“How should I invest my money?” is a question that cannot be avoided — to invest none of it is a tacit decision. Any good answer would be highly personalized, but the right information about risk can help anyone think about this question.
In the context of investment, one can consider risk of loss on a spectrum: some securities can safely be considered to carry no risk, like US Treasury savings bonds; some have moderate risk, such as diversified stock funds; and others carry extreme risk, including risk of total loss. The lowest-risk options generate small, stable returns. Stock market index funds require the investor to accept significant volatility, with the expectation of much greater reward. Different investments can also have different sources of risk.
See the plot below, which displays calendar year returns in the US stock and bond markets between 1995 and 2022. Note how most of the annual stock returns fall far from the average (the purple diamond). The returns for US aggregate bonds clustered more closely around the average, but in exchange for the benefit of reduced volatility, the average return was lower. The average return for US aggregate bonds was 4.5% during this period, while it was 9.8% for US cap-weighted stocks. This is higher than the global average for stocks of about 8% since 1900.[1] Although 28 years may seem like a long time, it's a small sample and not meant to be representative of broad historical returns.
A negative bond return occured in 14% of rolling years, and a negative stock return in 22% of rolling years. Viewing only annual returns obscures a lot of volatility — we can zoom in on monthly and daily returns. For US bonds, 33% of rolling months and 39% of days were negative. For US stocks, 35% of rolling months and 45% of days were negative. This illustrates one of the essential lessons of investing in volatile assets: returns in the short term are often negative — a single day is nearly a coin flip for stocks. But diversified investors can be assured that as they invest over long periods, their probability of reaping a positive return creeps up toward 100%.
The statistical term "expected return" means that out of the distribution of possible returns, that is the average return. Statistical expectation is counterintuitive: the expected value of rolling a six-sided die is 3.5, because that's the average of the possible outcomes {1,2,3,4,5,6}, and they're all equally likely. The expected value is 3.5 even though it's not a possible outcome! Stocks may have an expected return around 8%, but we don't actually anticipate a return close to 8% very often. You can see above that stock returns are widely distributed around the mean, so you should expect returns much higher or lower than 8% more often than returns that are roughly 8%. See this video for a great explanation.
Click to move to each section:
- Understanding bonds and their risks
- Total return
- Investing in bonds and navigating the spectrum of risk
- Learning from history
- Further lessons on risk
- Municipal bonds and foreign currencies
- Bond-like bond funds
- US Treasury Savings Bonds
- Summary
How can you invest money that can’t be exposed to the volatility of the stock market? The most common way of doing this is through bonds. Most people know that banks make money by providing loans in exchange for repayment with interest. Like banks, you can invest in debt through bonds, also known as fixed income. Bonds are liquid assets and can be traded, although not quite as easily as stocks. Anyone can invest in government and corporate bonds through an ETF or mutual fund. Some examples of large bond issuers include the US Treasury, Verizon, Bank of America, and Pfizer. A bond fund purchases many bonds representing debt on the part of each bond issuer, and the bond issuers pay the fund. Payments from the bond issuer to the bondholder are called coupon payments, and they usually occur semi-annually. The payments are complete for a particular bond when it reaches maturity. Upon maturity, the issuer pays back the amount they originally borrowed, an amount which is called the face value or par value of the bond (they are synonymous). Funds pass on these payments to shareholders in the form of cash dividends. The fund's share price corresponds to the market value of the bonds.
Individual stocks and bonds vary greatly in their risk but, as a whole, bonds have less risk and less long-term return than stocks. This is partly because, if a company declares bankruptcy, the bondholders' claim to company assets takes priority over that of common stockholders (with rare exceptions). If a bond issuer is unable to pay their debt, this is referred to as default. Bonds which are less likely to be paid back in full tend to command higher returns to accompany their risk. US Treasury bonds are less risky than corporate bonds, and corporate bonds are divided into two broad categories based on credit quality: investment-grade bonds (with comparatively low risk) and high-yield bonds (also known as junk bonds).
We mentioned the term "high-yield bond". What exactly is yield? There are various types:
-
Current yield: the sum of a bond's annual coupon payments divided by its current market price.
-
Yield to maturity: the annualized total return paid by a bond if held to maturity, with all coupon payments reinvested.
-
SEC yield: a standardized yield that bond funds must all calculate in the same way, based on yield in the last 30 days.
-
Coupon rate: the sum of annual coupon payments divided by the bond's face value. Unlike the other types of yield, the coupon rate of a bond with fixed coupon payments does not fluctuate over time.
Bond prices and yields have an inverse relationship. When you read in The Wall Street Journal that yields fell today, you can infer that prices rose.
Yield to maturity (YTM) expresses a very important metric for bonds: their expected total return. We can observe yield differences between bond funds by checking YTM on their webpages. SGOV, which holds very short US Treasury bonds, has a YTM of 5.25%, whereas the high-yield bond fund SPHY has a YTM of 7.62%. The SEC yield includes the expense ratio, but YTM does not. So for the true YTM of a bond fund, subtract the expense ratio.
Bonds present two broad dimensions of risk.
Longer-term bonds are riskier than shorter-term bonds. A primary driver of term risk is the more specific interest rate risk, because longer-term bonds are more sensitive to the risk of interest rates rising. Why is that a risk? Imagine you own a bond with semi-annual coupon payments of $15, for a total of $30 annually. Based on the market price of $1,000, this bond has a 3% current yield. To your dismay, interest rates rise drastically and similar new bonds are issued paying a 6% annual yield. No one will buy your bond for $1,000 anymore, because they can buy similar bonds that pay much more interest. To sell your bond now, you'd have to drop your price to $500 so that someone buying it would enjoy a 6% yield, which is now the going rate. Your bond will make the same coupon payments and the same principal payment at maturity, but it lost market value. See this video for more explanation.
Interest rate changes can also benefit bondholders: a decline in interest rates would be a boon to the market value of bonds, especially long-term bonds. It's important to stress that changes in interest rates do not affect the income from existing bonds. They affect the prices of existing bonds, which correspond to a fund's share price. Although not a strict prerequisite for investing in bonds, understanding the concept of bond duration will improve your appreciation for how interest rates affect bond prices.[2] Duration expresses interest rate sensitivity, and it can be found on any bond fund's webpage. The effective duration of a bond fund is a better gauge of its interest rate risk than the average maturity of its bonds.
