Before the covid pandemic, Starbucks (SBUX) - Get Free Report offered self-service stations for milk, cream and sometimes various alternatives. 

That went away during the pandemic because customers did not like the idea of touching a dispenser that another person had just touched. Never mind the shared counters drinks were placed on, the napkin and straw dispensers that everyone touched — pouring your own milk or cream came with an enhanced risk of illness.

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In reality, maintaining milk stations — sometimes more than one in each store — cost the chain a lot of money. Keeping the dispensers filled was labor intensive and customers got mad when one was empty. And people likely used or wasted more milk and cream compared with the current policy, where those are kept behind the counter. 

Starbucks made the change at a time when companies could do anything if they used "public safety" as the reason. Some of those changes, however, were not reversed once the impact of covid lessened and most of society returned to normal 

Walt Disney (DIS) - Get Free Report, for example, got rid of parking trams at Disney World. That made sense since the trams were not built for social distancing and smaller crowds meant shorter walks to the parks.

In September Disney fully restored that service, which surprised some park visitors. Now, the theme park giant has brought back another transportation option that some thought might be gone for good. 

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Disney World improves transportation

Disney World's massive property creates unique transportation challenges. Magic Kingdom, for example, is not within walking distance from its de facto parking lot, the Ticket & Transportation Center.

To get people to its signature theme park, the company offers its famed monorail and a ferry boat service. You can also ride the monorail to Epcot, between the Magic Kingdom and Epcot, and to the Contemporary, Grand Floridian, and Polynesian Resorts.   

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Disney World also offers a boat service between Epcot and Hollywood Studios. In 2019, the company added Skyliner, a gondola service that connects the Pop Century, Art of Animation, Caribbean Beach, and Riviera Resorts with Epcot's International Gateway and with Hollywood Studios.

Adding Skyliner made staying at the theme park's value resorts, Pop Century and Art of Animation, a lot easier. Those properties used to be served with buses, which were often stressed during peak times.

Skyliner, which is open air, did not close during the covid period, aside from areas where properties it connects were closed. 

The service has been popular as it has made it faster to get between parts of the massive theme park in a way that, like the monorail, feels like a ride, not simply transportation. 

Disney brings back a popular transportation choice

Disney World's size means that no one transportation solution will work.

The company has brought back another — one that many thought might be a permanent covid casualty. The theme park company disclosed the move on its Walt Disney World Cast and Community Facebook page.

"Guests at Walt Disney World will once again be able to sail across Bay Lake between Disney’s Contemporary Resort, Disney’s Wilderness Lodge, and Disney’s Fort Wilderness Resort & Campground. Marked with its signature blue flag, the watercraft 'blue route' will return for afternoon and evening voyages beginning Oct. 1, making it even easier to grab a bite to eat at neighboring resorts."

That was met with excitement from followers of the page.

DISNEY WORLD DEALS: Make your Disney World, Disneyland, or Universal Studios dream a reality

"I had almost given up hope on this completely! I am so happy to see this service return," Denis Iverson McGilvery wrote.

That was the general sentiment shared by hundreds of followers, while a few hoped for even more returns to service.

"This is great news! Hoping to see the second launch at Disney Springs open up soon as well," Elizabeth Kelley added.

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Since assuming the position of NAIOP chair in January, I’ve had the pleasure of visiting chapters from Orlando to Milwaukee to SoCal, talking with thousands of members about current market conditions, the forces impacting our industry, and our future as an organization. Four topics have frequently arisen during these conversations, regardless of chapter location or size. These include:  

1. Community Relations. In today’s environment, it’s essential that developers fully understand the impact of their product type on the communities in which they operate, particularly regarding the types of jobs, hours of operations and the environmental impacts of their project (traffic, water, energy, etc.). Whether developing in South Florida, New Jersey, Chicago or Los Angeles, our chapters report increased anti-growth sentiment and the importance of engaging with the community early and often.

2. E-commerce’s Role: Facility Demand and Data. E-commerce sales as a percentage of total retail sales were on a growth trajectory before the pandemic, turbocharging the industrial sector. While truck traffic associated with home deliveries has received attention from news organizations, non-governmental organizations and policymakers alike, consumer behavior as the driving force is often ignored. Further, some research suggests that ordering goods for delivery is better for the environment because people make fewer individual trips to malls, grocery stores and other local shops. Comprehensive research about e-commerce’s environmental footprint is needed to help educate our external audiences and debunk common misconceptions.

Regardless, developers need to clearly articulate e-commerce’s economic impact and the role industrial real estate plays in the community. For that sector – one I’ve been part of for four decades – it means helping policymakers, community groups, the media and the public understand that a) consumers are choosing e-commerce, which requires three times the amount of logistics space; and b) e-commerce can be a more sustainable option compared to traditional brick and mortar. In addition to the economic growth case, it’s important to explain our role as real estate developers in helping their community run smoothly and durably. We should partner with communities to underscore the importance our properties have in the ability to deliver essential goods, including baby formula, medicine, clothing and food.

3. EV Trends. In response to growing truck traffic and climate change concerns, many communities – typically on the West and East Coasts – are imposing requirements around the electrification of commercial vehicles. Southern California leads the pack.

