# Wealthfront Automated Bond Ladder Methodology White Paper

## Introduction

Wealthfront’s Automated Bond Ladder offers the opportunity to lock in a higher after-tax yield than cash or CDs with the safety of US Treasuries. Designed for clients with a desire for capital preservation over the short to medium term, or regular tax-advantaged income, the Automated Bond Ladder can provide the benefits of a laddering strategy in an easy, set-it-and-forget it product.

The Automated Bond Ladder holds US Treasuries, which are backed by the full faith and credit of the US government and are among the safest bonds available. US Treasuries preserve invested principal if held to maturity, but are also highly liquid and can be sold at any time before maturity. By investing in a portfolio of Treasuries with a range of maturities, Wealthfront’s Automated Bond Ladder provides a dependable stream of income that is exempt from state and local taxes.

## Introduction to Bonds

Bonds are debt securities issued by governments, governmental agencies, or corporations. When an investor buys a bond, they are essentially lending money to the issuer for a fixed period of time. In return, the issuer promises to repay the value of the loan (referred to as the *principal*) at the end of the period (when the bond *matures*), plus, in most cases, interest payments (also called *coupon* payments) along the way. The amount of annual interest paid relative to the bond’s price is called the *yield*. A bond may also experience price changes, measured in the form of price returns, which is the percentage change relative to its previous price. The sum of the two components gives us the *total return* of the bond.

Bonds compensate investors for taking on risks, including:

**1. Interest rate risk:** This is the risk that the price of a bond will change due to interest rate changes. Assuming the issuer will make all coupon and principal payments as promised, the value of a bond is the sum of the present values of all its future payments. The present value for each payment can be calculated by discounting the payment back to the present day, with the discount rate being set at the current interest rate corresponding to the amount of time until that payment occurs (for example, current 2-year rate for payment 2 years away).

**If interest rates rise, the present values of future payments, and thus the value of bonds, decrease. If interest rates decrease, the value of the bonds would increase.**

Interest rate risk can be quantified using *duration*, which measures the overall sensitivity of a bond’s price to interest rate changes. Higher duration means higher interest rate risk. All else equal, the present value of a principal or interest payment will be more sensitive to a change in interest rates when time until the principal and interest payment occurs is longer. This means that bonds with principal and interest payments that are further in the future will be more sensitive to changes in interest rates (since the value of a bond is just the sum of the present values of all of its future payments). The duration of a bond is the dollar-weighted average time to its payments. As an example, let’s imagine a three-year bond pays $3 in year one, $3 in year two, and then $103 in year three. The final payment includes the principal, while the first two only include interest. The duration of this bond is:

Duration provides a single number measuring the sensitivity of a bond to interest rates. As a rule of thumb, if interest rates rise (fall) by 1%, you can expect the value of a bond to decrease (increase) by roughly 1% multiplied by the bond’s duration.

**2. Credit risk:** This is the risk of the issuer failing to pay the interest or principal back. When we discussed interest rate risk, we made the assumption that the bond issuer made all of the bond’s payments as promised. This isn’t always the case—in some situations, the bond issuer may not have enough money and may stop making bond payments. This is known as *defaulting* on the bond. In general, bonds whose issuers are judged to have a higher chance of default will pay a higher rate of interest.

## US Treasuries

US Treasuries are issued by the US government to fund (along with taxes and other revenue sources) government spending. They are backed by the “full faith and credit” of the US government, meaning that the chance of default (either a missed coupon or principal payment) is *extremely* low. In fact, US Treasuries are considered so safe that they are often used to represent the “risk-free” rate of return that other (riskier) investment strategies can be compared against. Because of their relative safety, the returns earned by US Treasuries are generally lower than those earned by other bonds where there is a higher chance of default.

The United States Treasury issues various types of securities with different duration and payment characteristics. Wealthfront’s Automated Bond Ladder invests in two types of Treasury securities:

**Treasury bills**, or “T-bills”, are the shortest-duration securities issued by the Treasury. T-Bills have initial maturities of 4, 8, 13, 26, or 52 weeks and don’t pay any coupons between issue and maturity. Because of the lack of any intermediate coupons, T-bills are typically priced at a discount to their face value (the value paid at maturity). For example, a 52-week T-bill issued when short-term interest rates (such as the Federal Funds rate) are 5% might cost around $95 (for $100 in face value) at the time of initial issue. When such a T-bill matures and pays its $100 in face value, the investor will have received $5 in interest. Thus, T-bills interest are earned through the discount to their face value instead of periodic coupons.**Treasury notes**have initial maturities of 2, 3, 5, 7 or 10 years. Treasury notes pay coupons every six months, starting about six months after the initial issue. The coupon amount varies with interest rates (and expectations about future interest rates) at the time of issue, but is never less than 0.125% of face value annually.