If someone is fully committed to holding a bond to maturity, then interest rate risk is irrelevant. Price fluctuations would occur, but they wouldn't matter to such an investor. Very few bond buyers have that level of certainty.
The second type of risk is credit risk. The primary risk related to credit quality is default risk. Default means a bond issuer has missed payments, so for someone who owns shares of a diversified bond fund, default risk is the risk that defaults on debt will increase unexpectedly. Default has obvious negative effects on both income from the bond as well as its market value. A secondary risk is credit migration risk: the risk that credit ratings of the bond issuers will be downgraded. Upgrading or downgrading of a bond issuer's credit rating changes the market value of the bond, because market participants will pay less for a bond that is perceived as more likely to default. But credit ratings do not directly affect the income from a bond. Bonds with low credit quality provide higher expected return because investors must be compensated for accepting a greater risk of default.
Long-term bonds are typically defined as those with maturities of 10-30 years. Intermediate-term may be defined as 3-10 or 5-10 years, and short-term may be defined as 1-3 or 1-5 years. Bonds called ultrashort-term usually have about one year or less until maturity. US Treasury bonds with maturities of one year or less are called Treasury Bills or T-Bills, those with maturities between two and ten years are Treasury Notes, and those with longer maturities are Treasury Bonds. They're all bonds, but they have conventional names.
Bond funds typically pay monthly dividends. The best default for most people is to automatically reinvest these dividends in more shares of the fund. When you need to withdraw money from the fund, you could turn off automatic reinvestment and wait for the next dividend payment. However, selling shares of the fund is more likely to be suitable both in terms of timing and the dollar amount you need. See the section on taxes for the different tax implications these actions carry. I mentioned previously that stock ETFs are more tax-efficient than stock mutual funds, but the distinction does not apply as strongly to bond funds. This is because unlike stock ETFs, bond ETFs sometimes need to distribute capital gains. So for instance, someone investing in bonds in a taxable Schwab brokerage account has little tax-related incentive to prefer the ETF SCHZ to the mutual fund SWAGX. As long as buying shares of SWAGX does not entail a fee — which it does not because this person is using a Schwab account — they may prefer SWAGX because it allows them to invest a precise dollar amount. For those using a Fidelity account, FXNAX tracks the same index as SCHZ and SWAGX.
During most years from 2009 through 2021, interest rates were very low. So bond returns were relatively low, but it was a great time to be a borrower. Many companies loaded up on cheap debt, and many people secured fixed-rate mortgages with low rates. Interest rates are usually higher: the 1980s are a notorious period for home mortgages well above 10%, and unbelievably high rates for savings accounts and (even short-term) bonds. The Federal Reserve, often abbreviated as the Fed, is the central bank of the United States and has limited control over interest rates. The Fed does not control all interest rates: it exerts pressure on very short-term interest rates, which greatly influence many other interest rates. The Fed can also purchase assets in amounts ranging up to trillions of dollars, thus increasing the monetary supply and stimulating the economy. This is called quantitative easing; it is not something the average investor needs to understand. Due to its independence from the executive branch and the global importance of the US financial system, the Fed is an extremely powerful institution. Chairs of the Fed, who lead a 12-member board, are famous names among economic observers: Jerome Powell (2018-present), Janet Yellen (2014-18), Ben Bernanke (2006-14), and Alan Greenspan (1987-2006).
We'll explore how bond funds fit in your portfolio. But first, a brief interlude from our friend, total return.
Total return is a straightforward concept: the return provided by a security over a given period of time if you immediately reinvested all distributions. Yet many investors overlook a crucial implication: you cannot judge a fund's returns by its price chart! If I see that Fund ABC had a share price of $100 at the end of 2020, and a share price of $110 at the end of 2021, it's incorrect to assume that its 2021 return was 10%. Virtually all US-listed stock and bond funds have distributions, so price charts always understate performance (unless the period of interest is so short that it occurs between quarterly or monthly dividends).
Another mistake someone can make with a price chart is to use it to judge the duration of a drawdown. Price charts always exaggerate the amount of time it took for an investor to recover from unrealized losses — this will be important below. Price charts also exaggerate the depth of a drawdown: if a fund's price chart fell 20% over the last year, it does not mean investors lost 20%. They lost less, because they received dividends and possibly other distributions.
Total return is the key performance metric because it reflects the actual experience of an investor (before taxes).
Samuel Hartzmark provides a great explanation of these points in this Rational Reminder interview.
You can check a fund's webpage to see its total return, or you can use tools like Portfolio Visualizer. The asset allocation backtest tool lets you compare the total returns of various asset classes, and the portfolio backtest tool lets you compare the total returns of specific securities. For daily total return data, you can go to the "Historical Data" tab of any fund's Yahoo! Finance page (e.g., VT) and use the adjusted close figures. Most of the plots in this guide use Yahoo's adjusted close figures.
Now is a good time to define a few common terms. During a bull market, returns are generally positive. During a bear market, returns are generally negative. These terms refer to the stock market by default, but it's also possible to speak of a bond bear market. Bull markets are conventionally defined as price increases of at least 20% from the last trough, and bear markets as price decreases of at least 20% from the last peak. Note that the definition is based on price changes, not total return. Entrances into bull and bear markets for the S&P 500 and other indices are often noted by financial outlets like The Wall Street Journal. But like many conventions, 20% is an arbitrary number and shouldn't be taken too seriously. Price change calculations are based on daily closing prices. This is a widespread convention, and it means that intraday fluctuations don't effect calculations — only the price at the end of market hours. In this guide, a drawdown is expressed as a peak-to-trough decline in terms of total return, and it also uses daily closing prices. A drawdown is not over until the security's total return chart has recovered past its previous peak.
We can think about the role of bonds by walking through layers of risk and return. To illustrate the risk you should be prepared for, we'll cover historical disaster scenarios for each type of fund. See the fund proposal section for a summary table of many stock and bond funds. To view the total return history of any fund mentioned, you can use Portfolio Visualizer's backtest asset allocation tool.