Two years ago, Southern California’s local air quality regulatory body approved the unprecedented Indirect Source Rule (ISR), which required warehouse occupiers to quantify and report vehicle trips to and from warehouses to identify impact and be the basis for issuing taxes. Because of this, and in addition to new laws around electric vehicles at the state level, California businesses are investing heavily in electric trucks and vans and the infrastructure needed to support them.

Members from NAIOP’s California chapters, comprising the NAIOP California State Council, continue to experience the evolving spread of the ISR throughout the state. We also see other states looking at adopting similar “indirect source” concepts, including New Jersey, New York, Washington, Colorado and Nevada. NAIOP will continue to track and provide updates on this issue, as members in urban areas will no doubt keep seeing this policy impacting development projects.  

4. Designing Policies with Communities. We have seen an increase in antiwarehouse development sentiment. Some communities have used moratoriums to pause new projects in response to community pushback, typically on environmental impact grounds. NAIOP and other business associations continue to make the case that such moratoriums disrupt the supply chain, hamstring businesses from operating efficiently, and create job and economic losses.

In some communities, NAIOP members have worked with city staff and the community to create good neighbor policy agreements. These volunteer agreements can address issues like setbacks, landscape screening and noise abatement strategies. In some situations, these agreements can help speed up the entitlement process and create a positive relationship with the community. Developers have found that proactively incorporating neighborhood-friendly building features is a more effective approach than having aggressive approval conditions imposed upon their projects that impede functionality and are overwhelmingly expensive if legislated upon them.  

This year as NAIOP chair has been a meaningful one for me. As we begin the fourth quarter and the end of my term, I’ll continue to be steadfast in strengthening NAIOP and helping this organization and its members boldly talk about the value our industry brings to communities and the economy. I look forward to my remaining chapter visits and seeing many of you at CRE.Converge later this month in Seattle.

This piece has been adapted from the chair’s column in the fall issue of Development. Access the fall 2023 issue here.

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Jules van Binsbergen, William Diamond, and Peter Van Tassel

One of the most fundamental concepts in finance is the notion of a risk-free rate. This interest rate tells us how much money investors are guaranteed to receive in the future by saving one dollar today. As a result, risk-free rates reflect investors’ preferences for payoffs in the future relative to the present. Yields on U.S. Treasury securities are generally viewed as a standard benchmark for the risk-free rate, but they may also feature a “convenience yield,” reflecting Treasuries’ special, money-like properties. In this post, we estimate a risk-free rate implicit in the prices of S&P 500 index options—called the box rate—to measure investors’ time preference separate from Treasury convenience yields.

Risk-Free Payoffs from Options

Options with a European-style expiration can be used to replicate a risk-free payoff using the put-call parity relationship. By buying a put option and selling a call option of the same strike price and maturity, an investor receives the strike price in exchange for delivering the underlying asset on which the option is written. By then selling a put option and buying a call option for a different strike price with the same maturity, an investor can construct a risk-free payoff equal to the difference in strike prices, as shown in the chart below. In industry jargon, this trade is sometimes called the box spread. The difference between the price of the box spread portfolio today and its payoff at maturity reveals a risk-free rate that we call the box rate—the rate at which investors can borrow or lend in the option market. Historical estimates of the box rate from a recent paper are available here.

The Box Spread Trade: Replicating Risk-Free Payoffs with Options

Source: Authors’ calculation.
Notes: The chart plots the combined payoff at maturity (solid blue line) from purchasing a 95-strike call and selling a 95-strike put (squares) while also selling a 105-strike call and buying a 105-strike put (triangles). Regardless of the value of the underlying asset at maturity, the combined payoff is a constant value of $10, equal to the difference in the strike prices. This trade is known as the “box spread.”

Estimating Box Rates

We estimate box rates using S&P 500 index options (SPX options). SPX options are among the most liquid and heavily traded options in the world. They have a European-style expiration and long time-series of available historical data, serving as the basis for the Cboe Volatility Index (VIX Index).

The chart below presents an example of estimating box rates on March 15, 2022, the day before the Federal Open Market Committee (FOMC) began its most recent rate hiking cycle. The top panel estimates the one-year box rate from an ordinary least squares (OLS) regression that exploits put-call parity. The box rate implied by the slope coefficient is 1.59 percent. Since option markets are close to arbitrage-free because of the competitive forces in financial markets, put-call parity holds almost exactly. In this example, the R-squared is .99999992 out to seven nines and the standard error of the box rate estimate is less than .01 percent, or one basis point.

The bottom panel extends the analysis to multiple maturities. The box rates and Treasury yield curve have a similar upward slope. The convenience yield, which is the spread between these curves, ranges from 10 to 30 basis points across different maturities.