These securities are issued via auctions. Setting prices via auctions allows the government to keep its cost of debt as low as possible—every successful bidder pays the highest price that would result in the predetermined offering amount to be sold out. This also means that the initial price of Treasury securities isn’t known in advance—it depends on the bids received at the time of auction. For T-Bills, the initial price is almost always less than $100 (for $100 in face value to be paid at maturity). For treasury notes, the price is usually close to $100, but can be higher or lower depending on the result of the auction.

Of course, prices on the secondary market can change between the initial offering and maturity. Bond prices tend to increase when interest rates decrease, and vice versa. Because of this, it is not uncommon to find treasury notes or bonds that have market prices well above $100 when interest rates have decreased significantly. It’s important to note that there is nothing wrong with a bond that is priced higher than $100—it just means that interest rates have probably decreased since the bond’s initial issue. As an example, let’s imagine the Treasury issues a three-year Note when the Fed Funds rate, which is the overnight lending rate between commercial banks and the most short-end of the yield curve, is 8%. Let’s also assume, for simplicity, that the yield curve is somewhat flat. This bond might have a coupon of 8% and sell for around $100 at the initial auction. Two years later, let’s assume the Fed Funds rate has decreased to 5% and this leads to decreased interest rates across the yield curve. In this case, the bond might trade at a price of around $103 as we explained in the Introduction to Bonds section above that decreasing interest rate leads to higher bond value (price). An investor buying this bond would earn $5 in net interest ($8 from the remaining coupons minus $3 in premium, which is counted as negative interest). Dividing this by the purchase price of $103 gives a return of just under 5%.

Though individuals can participate in Treasury auctions, the primary buyers are banks, bond brokers, investment funds, and foreign entities. Most bond trading takes place on the secondary market, where investors buy bonds from (or sell bonds to) the brokers. The secondary market for Treasuries is enormous—according to a report from Securities Industry and Financial Markets Association (SIFMA), daily trading volume averaged over $700B in 2023. This heavy trading activity means that Treasury bonds are very liquid, meaning that investors can buy and sell Treasuries easily and quickly.

### Interest Earned by Treasuries

Treasuries earn interest not only through their semi-annual coupon payments, but also through price changes. For example, as described above, T-bills don’t pay coupons at all, investors earn interest through the discount (at purchase) from their face value. Investors buy T-bills for less than their face value, and then the price converges to face value as the bonds approach maturity. It’s important to remember that the convergence doesn’t always happen in a straight line, and the price of a bond may move away from face value between purchase and maturity.

Treasury notes and bonds are typically issued with coupon rates close to the market interest rate for their respective maturities, resulting in initial auction prices close to face value, but of course, prices may change later due to changes in interest rates.

A Treasury’s coupon rate, therefore, is not necessarily the best measure of how much interest it will earn because it ignores the interest that may be earned from price changes. To address this, a common metric to measure bond interest is *yield to maturity*, which is the annualized interest rate earned by an investor who buys a bond at the market price and holds it until maturity. This metric factors both coupon payments *and* price change. Mathematically, yield to maturity is the discount rate at which the total present value of all future cash flows from a bond equals its price. This calculation also assumes that all coupons paid by the bond are reinvested at the same rate.

As an example, let’s consider a bond with a face value of $100, an annual coupon of $3, and exactly two years to maturity. This bond has two remaining cash flows:

- A coupon payment of $3 in one year
- A final payment of $103, representing the final coupon and the maturing principal, in two years

Let’s assume this bond has a price of $96. For a given choice of discount rate, r, the present value of the bond’s future cash flows is given by this formula:

The yield to maturity is the value of r that makes this value equal to the bond’s price. In other words, the value of r that solves this equation:

In this example, the bond’s yield to maturity is approximately 5.16%.

Typically, Treasuries maturing on the same date will have roughly the same yield to maturity calculated based on their latest market price. Discount bonds (bonds with prices below their face value) have coupon rates lower than their yield to maturity, as their price change components are positive. Premium bonds (bonds with prices above their face value) have coupon rates higher than their yields to maturity.