First is your checking account, which holds money you anticipate using in the immediate future. A checking account has zero risk and zero return. What could you do to generate modest returns for the money you don’t need at your fingertips, without exposing it to substantial risk? We should seek a fund with low credit risk and low interest rate risk, which means it would hold high-quality, short-term bonds. There are funds with bonds so short that they never suffer a significant loss. These include SGOV — which invests in US Treasury bonds with an average maturity of about one month — and money market funds. Money market funds hold very low-risk securities and are intended to protect the principal investment regardless of market conditions.[3] They are mutual funds with the unique characteristic of always being priced at $1 per share. They pay out like savings accounts, with a monthly dividend based on the amount invested each day in the past month. Money market funds include SPRXX at Fidelity, SWVXX at Schwab, and VMFXX at Vanguard (or E*Trade). As you can see, money market fund tickers always end in XX. SGOV is an ETF and is not a money market fund, but because of its holdings, it's as safe as the safest money market funds. Of course, the returns from these funds are relatively low, but their yields exceed those offered by virtually all savings accounts. You can also buy US Treasury bills yourself on the government's website or through your broker.
Slightly above rock bottom in risk and return is a more typical short-term US Treasury bond fund like SCHO, whose average bond will mature in about two years. The main risk to which high-quality bonds are exposed is interest rate risk. Rapid, unexpected increases in interest rates recently led to the worst drawdown for high-quality bonds in modern US history. Nevertheless, disasters for high-quality, short-term bonds are comparatively mild. Between the peak on Aug 3 2021 and the trough on Oct 20 2022, the total return of SCHO was -5.7%. BSV is a broader short-term bond fund that holds both government and corporate bonds. It has a somewhat longer effective duration, so it's more exposed to interest rate risk. It drew down by 8.5% during the same interval.
Long-term bonds are far more sensitive to changes in interest rates. They are very risky assets and, in the deep historical data, we find that long-term bonds generate returns which often match and sometimes even exceed the returns of stocks. They're suitable only for long-term investing. Their risk was exhibited by the recent extraordinary fall in bond prices. Vanguard's broad long-term bond ETF (BLV) declined by 38.3% between August 6 2020 and October 19 2023. TLT holds US Treasury bonds with more than 20 years to maturity, so its interest rate risk is higher. TLT's total return chart peaked on August 4 2020 and fell 48.4% by October 19 2023. We can crank up interest rate risk even more with funds that invest in zero-coupon, long-term US Treasury bonds, also known as STRIPS. "Zero-coupon" means that the bond pays no coupons throughout its entire life; the value of the bond lies in the payment of the bond's face value when it matures. Due to this feature, interest rate risk is maximized in funds like EDV and ZROZ. ZROZ experienced a drawdown of 63.3% between March 9 2020 and October 19 2023.
Intermediate-term bonds, of course, have moderate risk and expected return. The broad intermediate bond fund BIV drew down by 18.9% between Aug 6 2020 and Oct 20 2022. The intermediate US Treasury bond fund VGIT, which has slightly lower effective duration, lost 16.1%. Intermediate- and long-term US Treasury bonds in particular have low correlation to stocks, providing a diversification benefit.
Other funds have average maturities that are similar to those of intermediate funds, but instead they're aggregate funds with bonds balanced between short, intermediate, and long maturities. If someone says they're invested in "bonds" rather vaguely, they're probably invested in a fund like this. These aggregate bond market funds are usually a US bond fund (e.g., AGG) or a combination of US and international funds (BNDW). Aggregate funds like AGG are the core bond holding for many people. They're also a common offering in retirement plans. In addition to government and corporate bonds, aggregate funds contain mortgage-backed securities. These are bonds created by pooling mortgage debt from many people. I'm not recommending shares in a mortgage-backed securities fund (e.g., MBB), but it's useful to understand the different types of debt held in aggregate funds. The drawdown of BNDW, Vanguard's total world bond fund, was 17.2% between Dec 31 2020 and Oct 20 2022.
Aside from high-quality bonds of various maturities, high-yield bonds (AKA junk bonds) might play a role in your portfolio. These bonds are issued by companies with low credit ratings. With inception in 1978, VWEHX has the longest history you can observe. While bonds with high credit quality can act as a countervailing force when stocks crash, high-yield bonds tend to fall along with stocks (by much less). This is because they are issued by companies which are more vulnerable to economic downturns. So they do not occupy the same role as a potential hedge in your portfolio.
For high-yield bonds, the 2008 financial crisis was the worst period in modern US history. Beginning in May 2007, but mainly between May 2008 and November 2008, VWEHX experienced a drawdown of 30.2%, and recovered by September 2009. SPHY is currently the high-yield fund with the lowest fees. SHYG is a fund that invests in short-term, high-yield bonds, combining low interest rate risk with high credit risk. During the early COVID-19 pandemic, when stock markets experienced a rapid contraction and expansion, SPHY and SHYG drew down by 22.0% and 18.4%, respectively, between February and March 2020. They recovered quickly by November 2020.
Stocks are very risky assets. Volatility is routine in the stock market. In October 1989, to pick a random example, the S&P 500 began a drawdown of 7.3% that reached its bottom four weeks later. Recovery above the previous peak occurred in January 1990. This period of unrealized loss lasted less than three months and was an unremarkable event. Minor drawdowns like these are common and relatively easy to experience. Drawdowns are occasionally much worse.
In February and March 2020, the total US stock market crashed by 35% due to COVID-19. In spite of such a rapid and brutal drawdown, it took only until August 2020 for the market to exceed its previous peak. This process can also take several years. The 55% decline beginning in October 2007 lasted until March 2009, and persistent recovery above the previous peak did not arrive until August 2012, nearly five years after the drawdown began. The global financial crisis of 2008 was not the only deep, extended period of loss in modern history: a bear market starting in January 1973 did not see its bottom until October 1974 — a 47% loss — or a persistent recovery until May 1978, for a total of more than five years. A drawdown of similar depth occurred in the early 2000s, with recovery by 2006.[4] Keep in mind that the bear markets in 1973-74, 2000-02, and 2007-09 were unusually severe; only the Great Depression was deeper.[5] The take-home message is that periods of major unrealized loss vary greatly, and this uncertainty is part of the psychological struggle. Participation in the stock market means being prepared for a multiyear period in which returns are negative.
The chart below displays the total return of VTI, Vanguard's total US stock ETF, during the financial crisis.
There are two positive notes to counterbalance this bleak reminder. First, as disastrous as these bear markets might seem in real time, diversified stockholders can endure them with the knowledge that global markets have recovered after all the calamities of the past. A single stock carries risk of total loss, but the risk of a diversified portfolio is better thought of as volatility. Second, diversification can significantly reduce the duration of these drawdowns, compared to a portfolio of only the S&P 500 or only the total market. US small cap value stocks recovered from the 1970s bear market a couple years earlier than the S&P 500, and their overall performance by the end of the decade crushed the performance of large cap stocks (like the S&P 500). The 1970s would have been a decade of strong growth for someone who highly overweighted small cap value stocks. The section on stock portfolios will expand on risk factor diversification and explain the term "small cap value".
