Here’s a very simple game that does a great job of illustrating the pitfalls of investing, despite the long-term odds being in your favor.

• Imagine that you are given $25 that you can bet on a coin toss for 30 minutes.
• You know that the coin will come up heads 60% of the time, and tails 40% of the time.
• You can bet as little or as much of your available cash on each flip. You double your wager if you are correct. You lose all of your wager if you are wrong.

There are many ways you could play this game. You could bet your entire $25 at once since you have an edge. But then there is a 40% chance you’d be instantly broke. You could bet nothing, as that would guarantee yourself $25 at the end of the session. You could vary your bets according to instinct. You could use mathematical theory to form an optimal solution.

Stock market investing works in a similar manner. People invest because the long-term odds are in our favor. Things look good over the long run, but there is volatility in the short run. Some people instead choose to take zero risk, but their money stagnates. Some people trade based on their intuition. Some people trade based on pre-set strategies.

The ideal result? If everyone bet optimally, they would have had a 95% chance of reaching 1000% of their initial wager (real-world maximum payout of $250). A mathematical formula called the Kelly Criterion tells you to bet a constant 20% of your bankroll every time. This is the optimal balance between the reward upside and keeping enough padding to avoid bankruptcy.

The actual results? The average ending balance was only $75. 33% of the participants actually lost money. 28% went completely broke! This comes from a research paper draft authored by Victor Haghani and Richard Dewey, who conducted this experiment on 61 “quantitatively trained test subjects” (appears to be finance workers that showed up for a hedge panel talk). Here’s a quote from the paper:

Given that many of our subjects received formal training in finance, we were surprised that the Kelly Criterion was virtually unknown and that they didn?t seem to possess the analytical tool-kit to lead them to constant proportion betting as an intuitively appealing heuristic. Without a Kelly-like framework to rely upon, we found that our subjects exhibited a menu of widely documented behavioral biases such as illusion of control, anchoring, over-betting, sunk- cost bias, and gambler?s fallacy.

That certainly sounds like real-world investing to me. Even in a situation with a clear advantage, people still mess it up all the time due to behaviorial and cognitive biases. People can argue whether volatility is a good proxy for risk, but the bottom line is that volatility in this game directly causes bad behavior. Big drops are always scary.

John Rekenthaler of Morningstar argues that the results of this experiment support the idea of auto-pilot investing.

My takeaways? Like this game, long-term investing is simple but not easy. You need to risk enough of your portfolio in order to expose yourself to the upside potential. However, you also need to keep enough safe such that you won’t flame out during a losing streak. I think that auto-pilot might work well in many situations, but people can also turn off autopilot in times of crisis if they don’t understand what’s “inside the box”. It’s best to calmly figure out an investment plan based on both market history and your personal situation, and then stick with it. Just winging it usually turns out poorly.

Every day, new articles are published telling you to buy this! Sell that! Hedge against this other thing! One of the most underrated skills in investing is the ability to stick to your plan and do nothing.

Some folks argue that that solution is to never listen to any market commentary (or “noise”). Keep your head down, plow your money into index funds and don’t look up until you’re ready to retire. Well, if you can do that, more power to you. However, I’ve been getting more e-mails from people scared to invest due to reports of high stock market valuations and rising interest rates. Here’s an example of how I read market commentary and keep on truckin’ ahead.

The Blackrock Investment Institute recently released their Q4 2016 Global Investment Outlook, which has a lot of carefully-considered statistics, charts, and predictions. The chart below compares the current yields of various asset classes as compared to their pre-crisis averages (2003-2008):

Blackrock’s analysis:

High valuations versus history point to more muted returns across asset classes in the long run. Yet slowing nominal GDP growth and aging populations argue for lower bond yields than in the past — and sustained demand for high-quality bonds. This structural shift changes the prism of assessing today’s valuations. It makes risk assets such as equities, credit, local EM bonds and selected alternatives look attractive on a relative basis.

I choose to take my risk and upside potential with stocks. While stocks have lower earnings yields (higher P/E) than pre-2008, they are still more attractive than high-quality bonds on a long-term basis. They are certainly more attractive than cash. US, European, Japan, Emerging Markets, nothing looks horrible.

I only invest in high-quality bonds because I want bonds to serve as portfolio ballast and help keep the ship steady. Risky bonds are more correlated with stocks, meaning if stocks go down then they are more likely to go down as well. I simply don’t want to own those types of bonds, even if they yield a bit more. Thus, I ignore any recommendation to buy high-yield corporate bonds, high-yield municipal bonds, and emerging markets bonds.

You can see that the high-quality bond yields are all significantly lower in the current environment. This second chart below looks more closely at the current bond picture. If you are in a high tax bracket, you should consider investment-grade municipal bond funds due to their high effective yields. Otherwise, a broad US Corporate bond fund (Investment Grade) is still a pretty good choice, and a a broad Total US Bond fund (US Aggregate) is in the “okay” zone.

If you’re doing the sensible index fund thing, perhaps via Vanguard Target Retirement fund, then I see nothing wrong with staying the course. Nobody knows what will happen in the next 1, 3, or 12 months. Stocks could drop. Rates could rise. But stocks could also keep going up. Rates could also stay flat for a decade. Investing for the long-term requires perseverance. Stocks are still compensating investors for taking risk and are more attractive than bonds in the long-term. I would still add some high-quality bonds to smooth out the ride.

Finally, keep on saving. As Jack Bogle says, “If we’re going to have lower returns, well, the worst thing you can do is reach for more yield. You just have to save more.”