Because bond prices can change daily, a bond’s yield to maturity can change daily as well. The current yield to maturity for a bond in your portfolio tells you the return that you would earn if you were to purchase that bond at its current price. In Wealthfront’s Automated Bond Ladder, we also calculate the yield to maturity of each bond you hold as of its date of purchase, using the purchase price rather than the current price. This metric, called the *yield to maturity at purchase*, tells you the return you’ll earn on the bond from the time of purchase until its maturity.

One attractive feature of US Treasuries is that, unlike interest earned from savings accounts or CDs, the interest they pay is generally exempt from state and local taxes. Depending on your state of residence and tax bracket, this tax exemption can be significant. **For example, a California resident facing a 24% marginal fed tax rate and 9.3% marginal state tax rate would have to earn a 5.7% pre-tax return from another investment with no state and local tax exemptions to earn the same after-tax return as a Treasury earning a 5% yield. **This is because paying 24% federal and 9.3% state tax on a pre-tax yield of 5.7% would make the after-tax yield to be 5.7% * (1-24%-9.3%) = 3.8%. This is the same as paying just the 24% federal tax on a Treasury with 5% yield, since 5%*(1-24%) = 3.8% as well. Buying Treasuries enables investors to earn yield directly free of state tax.

Treasuries typically do not earn capital gains if held to maturity. As mentioned above, the earnings are typically taxed as interest. However, if bonds are sold before maturity, capital gains or losses may be realized if they are sold above or below their cost basis. These capital gains are not exempt from state and local taxes.

## Bond Ladders

A bond ladder is a portfolio of bonds with staggered times to maturity, designed to preserve capital, provide steady interest payments, and more diversified exposure to interest rates than buying a single bond. As bonds in the ladder mature or pay coupons, the investor can either reinvest the proceeds into a new bond (this bond will have a time to maturity equal to the maximum time to maturity defined by the ladder) or take the cash out of the portfolio.

Let’s look at an illustration of a six-month bond ladder in Figure 1. On day one, the portfolio contains six bonds with one to six months to maturity. In one month's time, bond A, which originally had one month to maturity, will have matured. The proceeds from bond A are used to buy bond G, which has six months left to maturity at that time. The rest of the bonds remain in the portfolio, and each of them are one month closer to maturity than when they were initially purchased. The reinvestment into a new longest rung is called *rolling* the ladder. In two months’ time, bond B will mature and the proceeds will be rolled into another new bond with six months left to maturity. At any given time, the ladder will always hold six bonds with approximately one to six months to maturity, and every month when a bond matures, the proceeds will be used to buy a new bond with six months left to maturity.

Generally, bonds within bond ladders are expected to be held until maturity. This is not necessarily the case for bond ETFs, which often have mandates to hold bonds within a specific range of maturities. These ETFs will sell bonds when their remaining maturities become shorter than the minimum specified by the funds’ strategies. Hence, bond ETFs typically do not offer capital preservation, as they do not hold bonds to maturity. It is also hard to know the fraction of the portfolio’s yield that is locked-in for bond ETFs. ETFs buy and sell bonds on a regular basis and it is hard to predict what part of the portfolio will be replaced, whereas a rolling bond ladder can be configured to reinvest a fixed fraction of the portfolio every time a rung matures. On the flip side, bond ETFs are often more diversified (holding large numbers of bonds), likely more liquid as they trade on the exchanges, and require less maintenance since they do not mature.

By holding a portfolio of bonds with varying maturities, bond ladders provide more diversification when compared to holding a single bond. Just like stocks, bonds respond differently to changes in interest rates and economic conditions. Investing in a portfolio of bonds with a variety of maturities helps to diversify this risk while providing a more steady flow of interest over time. Diversification also helps to reduce reinvestment risk—the risk of receiving a lower yield when reinvesting the proceeds from sold or matured bonds. If a portfolio contains only one bond or bonds with the same maturities, the full portfolio is subject to reinvestment risk when the bond(s) mature. Holding a bond portfolio with varying maturities helps to mitigate this risk by spreading the reinvestment needs over time.

## Wealthfront’s Treasury Ladders

When you open an Automated Bond Ladder, you can configure its length - the longest time to maturity that the portfolio will hold. Wealthfront offers ladder lengths from six months to six years. All proceeds from maturing bonds and coupons will be automatically invested into new bonds based on your ladder configuration.