We've reviewed some of the worst experiences for US stocks and bonds, like the 2008 financial crisis and the recent nose-dive in bond prices. Such events are expected to be rare, and they are not characteristic of an overwhelming majority of bear markets for stocks and bonds. In his book on retirement, Larry Swedroe used 60% as the potential drawdown of stocks for which you should be prepared. This is a reasonable guideline for a highly diversified portfolio (but not a portfolio of ten stocks). However, it cannot be ruled out that US or global stocks could fall by more than 60%. Based on the historical data, I will suggest the following scenarios for financial planning. Think of the lower bound as a disaster — rare and unusually bad — and the upper bound as a catastrophe — perhaps once or twice in a lifetime (and hopefully never).
- a 3-6% drawdown for short-term US Treasury bonds (SCHO)
- a 5-9% drawdown for short-term bonds (BSV)
- a 10-20% drawdown for intermediate-term bonds / aggregate funds (BIV / BNDW)
- a 20-40% drawdown for long-term bonds (BLV)
- a 25-45% drawdown for high-yield bonds (SPHY)
- a 25-45% drawdown for 20+ year US Treasury bonds (TLT)
- a 30-60% drawdown for long-term US Treasury STRIPS (EDV, ZROZ)
- a 50-75% drawdown for cap-weighted stocks (VT)
The risks of a fund depend on specifics, so take these numbers only as guidelines when applying them to other funds. Two high-yield bond funds may differ greatly in risk if one invests broadly in US companies while another buys in emerging markets. As discussed above, a fund like SCHO is not the safest bond fund. Risk of short-term loss can be lowered to nearly zero with funds like SGOV and money market funds.
Could all of these drawdowns happen at the same time? Large declines in the value of stocks and high-quality bonds rarely co-occur for very long. During economic downturns that hurt stocks, the Federal Reserve tends to lower interest rates to encourage borrowing and spending, which lifts bond prices. So it may be most realistic to work out your financial situation if you needed to draw on your investments at the bottom of a 50-75% decline in stocks or the suggested declines in various types of high-quality bonds. Bonds with high credit risk are in particular jeopardy when the stock market plummets, so drawdowns of high-yield bonds should be mentally grouped with those of stocks, not other bonds. Keep in mind that this is a rule of thumb optimizing for simplicity. The guideline is deliberately conservative, so a vast majority of future drawdowns will not approach these extremes. As discussed in the first footnote, wars and revolutions have caused the financial markets of individual countries to collapse. For US investors this concern is not especially salient in the domestic market, but it speaks to the merits of geographic diversification. The disasters in US history do not reflect the full range of possibilities.
The plot below exhibits a situation which began in late 2021: stocks and high-quality bonds fell significantly at the same time. It shows the total return of global stocks (VT) in purple, global bonds (BNDW) in red, and long-term US Treasury STRIPS (ZROZ) in green. All three are scaled to a value of 100 on Nov 8 2021, because that was the all-time high for VT. The drawdown for VT reached only 26.4% (on Oct 12 2022), an ordinary bad run for stocks. But because it coincided with the worst bond drawdown in living memory, a 60/40 portfolio — 60% cap-weighted stocks, 40% aggregate bonds — drew down by 22.3% during roughly the same interval. The losses were unusually close to those of a 100% stock allocation. The green line shows that someone invested in bond funds with greater duration (i.e., interest rate risk) suffered a larger drawdown. Due to the need to suppress inflation, the Federal Reserve could not reduce interest rates to stimulate the economy; in fact, it had to do the opposite. High inflation presents unpleasant conditions for financial markets. This is discussed further in the advanced topics.
If Mark Zuckerberg announced that in six months, he will direct his company to buy a billion dollars of collectible beanie babies as an investment, the company's stock would likely fall. Notice that the reaction would not wait for the purchase to occur six months later; the stock price would fall in anticipation of the poor business decision. This is what it means for an event to be "priced in". As the event unfolds, details that were not fully anticipated might cause further price movement.
For simplicity, I've used language like "bond prices fall when interest rates rise". A more accurate phrasing would be: "Bond prices fall when expectations change in the direction of interest rates rising (which includes rising more or falling less than previously anticipated)." This situation occurred recently: even though the Federal Reserve did not increase interest rates until March 16 2022, bond prices fell significantly prior to that date. Plausibly, this is because the Federal Reserve signaled that it would raise rates more aggressively than previously planned, in response to unexpected inflation. In late April, additional warnings of larger rate hikes led bond prices to fall further. This was followed by unexpectedly persistent inflation figures released in June, which triggered larger interest rate hikes from the Fed and pummeled bond prices even more. September's report found that inflation was still hot, and again the Fed raised interest rates by a large increment. The total return of BND shows an 18.6% drawdown from Aug 6 2020 to Oct 20 2022, the worst for the US bond market in many decades (and perhaps ever). Bond markets reacted in anticipation of interest rate hikes; they did not react to them in real time.
The same lesson applies to economic recessions: some people become upset when the stock market starts booming in the middle of a recession, declaring the stock market to be disconnected from the economic struggles of real people. But when the stock market begins recovering, it simply means that expectations for the future are being revised in a positive direction. Even bad news can generate positive returns in the stock market if the news was not as bad as expected. See this footnote for another example.
It is probably not surprising to read that there are smart and dumb ways to take investment risks. Some people seem to find it entertaining to embrace catastrophic risk and and suffer crippling financial losses. These smart and dumb types of risk are referred to as "compensated" and "uncompensated" risk, respectively. For example, it is riskier to own shares of a globally diversified fund of stocks than a globally diversified fund of bonds. Why are many investors willing to hold stocks despite their greater risk? Because stockholders are compensated for this elevated risk with higher expected return than bondholders. Accepting risk that increases expected return means you are taking a compensated risk.
A primary way in which many people assume uncompensated risk is by holding small numbers of stocks. This exposes them to idiosyncratic risks of individual stocks, for which they are not compensated. The general solution to uncompensated risk is diversification — a portfolio of thousands of stocks has nearly eliminated idiosyncratic risk. If you want more uncompensated risk, there are many options: short selling volatile biotech stocks, getting too much leverage with total return swaps, or buying short-term, out-of-the-money options. If you don't know what these mean, that's for the best. It should be the goal of an investor to create a portfolio with the appropriate level of risk, and to assume only compensated risks.