Example of Estimating the Box Rate

Sources: OptionMetrics; Federal Reserve Board.
Notes: The top panel plots put minus call mid-quote prices for the same strike price and maturity on March 15, 2022, alongside fitted values from an ordinary least squares (OLS) regression. The box rate implied by the slope coefficient from the regression is 1.59 percent for a maturity in 367 calendar days on March 17, 2023. The bottom panel plots the term structure of box rates from index options of different maturities alongside estimates of Treasury rates from a smoothed yield curve found here. All rates are zero-coupon discount rates with continuous compounding. Years-to-maturity is actual calendar days divided by 365. The option data is from OptionMetrics for S&P 500 index options with maturities between one month and five years whose bid quotes are greater than zero.

Box Rates and Treasury Convenience Yields over Time

Analyzing box rates and Treasury yields over time, we find three main results. First, from January 1996 to April 2023, the box rate is 35 basis points above the Treasury rate on average, implying a 35 basis point convenience yield. Second, convenience yields grow dramatically during the financial crisis of 2007-09, reaching a peak of roughly      130 basis points in October 2008 as a one-month moving average. Third, the average term structure of convenience yields is almost flat across maturities out to three years. 

The chart below illustrates the first two results. The top panel plots the time series of the one-year box rate and Treasury rate over time. The bottom panel plots the convenience yield, which equals the difference between the two rates. Box rates and Treasury rates closely comove, with the Treasury rate consistently below the box rate throughout the sample. In addition to being consistently positive, the convenience yield also exhibits some time-series variation, spiking most significantly during the 2007-09 financial crisis, while staying at more stable levels between 20 and 40 basis points in recent years.

Box Rate Closely Tracks the Treasury Rate and Implies a Positive Convenience Yield

Sources: OptionMetrics; Federal Reserve Board.
Notes: The chart plots the one-year box rate, Treasury rate, and convenience yield estimate from January 1996 through April 2023 as a twenty-one-day moving average across trading days. The box rate is estimated by ordinary least squares (OLS) from put-call parity. To obtain a constant one-year maturity, we linearly interpolate the nearest S&P 500 index option maturities whose put-call parity regressions have an R-squared of at least .99999 out to five nines. Treasury rates are from a smoothed yield curve to obtain a one-year, constant maturity, zero-coupon rate. Both rates are zero-coupon discount rates with continuous compounding. Results are similar using the Theil-Sen estimate of the box rate from the box spread trade.

The chart below illustrates our third result by plotting the average term structure of convenience yields. As we saw in the example above, box rates can be estimated for different index option maturities. We find that the average level of convenience yields is relatively stable and close to 35 basis points across maturities. This means that when the Treasury issues debt at any maturity out to three years, it tends to save around 35 basis points relative to the risk-free rates implicit in the option market.

Convenience Yield Term Structure Relatively Flat out to Three Years, 35 Basis Points on Average

Sources: OptionMetrics; Federal Reserve Board.
Notes: The chart plots the nonparametric binned regression of convenience yield onto time-to-maturity using the binsreg package. It reports a 95 percent uniform confidence band and pointwise confidence bands after partitioning time-to-maturity into ten bins. We use a binned regression approach to account for the fact that option maturities are fixed in calendar time and are not constant maturity. The regression includes maturities from six months to three years. The sample period is January 1996 to April 2023.

Interpretation and Applications

Treasuries are generally considered to be one of the most liquid securities in the world, as they can be traded quickly, in large scale, and at low cost. Treasuries are also a common form of collateral that play a unique role in regulatory capital and liquidity constraints. Because options are risky financial derivatives, the box rate is an alternative risk-free rate benchmark that is based on option prices that do not embed a safe asset premium. Note that the recent effort to replace LIBOR with a new benchmark interest rate shows the importance of finding risk-free rate alternatives. The box rate, which is based on market prices, is one candidate that may be considered alongside other robust reference rates such as SOFR (Secured Overnight Financing Rate) to support financial stability.

The convenience yield estimated with the box rate is also a potentially useful barometer for stress in the financial system. It measures how much investors are willing to pay to hold Treasury securities instead of less money-like assets with identical cashflows. In historical data, the convenience yield was largest during the financial crisis of 2007-09. Investors and policymakers who want a real-time measure of the scarcity of safe assets may therefore find convenience yields based on box rates useful.

Economic Magnitude of Treasury Convenience Yield

As a back-of-the-envelope approximation, if we apply the one-year convenience yield estimated with the box rate to the amount of Treasury marketable debt outstanding each year, the Treasury convenience yield has saved taxpayers around $35 billion per year over the past twenty years. Given the increase in debt following the    COVID-19 crisis, this amount has increased to $70 billion per year since 2020. These significant taxpayer savings bring into focus the importance of suggested reforms and recent research on the Treasury market, where improving the resiliency and functioning of the Treasury market may help to maintain Treasuries’ convenience yield.

Jules H. van Binsbergen is the Nippon Life Professor in Finance at the Wharton School of the University of Pennsylvania.

William Diamond is an assistant professor of finance at the Wharton School of the University of Pennsylvania.

How to cite this post:
Jules van Binsbergen, William Diamond, and Peter Van Tassel, “Options for Calculating Risk-Free Rates,” Federal Reserve Bank of New York Liberty Street Economics, October 2, 2023, https://libertystreeteconomics.newyorkfed.org/2023/10/options-for-calculating-risk-free-rates/.

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