### Treasury Ladder Construction

We construct treasury ladders with monthly rungs, meaning the target time interval between each rung is roughly one month. This helps to provide a consistent and frequent stream of income, even though each individual treasury notes and bonds only pay coupons every six months and Treasury Bills only earn interest at maturity.

Wealthfront’s treasury ladders target equal weight on all rungs, with weight calculated using the face value of each bond. This means we will seek to buy an equal amount measured by face value for every rung whenever possible. This approach reduces the need for trading in the portfolio, other than investing deposits or reinvesting proceeds:

- Equal weighting reduces the need for rebalancing the portfolio. If the target weights were not equal, then the portfolio would naturally drift away from its targets as time passes.
- Unlike prices, face values stay constant over time. Weights based on prices would fluctuate daily with the prices of the bonds themselves, with bonds farther from maturity generally fluctuating more. Correcting deviations from targets would require trading, which could result in realizing capital gains or losses.

The Treasuries we buy in treasury ladder portfolios will usually have maturity dates on or around the 15th of each month. This decision stems from the availability of Treasuries. The US Treasury typically issues longer-term securities (more than one year of initial maturity) with maturities on the 15th or last day of each month, and the longest-maturity securities with maturities only on the 15th. Although we target the 15th, we will generally consider bonds within a small time window around the 15th of each month as well.

When we see multiple bonds eligible for a single target maturity date, we use the following process to identify a particular bond to purchase:

- Exclude bonds with lower expected liquidity, such as bonds issued a long time ago or ones that are very close to maturity
- Remove bonds that may cause a wash sale (for example, because they have been recently sold at a loss)
- Select a bond from the ones remaining. For target maturity dates that are six months or less from the time of investment (and have no coupons remaining), we choose the most-recently-issued bond, since these tend to be the most liquid. Otherwise, we choose the one with the highest coupon rate.

The third step is the most important, because selecting bonds with higher coupons gives investors a steadier stream of interest income as interest is paid each month. In rare instances, if the only available bonds would cause a wash sale when purchased,we will seek to buy the bond that results in the least amount of losses being “washed.”

In some cases, we may not be able to find any bonds maturing on or near the target maturity date. This means there may be instances when some ladders may not have bonds maturing in every calendar month. When this happens, we will simply buy eligible bonds with the closest maturity dates that we can find.

To avoid unnecessary trading costs, we will not buy bonds with less than fifteen days to maturity—these bonds tend to be less liquid (meaning they cost more to trade), making them unattractive, especially since they have so little time left to maturity.

### Deposits and Withdrawals

Like shares of stock, bonds trade in minimum increments. In the case of US Treasuries, Wealthfront can trade in increments as small as $100 of face value. This means that we won’t always be able to achieve a Treasury portfolio whose weights are exactly equal to their targets. For example, when investing a deposit of $1,000 into a four-year ladder (which has 48 rungs), it won’t be possible to buy bonds so that the portfolio has equal weight in each rung. To handle situations like these, we need to define an order in which to buy (or in the case of withdrawals, sell) rungs of a ladder in cases where we aren’t able to buy (or sell) an equal amount of every rung.

When designing the order in which we buy bonds, we have two goals. First, we want the average maturity of the portfolio to reach the target average maturity (approximately half the maturity of the farthest rung) quickly. Secondly, we want to limit the sensitivity of the portfolio to interest rates movements by starting with bonds that are closer to maturity.

We describe the order in which we buy rungs of a ladder as a sequence of twelve “waves,” each consisting of maturity dates within one specific month of the year (for example January or March). Each wave contains bonds maturing in their corresponding month, purchased in order of increasing time to maturity.

- Wave 1: Maturities of 1 month, 1 year and 1 month, 2 years and 1 month …
- Wave 2: Maturities of 2 months, 1 year and 2 months, 2 years and 2 months …
- …
- Wave 11: Maturities of 11 months, 1 year and 11 months, 2 years and 11 months …
- Wave 12: Maturities of 1 year, 2 years, 3 years …

When determining which rungs to buy, we iterate through the waves one at a time until the remaining cash is not enough to buy another $100 increment of face value for any Treasuries in the ladder.

Let’s illustrate this with an example. We will start with three assumptions:

- The ladder has a maximum maturity of three years, with rungs ranging from January 2024 to December 2026 and has no current holdings
- All bonds cost exactly $100
- The initial deposit into the ladder is $4,500

Since $4,500 is enough to buy $100 in face value in each of the 36 rungs, we first buy $100 evenly across all rungs. This costs $3,600 and leaves $900 in cash to invest. At this point, the ladder is equally weighted and its average time to maturity is 18.5 months - equal to the target. In Figure 2, the holdings from these purchases are shown in blue.