The primary influence on the risk of a portfolio is its allocation of stocks and bonds. An 80/20 portfolio — with 80% stocks and 20% bonds — is usually far riskier than a 20/80 portfolio, with 20% stocks and 80% bonds. Secondarily, the risk-return characteristics are affected by allocation to different stock and bond funds within the two broad categories. As discussed above, bond funds vary in risk based on a combination of term risk and credit risk.
Over time, some portions of a portfolio will depart from their initial allocation. During a bull market, in which stock returns are generally positive, stock funds tend to become overweighted. During a bear market, in which stock returns are persistently negative, bond funds tend to become overweighted. When weights of different funds drift from their initial weights, the portfolio's risk-return profile changes. The solution to this drift is rebalancing, which conserves the portfolio's intended risk level.
The most straightforward method of rebalancing is to sell shares in overweighted funds and use the proceeds to buy shares in underweighted funds. For example, an 80/20 allocation might drift to 83/17 during a long bull market. To restore the intended risk-return characteristics, we could sell shares of stock funds and buy shares of bond funds. The actual mechanics of rebalancing are covered in the section on practical information.
On an episode of the Odd Lots podcast, the hosts interviewed a co-founder of theGlobe.com, an early social network on the internet that went public in 1998. Like many speculative tech companies, their stock price skyrocketed and crashed in the early 2000s. We learn in the interview that on paper, the co-founder Stephan Paternot was worth as much as $100 million. Yet he later mentioned that after his company eventually failed, he was a million dollars in debt. He referenced two decisions that amounted to phenomenally bad risk management. Not only did he invest a great deal in other tech startups whose fortunes were correlated with that of his company, but he borrowed money to do it. It would have been prudent to invest in assets that diversified the massive exposure to his company's stock, like value stocks or high-quality bonds. Instead, not only did he load up on more speculative tech exposure, he went into debt for the opportunity. When the value of his own company and his other dot-com investments fell to nearly zero, he was left with nothing but his debt.
A well-known book by Moshe Milevsky is entitled Are You a Stock or a Bond?. The question refers to the risk of your human capital, also known as labor capital. Your ability to earn income is an enormous asset, and the stability of the cash flow produced by this asset is an important part of the risk you can accept in financial markets. The classic example of a bond-like person is a tenured university professor, who likely has high job security and uniform income across time. A person with stock-like human capital, in contrast, might be a commissioned salesperson in a volatile industry. He is at risk of losing income or losing his job altogether in adverse economic conditions.
Even if the professor and salesperson have the same average income and the same expenses, the professor can afford to embrace more risk in her portfolio, because her human capital generates a stable, bond-like cash flow. The salesperson would need to have a higher risk tolerance to hold the same ratio of stocks to bonds in his brokerage account. If income or job security in someone's line of work is economically vulnerable, they should be especially eager to hold more high-quality bonds, because they could be laid off when stocks have crashed. In addition to the salesperson mentioned above, this could include people who work in restaurants, casinos, tourism and hospitality, real estate, and investment banking. (Stephan Paternot was a quintessential stock-like person.) Recession-resistant positions might include tenured professors and teachers, medical professionals, government employees, and skilled tradespeople. Milevsky's interview on The Rational Reminder is here. Another episode of the same podcast discusses how the types of risk in your portfolio can complement the economic risks to which you're personally exposed (and see this section for further explanation).
US Treasury bonds are tax-exempt at the state and local levels, so they're subject only to federal tax. Municipal bonds are issued by state or local jurisdictions, and they have even more tax benefits. Income from muni bonds is always tax-exempt at the federal level, and exempt at the state level if the bond is issued by your home state (or by any US territory like Puerto Rico). Due to their tax benefits, muni bonds have lower yields than they otherwise would. This makes them worthwhile only for those with high income, because reducing tax is especially valuable for those who pay a high marginal tax rate. If you consider investing in municipal bonds, make sure you understand their fairly complex tax policy — certain capital gains are taxable even though income is not — and the potentially weird dynamics that follow from their mostly tax-exempt status. Muni bond funds have higher expense ratios than more typical bond funds, although Vanguard muni funds keep their expense ratios pretty low. In addition, municipal bonds have more credit risk than debt backed by the federal US government.
Bond funds have multiple advantages over individual bonds: you own a diversified portfolio in a single security; transaction costs are lower because large asset managers trade in bulk; international bond funds can eliminate currency risk through currency hedging; and you can reinvest any income back into the fund, rather than needing enough to buy more bonds. Finally, bond funds do the work of maintaining the same characteristics over time. If you built your own bond portfolio with an average maturity of six years, a year later the average maturity would be five years, and the risk profile would have changed. But as you get older, a bond fund stays the same age.
However, what if you don't want the bond fund to stay the same? Let's say you're saving for a specific goal at the beginning of 2029, and you want the bonds in your portfolio to approach maturity at the end of 2028, becoming gradually less risky as time passes. Many people think the only way to achieve this stream of returns is by purchasing individual bonds: with high-quality bonds, the expected return is nearly guaranteed if you can wait until maturity. But for those who want this, there are bond funds that terminate on a specific date like an individual bond. You could invest in IBTI and BSCS, which currently hold intermediate-term bonds, but will hold short-term bonds in four years. The bonds will mature throughout 2028, and the funds will distribute remaining cash to shareholders in December 2028 and close down. They're called term-maturity bond funds or target maturity bond funds, and you can choose from BlackRock's iBonds ETFs and Invesco's Bulletshares ETFs.
Except for a situation like the one I described — in which you're investing for a spending event at a particular point in time — these funds are probably not suitable. Perhaps there is psychological comfort in knowing that you can wait out price volatility until the bonds reach maturity on a certain date, but there is no real benefit. For most investing objectives, a bond portfolio that becomes gradually less risky does not make sense.[6]
All other bonds discussed here are marketable: their value is determined by the market, and is subject to potential loss. In contrast, US Treasury savings bonds are as close to risk-free as any investment can be. They are not tradable on the secondary market: you purchase and redeem them directly from the US Treasury, and interest is guaranteed. Unlike marketable bonds, there is a one-year lock-up period during which you cannot redeem the bonds, so you need to be certain you won't need the money for a year. They must be purchased at treasurydirect.gov, not through a brokerage account. There are two types, called Series I and Series EE.
