difference in portfolio returns, and the grey spikes show the 95% confidence interval. Darker spikes indicate portfolios using less stringent matching criteria but including more firms (thus they also have smaller confidence intervals). The bold dashed line shows the estimate reported by EIS. The overlap of its confidence interval with zero demonstrates again that it does not meet traditional requirements for significance.

Across the 1600 runs, 72% estimate a higher return for the High Sustainability Portfolio, but the high variance in all of these estimates mean that all confidence intervals include zero. This means that had any researcher chosen to evaluate one of these 400 pairs of portfolios, they would not have been able to report a “significant” estimate of performance difference.

EIS report that they also compared returns from value-weighted portfolios. They do not disclose their process, but such weighting usually means that investments in the portfolio are rebalanced at the beginning of each year to be proportional to the market capitalization of the firms. I recalculated portfolios for all 1600 cases using this value-weighting method and reran the Fama French analysis.

As shown in Figure 3b, 78.5% of my models result in an estimate where the High Sustainability portfolio has higher returns. However, none of these estimates can be confidently differentiated from zero. Moreover, portfolios with a smaller number of matched firms (lighter interval lines) dominate the extremes of the estimates. This is unsurprising given the higher variance caused by smaller portfolio size.

EIS’s reported estimate is near the extreme. Only five of my portfolios result in return differences larger than the one reported by EIS, and these portfolios have 9 or 10 treated firms not 90. For none of the 5 is the difference in portfolio performance “statistically significant.” Thus, EIS’s one report of significant superior performance for HS firms is an extreme outlier in my replication.

The ball is now back in Robert G. Eccles', Ioannis Ioannou's, and George Serafeim's court to back up their claim of financial outpeformance for firms that follow the ESG playbook in their business practices. As it stands, the failure of their results to be successfully replicated raises serious questions about both those results and their methods.

References

Eccles, Robert G. and Ioannou, Ioannis and Serafeim, George, The Impact of Corporate Sustainability on Organizational Processes and Performance (December 23, 2014). Management Science, Volume 60, Issue 11, pp. 2835-2857. February 2014. DOI: 10.2139/ssrn.1964011.

King, Andrew A., Comment and Replication: The Impact of Corporate Sustainability on Organizational Processes and Performance (November 29, 2023). DOI: 10.2139/ssrn.4648438Z.

Image Credit: Microsoft Bing Image Generator. Prompt: "Environment Social Governance for a corporation".