Because the $900 left to invest isn’t enough to buy all the rungs in the ladder, we need to use the ordering we described earlier. The first wave for this ladder consists of the three January rungs. Buying $100 of face value in each of these costs $300, leaving $600 to invest. These purchases are shown in yellow in Figure 2. The next $300 is invested similarly, with $100 going into each of the three February rungs. These are shown in green.

With the last $200, we are able to buy the first two March rungs in wave three, but no more. Purchasing these two rungs uses all of the remaining cash. The final average maturity of the ladder is 17.4 months, just slightly below the target of 18.5 months.

For subsequent deposits or reinvestments of coupons and cash from matured bonds, we prioritize filling any rungs that have a lower weight in the portfolio than others, while using the ordering described above whenever needed. In the example, the next $100 invested into the portfolio would be used to buy the March 2026 rung.

For withdrawals, we use a similar methodology. Whenever possible, we sell all rungs of the ladder evenly, but this won’t always be possible depending on the size of the withdrawal relative to the number of rungs in the ladder. When selling evenly isn’t possible, we use the same ordering as when we invest deposits.

One consideration that can arise when selling is taxes. In some cases, we may have purchased multiple bonds for a single rung, or the same bond on multiple occasions. When we have multiple tax lots for a single rung, we prioritize selling lots with the smallest tax exposure, meaning we prefer to sell lots with capital losses instead of capital gains.

In general, to minimize the costs of trading and the possibility of a realized principal loss, we do not sell bonds except to satisfy withdrawals. When there is a deposit into the ladder, we only buy underweight Treasuries and do not sell overweight rungs, even if the deposit is not enough to completely balance the ladder.

## Conclusion

Designed for investors with short-to-medium term savings goals or regular income needs, Wealthfront’s Automated Bond Ladder provides an easy way to lock in tax-advantaged yield through US Treasuries. By investing in a portfolio of bonds with a range of maturities, bond ladders help diversify your interest rate risk and provide a steady stream of interest income, while preserving your invested capital through the safety of Treasuries. You only need to select the length of the ladder you want, and we do the work of selecting bonds, investing your deposits, and handling reinvestments when you receive cash from maturing bonds or coupons.

^{1}SIFMA, Research Quarterly Fixed Income - Issuance and Trading, report as of Jan 26, 2024

## Disclosures

The information contained in this communication is provided for general informational purposes only, and should not be construed as investment or tax advice. Nothing in this communication should be construed as a solicitation, offer or recommendation to buy or sell any security. Any links provided to other server sites are offered as a matter of convenience and are not intended to imply that Wealthfront Advisers, Wealthfront Brokerage or any affiliate endorses, sponsors, promotes and/or is affiliated with the owners of or participants in those sites, or endorses any information contained on those sites, unless expressly stated otherwise.

Investing in US Treasuries involves risks, including but not limited to interest rate risk, credit risk, and market risk. While US Treasuries are considered to be among the safest investments, they are not entirely risk-free, and there is a potential for loss of principal. Returns on US Treasuries can also be affected by changes in the credit rating of the US government, although such occurrences are rare. Investors should consider their tolerance for these risks and their overall investment objectives before investing in US Treasuries. Past performance does not guarantee future results.

The yield earned from U.S. Treasuries is exempt from state and local income taxes. However, interest income from Treasuries is subject to federal income tax. Tax treatment may vary depending on your individual circumstances. To understand implications for your specific financial situation, consult with a tax professional.

Selling Treasuries from the Automated Bond Ladder involves strategic considerations to minimize tax impact for investors. Often, we hold multiple securities in the same ladder rung to avoid tax complications, such as wash sales. In these instances, we prioritize selling bonds that will result in the lowest tax impact, typically choosing those that might incur losses rather than gains.This strategy is designed to keep the tax impact low. However, tax implications can vary greatly among individuals, so we recommend consulting with a tax professional to understand how these actions may affect your personal tax situation.

Investment management and advisory services are provided by Wealthfront Advisers LLC (“Wealthfront Advisers”), an SEC-registered investment adviser, and brokerage related products, including the Cash Account, are provided by Wealthfront Brokerage LLC, a Member of FINRA/SIPC.

Wealthfront, Wealthfront Advisers and Wealthfront Brokerage are wholly owned subsidiaries of Wealthfront Corporation.

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