Series I savings bonds, often just called I-bonds, are linked to inflation. The interest rate they pay is a composite rate calculated by combining a "variable rate" that changes every six months and a "fixed rate" that is constant for as long as you hold the bond. A new variable rate is set every six months in November and May based on recent changes in the urban consumer price index (CPI-U). I'll express these rates in annualized terms. Because inflation was high in 2021 and 2022, the variable rate determined by inflation reached a record 9.62% in May 2022, and is currently 3.94%. No matter when you buy I-bonds, the variable rate persists for six months, then switches to a new variable rate every six months. So if you bought I-bonds in June 2023, the variable rate would be 3.38% and would not change to the new rate of 3.94% until December (even though the new rate is determined in November). The current fixed rate of I-bonds is 1.30%, so the composite rate for newly purchased bonds is 5.27%. Those who purchased I-bonds before November 2023 receive the same fixed rate as when they bought the bonds, so their composite rate usually differs. Because the variable rate is equal to the CPI-U, it is possible for deflation to cause a negative variable rate. If the fixed rate were positive and the variable rate were negative, the composite rate could be less than the fixed rate. But the composite rate cannot fall below zero. These bonds never lose value.
Series EE bonds are simpler: they have a fixed rate which is currently 2.70%. However, their special feature is that they double in value if held for 20 years, through a one-time adjustment. 2^(1/20) = 1.0353, so the interest rate if left for 20 years is a guaranteed 3.53%. It would make sense to prefer Series EE bonds if (a) you will certainly stay invested for at least 20 years, and (b) you believe the average I-bond return is likely to be less than 3.53% during the subsequent 20 years. Most people should not choose the Series EE bonds at the current rate.
The maximum purchase per calendar year is $10,000 of each type of savings bond per person. However, you can add an additional $5,000 of I-bonds per year by overpaying your taxes and directing the IRS to use your refund to buy these bonds. Your spouse and your children have their own $10,000 limits, so you could buy one in your child's name (or the names of other trusted relatives). You can purchase another $10,000 if you have a corporation, using its employer identification number (EIN) instead of your Social Security number. It's not hard to register a corporation if you really wanted to use it for this. You can also buy more with a trust. If you think the interest rates are going to be lower in the near future and want to load up while they're high, you and a trusted person can buy them for each other in the gift box and deliver them in a later year. There is no limit to how much you can buy with this method, although receiving a delivery of $10K in I-bonds in a given year would mean that you cannot buy any more for yourself in that year. Because you can receive delivery of only $10K per year, buying tens of thousands of dollars of I-bonds as gifts would mean that some of them are illiquid for more than the usual one year. See this link for more explanation.
If you buy I-bonds every year, you'll build up an asset with no downside risk that thrives when inflation is high and can be cashed out at any time (except the most recent year's purchase). This is important, because there are no reliably good investments in high-inflation environments (gold is not, although some people think it is). The government created I-bonds because inflation — in particular, unexpectedly high inflation — is so harmful to investments as well as cash savings. They also created treasury inflation-protected securities, but their properties are quite different.[7] You can designate I-bonds as your emergency fund, once the one-year lock-up period has ended.
If you redeem the bonds in less than five years, the last three months of interest will be forfeited. The interest from these bonds is not pro rata if you buy in the middle of a month (e.g., half the month's interest if bought on the 15th). Instead, the government is magnanimous and will provide the full month's interest regardless of when you buy in a given month. However, bonds are purchased one business day after you submit the order. So, for instance, if you submit an order on the last business day of April — thinking you'll reap the whole month's interest — you'll accidentally purchase them on the first business day of May. This can also change the interest rate for the first six months, since you would receive the new rate in May rather than the rate from the previous November.
The bonds are exempt from state and local taxes, but are subject to federal income tax (unless used for educational expenses under certain conditions). You do not pay tax on the interest until the bond is redeemed, unless you choose to do so early because it benefits your tax situation. Savings bonds earn interest for 30 years, after which you can redeem them and pay tax (or wait to redeem them, but that's rarely suitable).
This explainer is a good summary of I-bonds and has links to various details. I suggest reading it before starting because the Treasury Direct website has unfortunate quirks.[8] Due to the quirks described in that footnote, I recommend creating an account now regardless of whether you want to buy bonds. This footnote[9] explains how to calculate the interest you'll receive from buying I-bonds. To indicate the three-month penalty, the website won't show any interest accrued until the first day after the fourth month (i.e., on May 1 for bonds purchased in January). If you hold for five years, you'll see a big jump due to removal of the penalty.
Investment risk has two components: loss due to risk you took, and missed opportunities due to risk you didn’t take. Careful planning helps you balance them. In particular, the stock market provides stunning returns in the long term, but presents the risk of significant loss in the short term. Risk of short-term loss can be dialed down by investing in bonds with differing characteristics, the lowest risk being in short-term US Treasury bonds. Bonds with high credit quality can (but do not always) offset losses when stocks plummet. In contrast, high-yield bonds tend to fall with stocks.
Financial markets do not react to events in real time; they react to changing expectations about the future. Risk that increases expected return is called compensated risk. Rebalancing is how you conserve the risk and expected return of your portfolio. You should consider how the risks of your investments relate to the security of your income, and how likely you are to lose your job during economic downturns and associated stock market crashes. US Treasury savings bonds are sometimes a great alternative to marketable bonds.
Click here for the next section — Tax-advantaged accounts
All sections:
- Cover page
- Introduction to index funds
- Thinking about risk
- Tax-advantaged accounts
- Your psychology
- Investing for retirement
- Guidelines for personal finance
- Building a stock portfolio
- Fund proposals
- Advice
- Practical information for execution
- Taxes
- Vocabulary and further resources
- Advanced topics
Footnotes:
1 What are realistic expectations for stock market returns? First we should understand inflation. It will become evident in the section on retirement planning that returns after accounting for inflation are what matter to long-term investors. Your return before inflation is called the "nominal return", and your return after inflation is called the "real return". Imagine a 10% average annual return over some number of years, accompanied by average annual inflation of 3.5%. To correctly calculate the real return, we need to convert these percentage changes to multipliers. The nominal return of 10% as a multiplier is 1.1, and 3.5% inflation as a multiplier is 1.035, so the real return as a multiplier is 1.1/1.035 = 1.0628, which is a 6.28% real return. There are other paths to the same real return: 7.34% nominal return and 1% inflation provides a real return of 1.0734/1.01 = 1.0628, again 6.28%.