Updated 10/12/16. 18 iShares Core ETFs now trade commission-free at Fidelity. Blackrock announced price cuts to 15 out of its 22 iShares Core ETFs last week. The iShares Core series is their low-cost, index ETF line-up targeted towards buy-and-hold investors. Here are the updated expense ratios, alongside the expense ratios of the closest equivalent ETF from Vanguard for comparison. (Can you tell what their benchmark was?) Numbers are taken from the respective official websites as of 10/8/16.

* Note: Vanguard does not have ETF versions of their “all-in-one” asset allocation mutual funds.

Commission-free ETF trades. As of 10/12/2016, all 18 of the primary iShares Core ETFs can be traded commission-free in a Fidelity brokerage account (only the 4 Asset Allocation ETFs are excluded out of the 22 total). Here is the full Fidelity commission-free iShares ETFs list. Fidelity also has their own line-up of index fund options. You can trade all 4 of the iShares Asset Allocation ETFs plus 4 other iShares ETFs for free at TD Ameritrade.

You can also use a broker with free trades overall like the Robinhood app (review) and Merrill Edge which gives you 30 free trades per month with $50,000 in assets across your Bank of America and Merrill Edge accounts.

Bottom line. The demand for low-cost, well-run, index ETFs continues to grow. This move by Blackrock is more about professional money managers, as they’ll feel less pressure to move elsewhere due to higher costs due to fiduciary rules. The competition between iShares/Fidelity, Vanguard, and Schwab is making better products at lower prices for consumers. (Side bet: Blackrock will buy Fidelity in the next 5 years.) My personal investments (and lots of unrealized capital gains) are with Vanguard, but new DIY investors can now open an account at any of these three and build their own diversified, low-cost portfolio with no trade commissions.

See also: Schwab Index ETF Expense Ratios vs. Vanguard ETF Comparison

Schwab also had some reactionary price cuts to some of their Schwab Index ETFs last week. Here are the updated expense ratios, alongside the expense ratios of the closest equivalent ETF from Vanguard. In cases where both Vanguard and iShares compete, Schwab is now 2 basis points cheaper than Vanguard. This is because iShares recently dropped to mostly 1 basis point cheaper than Vanguard, and Schwab wants to keep the title of “cheapest”.

But let’s be clear, Vanguard’s success and mere presence (the “Vanguard effect“) is why these low-cost ETFs exist in the first place. Numbers are taken from the respective official websites as of 10/8/16.

* indicates ETFs that had a price cut 10/7/16.

Where should self-directed investors buy these ETFs? You can trade all Schwab Index ETFs commission-free in a Schwab brokerage account. Here is the full of over 200 commission-free ETFs at Schwab OneSource.

You can also use a broker with free trades like the Robinhood app (review) and Merrill Edge which gives you 30 free trades per month with $50,000 in assets across your Bank of America and Merrill Edge accounts.

Bottom line. Schwab has shown a willingness to sacrifice profits in the short-term in order to keep the title of “cheapest index funds”. I think this is brave move with long-term vision, and hopefully they can keep it up. The competition between iShares/Fidelity, Vanguard, and Schwab continues to lead to better products at lower prices for consumers. My personal investments (and lots of unrealized capital gains) are with Vanguard, but new DIY investors can now open an account at any of these three and build their own diversified, low-cost portfolio with no trade commissions.

See also: iShares Core ETF Expense Ratios vs. Vanguard ETF Comparison

Vanguard recently celebrated the 40th anniversary of the Vanguard 500 Index Fund, the first index fund available to individual investors. If you are like me and have a significant portion of your net worth in Vanguard products and services, you should read this Morningstar article No Signs of Complacency at Vanguard which includes excerpts from interviews with Vanguard executives. Here are highly-condensed highlights:

• Vanguard is huge and getting bigger.
• Vanguard is still the only place where the firm is owned by the fundholders.
• Vanguard costs are low, but it will be hard to get much lower.
• Competitors can sell their products at a loss. Vanguard can’t, so they may not be the cheapest.
• So far, there are no signs of complacency, wasted money, or ego-driven moves.
• Vanguard’s next move will be focusing on better service for clients.

My thoughts. Vanguard has focused primarily on asset growth. This was okay, as bigger assets meant lower costs for fundholders. Now that costs really can’t go that much lower, I agree their next move should be to focus on customer service, both in terms of human interactions and online user experience.

Compared to Fidelity and Schwab, it has been in my experience more difficult to get specific, custom requests accomplished with Vanguard. This includes estate paperwork and large transactions. That means it is harder to get someone on the phone, the person on the phone is less responsive and/or knowledgeable, and overall it takes longer for the action to get done (if it is even allowed). These limitations are probably reflective of their focus on cost savings, but hopefully they can find a better balance. (I’d rather they spend money on this, than more advertising.) I do feel that Vanguard has been improving their technology, so I hope they keep that up.

When Jack Bogle grants an interview, I sit down and take notes in case he drops something significant. Here is a link to his WSJ interview dated 9/2/2016 (paywall, use Google redirection if needed).

• Bogle estimates 2% annualized returns over the next decade (he does not forecast past that).
• Stay invested in a diversified portfolio of stocks and bonds at very low cost.
• Don’t reach for yield. You just have to save more.
• Don’t go to cash.
• He’s fine with 5% of your portfolio in gold, if you like that.
• He’s still sees no need for international stocks.
• He’s not worried about too much money flowing into index funds.
• Bogle predicts that in five years, Fidelity will be sold.

The interview is rather vague in a few areas. I am assuming that the 2% annual returns forecast applies to after-inflation returns of a 50% stock and 50% bond portfolio. This is based on Bogle’s October 2015 presentation which predicted 3% after-inflation returns for a 50/50 portfolio. Since then, stock markets are up and bond yields are down, so future expected returns are now even lower.

Another little nugget is a link to a previous WSJ interview from exactly 10 years ago – 9/2/2006. It provides some additional background to the initial creation of the first index fund for individual investors.