What are average stock market returns in real terms (i.e., after inflation)? I will use data from the summary of the Credit Suisse Global Investment Returns Yearbook 2021, which contains data from 1900 through 2020. Globally, the average annual real return was 5.3% (in US dollar terms; Figure 38). After excluding hyperinflation events in Germany and Austria in the early 1920s, average annual inflation was 2.6% (Figure 5). This implies an average nominal return of about 8.0%. The average real return in the US was 6.6%, with an average nominal return of nearly 10%.
The superior results of the US market were partially caused by the lack of widespread physical or political devastation since 1900. Japanese stocks lost 97% of value and bonds lost 99% of value due to World War II (in US dollar terms; pp. 38, 40). The stock markets of Russia and China closed down in 1917 and 1949, respectively, due to their communist revolutions. Stock- and bondholders experienced virtually total loss and markets did not reopen for decades. The global average of 5.3% real annual returns includes catastrophic losses like these.
The update from the 2023 summary edition shows that Australia, South Africa, and the US continue to shuffle around in the top ranks of real stock performance since 1900. In local currency terms, the US ranks third behind South Africa and Australia (Figure 11). In USD terms, the US has been second only to Australia (p. 16).
Although the US had exceptional performance in the past, this does not imply that we can expect the US to outperform the rest of the world over the next several decades. To paraphrase Cliff Asness, the long run can lie to you. He showed in the linked article that US outperformance of international stocks from 1980 to 2020 was due almost entirely to higher growth in valuations rather than higher growth in fundamentals. That is, US companies did not experience significantly greater growth per share in fundamentals like earnings, but US stocks became more expensive than international stocks. There are some long-run trends we have good reason to think will persist, like stocks outperforming bonds, but this is not one of them. Simply observing that something has occurred over a long period of time is not a valid justification for assuming that it will continue to occur. ↩
2 Another level deeper in understanding bonds involves the term convexity. Duration expresses the rate at which a bond's market value changes in response to a given change in interest rates. It measures interest rate sensitivity. Convexity expresses the rate at which a bond's duration changes in response to a given change in interest rates. For those familiar with calculus, duration is the first derivative of market value with respect to interest rate, and convexity is the second derivative. A good explanation of these concepts is in this video. Bond portfolios with the same average duration can have different expected responses to changes in the yield curve, and this is expressed by convexity. To put it more concretely, the properties of a portfolio split between short-term and long-term bonds are different than those of a portfolio of intermediate-term bonds with the same average duration. The former is called a barbell portfolio (heavy on short and long), while the latter is called a bullet portfolio.
The yield curve is another essential concept in fixed income. ↩
3 Money market funds don't have a perfect record of protecting the principal investment. The only major failure was in 2008 when a large money fund "broke the buck" during the financial crisis. Loss was due to exposing the fund to excessive credit risk, and the bankruptcy of Lehman Brothers exposed that risk. That fund, the Reserve Primary Fund, eventually returned 99% of assets to investors, but the last 10% of distributions were so delayed that the effective loss was somewhat greater than 1%, because it deprived shareholders of the opportunity to keep investing that money.
Fortunately, you don't have to accept any credit risk in money market funds if you don't want to. You can invest in funds with federal US government debt: SPAXX or FDLXX at Fidelity, SNVXX or SNSXX at Schwab, VUSXX at Vanguard, or SGOV. (Again, SGOV is an ETF and not a money market fund, even though it's as safe as the others.) SNSXX, FDLXX, and SGOV hold only US Treasury bonds, which are exempt from state and local tax. SPAXX, SNVXX, and VUSXX hold those as well as other federal US government obligations (which are not exempt from state and local tax), so their dividends are potentially subject to more tax. Money market funds are explored further in the discussion of emergency funds in the Guidelines section. ↩
4 Further detail on S&P 500 total return. 1989-90 drawdown: peak Oct 10 1989, nadir Nov 6 1989 with drawdown of 7.3%, recovery by Jan 2 1990. 2020 crash: peak Feb 19 2020, nadir Mar 23 2020 with drawdown of 33.8%, recovery by Aug 10 2020. Global Financial Crisis: peak Oct 9 2007, nadir Mar 9 2009 with drawdown of 55.3%, recovery by Apr 2 2012. (This was short-lived: it fell again after that day and took until Aug 16 2012 to exceed the 2007 peak again, after which it rose steadily.) 1970s crash: peak Jan 1973, nadir Oct 1974 with drawdown of roughly 47%, recovery by May 1978. 2000-2002 bear market: peak Sep 1 2000, nadir Oct 9 2002 with drawdown of 47.4%, recovery by Oct 23 2006. (There was also a peak on Mar 24 2000 with a value of 99.93% that of the peak on Sep 1. This extends the period of unrealized loss from six years and two months to six years and seven months.)
The 2000s were disappointing because the combination of two severe bear markets led to extended periods of zero return. How far can we go back and still find a higher value than the bottom of the Great Recession on Mar 9 2009? May 5 1997 — nearly 12 years. And how far forward do we need to move before we permanently exceed the peak reached on Mar 24 2000? This finally happens on Dec 21 2010, well over ten years later. Note that this does not mean 12 years of investing would have turned out useless: there is no way to reliably time the market and sell at a peak like Mar 24 2000, or buy at the bottom of a trough like Mar 9 2009.
Calculations for the 1989-90 drawdown, 2020 crash, Great Recession, and 2000-2002 bear market relied on values of the S&P 500 total return from Yahoo! Finance. Using the S&P 500 price ignores dividends. This leads to exaggeration of bear markets, especially when calculating the time between nadir and recovery to previous peak. Calculations for the duration of the 1970s drawdown relied on this calculator, which uses Robert Shiller's data. The drawdown estimate of 47% relied on the S&P 500 price on Oct 3 1974, because distortions due to omitting dividends are mild on the downward half. The price chart had a drawdown of 48%, from which I subtracted one percentage point, based on similar differences during other long drawdowns. ↩
5 How bad was the Great Depression? A seemingly widespread misconception among those who read about investing is that the US stock market took 25 years to recover from the crash that started in 1929. It's true that the prices of the Dow Jones Industrial Average and the predecessor to the S&P 500 didn't recover to their 1929 peaks until 1954. But as stated above, this is a misleading and often very incorrect way of computing the duration of a drawdown. Price charts do not include dividends, which means they always understate performance in terms of total return. On top of this, the Great Depression was a highly deflationary period. Most bear markets are extended if you account for inflation, but the Great Depression is exaggerated by neglecting deflation. After factoring in dividends, we can use this calculator based on Robert Shiller's data to see that the drawdown beginning in Sep 1929 lasted about 15 years (until Jan 1945, roughly). In real terms — that is, accounting for deflation — the drawdown beginning in Sep 1929 lasted only about seven years (until Nov 1936). The nadir of the drawdown was in June 1932 at a loss of slightly over 80%. ↩
6 Cliff Asness wrote in a 2014 opinion piece:
Many advisers and investors say things like, “You should own bonds directly, not bond funds, because bond funds can fall in value but you can always hold a bond to maturity and get your money back.” Let me try to be polite: Those who say this belong in one of Dante’s circles at about three and a half (between gluttony and greed).
Bond funds are just portfolios of bonds marked to market every day. How can they be worse than the sum of what they own? The option to hold a bond to maturity and “get your money back” (let’s assume no default risk, you know, like we used to assume for US government bonds) is, apparently, greatly valued by many but is in reality valueless. The day interest rates go up, individual bonds fall in value just like the bond fund. By holding the bonds to maturity, you will indeed get your principal back, but in an environment with higher interest rates and inflation, those same nominal dollars will be worth less. The excitement about getting your nominal dollars back eludes me.
But getting your dollars back at maturity isn’t even the real issue. Individual bond prices are published in the same newspapers that publish bond fund prices, although many don’t seem to know that. If you own the bond fund that fell in value, you can sell it right after the fall and still buy the portfolio of individual bonds some say you should have owned to begin with (which, again, also fell in value!). Then, if you really want, you can still hold these individual bonds to maturity and get your irrelevant nominal dollars back. It’s just the same thing.
Those believing in the subject fallacy often also assert that another negative feature of bond funds is that “they never mature” whereas individual bonds do. That’s true. I’m not sure why anyone would care, but it’s true. But the real irony is that it’s only true for individual bonds—not the actual individual bond portfolio these same investors usually own. Investors in individual bonds typically reinvest the proceeds of maturing bonds in new long-term bonds (often through the use of a “laddered portfolio”). In other words, their portfolio of individual bonds, each of which individually has the wonderful property of eventually maturing, never itself matures. Again, this is precisely like the bond funds that they believe they must avoid at all costs.
There is nothing magical about holding a bond to maturity. As you hold a bond to maturity, the potential downside and upside of interest rate changes gradually decrease. ↩
7 The US Treasury issues Series I savings bonds to help US citizens and residents cope with inflation. It also issues treasury inflation-protected securities (TIPS), which are marketable bonds in contrast to savings bonds. They are sometimes misunderstood as providing the same kind of protection against inflation that I-bonds do. Coupon payments from a TIP security increase as inflation rises and decrease as inflation falls. The face value also changes with inflation. But a TIP security is not an inherently better investment than a fixed-rate bond during high inflation. If inflation were high but remained in line with market expectations, buying a TIP security would not benefit you compared to buying a fixed-rate treasury bond with the same maturity date. TIP securities are exposed to the risk of inflation expectations being revised downward, a shift which tends to benefit fixed-rate bonds.
As an illustration, inflation was similarly high in 2021 (7.0%) and 2022 (6.5%). TIPS funds had positive returns in 2021 while similar fixed-rate Treasury bonds fell slightly. Then in 2022, TIPS funds had negative returns, barely better than their fixed-rate counterparts.
Buying TIP securities should be done to express a prediction that unexpected inflation will cause the value of the bond to increase. They can also be purchased as a general hedge against unexpected inflation, without a specific prediction that unexpected inflation will occur soon. TIP security funds are listed in this footnote. ↩
8 A notable quirk worth reiterating is the delay of one business day between the order submission and the order execution.
In addition, Treasury Direct has hair-trigger sensitivity to identity fraud. Occasionally when someone opens a new account, they'll put a hold on it and instruct you to print out a form, have it signed and validated at your bank or credit union, and mail it to them. Bank employees see this so rarely that they're sometimes unsure of the correct procedures, so you could spend an hour or more at the bank figuring it out. To minimize your chances of encountering this, use a bank account, mailing address, and email address that you use frequently and have had for a long time, rather than (say) a random email address you don't often use. It's impossible to say exactly what triggers the alarm, but you want the info entered to match the publicly available info they're drawing on. Not only is an account hold an inconvenience, but the process of mailing the form and verifying your identity can take long enough that the month in which you wanted to buy I-bonds has passed. You can avoid this outcome by opening your account now, even if you don't plan to buy savings bonds soon. Link a bank account you intend to keep for a long time, because they make it difficult to change. ↩
9 Let's say you purchased I-bonds in January 2022. You receive 7.12% annualized interest for the first six months, then the rate changes to 9.62% for the next six months. We'll start with the simplest scenario: you hold for a year plus three months to neutralize the three-month penalty. With a 15-month holding period, you'll experience half a year of 7.12% interest (a 3.56% gain), plus half a year of 9.62% interest (a 4.81% gain). If we invested $10,000, it's almost correct to say that the value at the end of 15 months would be $10,000 × 1.0356 × 1.0481 = $10,854.12. But that isn't quite how it works. The Treasury counts savings bonds in increments of $25, which means that interest is calculated for every $25 bond and rounded to the nearest cent. $10,000 of savings bonds is actually a group of 400 $25 bonds. So we should calculate $25 × 1.0356 × 1.0481 = $27.14, then multiply $27.14 × 400 = $10,856. The whole dollar amount is not a coincidence: because the value is rounded to the nearest cent and multiplied by 400, the final value will always be a multiple of $4.
What if we hold for the minimum one year? The interest compounds semi-annually, so the three-month penalty consumes exactly half of the 4.81% gain in the last six months. The 4.81% gain is now a 2.405% gain, so the value of a $25 bond at the end of one year is $25 × 1.0356 × 1.02405 = $26.51, and $26.51 × 400 = $10,604.
And what if we buy $10,000 of bonds in Jan 2022 and hold for 21 months? We receive 6.48% annualized interest in the third six-month period. Each $25 bond grows to $25 × 1.0356 × 1.0481 × 1.0324 = $28.01. So if we redeem in Oct 2023, the value is $28.01 × 400 = $11,204.
This Reddit post describes more details. It links to this helpful website that calculates I-bond interest (but doesn't account for the three-month penalty, so make sure you don't count the final three months for holding periods of less than five years). ↩