May 10, 2022

Client Alert:
Kroll U.S. Normalized Risk-Free Rate
Increased from 2.5% to 3.0%,
Effective April 7, 2022

1

Executive Summary
Kroll regularly reviews fluctuations in global economic and financial market conditions that
may warrant changes to our equity risk premium (ERP) and accompanying risk-free rate
recommendations. The risk-free rate and ERP are key inputs used to calculate the cost ofequity capital in the context of the Capital Asset Pricing Model (CAPM) and other models
used to develop discount rates.
Based on market conditions prevailing at the end of March 2022, Kroll increased the U.S.
normalized risk-free rate from 2.5% to 3.0%, when developing USD-denominateddiscount rates as of April 7, 2022 and thereafter, until further guidance is issued. This rateis to be used with Kroll’s Recommended U.S. ERP of 5.5%, implying a base U.S. cost of equity
capital of 8.5% (= 3.0% + 5.5%). However, given how fast U.S. inflation expectations arerising, the current guidance could be changed again in the near future.

BackgroundIn 2020, the outbreak of the novel coronavirus (a.k.a., COVID-19) generated an unprecedented reaction inboth global financial markets and the real economy. Back then, based on declining real interest rate andgrowth estimates for the U.S. economy, we lowered the U.S. normalized risk-free rate from 3.0% to 2.5%,
when developing discount rates as of June 30, 2020, until further guidance was issued.
In December 2021, despite some uncertainty regarding the impact of the omicron variant of COVID-19,
the global economy appeared to be on a strong path to recovery, although with some unevenness acrossregions. Major central banks were considering some level of normalization of monetary policy, both byslowing down (or stopping altogether) quantitative easing (QE) measures and by raising policy interest
rates, particularly as inflationary pressures proved to be more than transitory in many countries. On January
3, 2022, the S&P 500 index achieved a new record high, while two days later the STOXX® Europe 600
reached its own record high. At that time, we began discussing when and under which circumstances it
might be appropriate to lower our recommended ERPs for the U.S. and the Eurozone. 1
Since then, economic and financial market conditions have changed markedly. Starting in mid-January2022, as inflation continued to surprise with increasingly higher-than-expected readings (to levels notseen in 30 to 40 years in some countries), global equity markets have become more volatile. Investors tried
to ascertain the magnitude and speed at which central banks would raise interest rates, which could leadto a potential decrease in the value of companies in various industries due to an increase in discount rates.
In addition, tensions between Russia and Ukraine – which had been rising to new levels since late 2021 –culminated in Russia’s invasion of Ukraine on February 24, 2022. Country risk measures for these twocountries have surged, but the increase in risk has extended to other markets and indicators.

1

The term ‘equity risk premium’ may be known as ‘market risk premium’ or ‘equity market risk premium’ in different geographies,
but they all refer to the same concept. In this document we use ‘equity risk premium’ or ERP.
2

The remainder of this Client Alert will focus on the following topics and how they formed the basis for our
new recommendation issued on April 7, 2022. 2
1.
2.
3.
4.

Global Interest Rate Trends
U.S. Risk-Free Rate and Inflation – Recent Trends and Challenges
Methods of Estimating a Normalized Risk-free Rate
Conclusion

Global Interest Rate Trends
From the onset of the 2008 Global Financial Crisis, major economies have seen a significant downward
trend in nominal interest rates. Since then, valuation analysts have reexamined whether the “spot” riskfree rate is still a reliable building block upon which to base their cost of equity capital estimates. The 2008
Global Financial Crisis challenged long-accepted practices and highlighted potential problems of using the
spot yield-to-maturity on a safe government security as the risk-free rate, without any further adjustments.
Material distortions to spot government debt yields can occur during periods characterized by significant
flight-to-quality investment flows or by central bank monetary policies that entail significant intervention
in sovereign debt securities markets and/or the implementation of negative interest rate policies. These
actions may: (i) distort long-term yields by reducing term premiums that no longer reflect market
expectations of long-term inflation, and (ii) potentially drive short-term real yields to negative levels (i.e.,
below 0.0%), which will no longer reflect the time value of money, and imply that the real rate of growth
for the overall economy is expected to be negative for an extended period.
Since the 2008 Global Financial Crisis, major central banks in developed markets – including, but not limited
to the Federal Reserve Bank (Fed) in the U.S., the European Central
Bank (ECB) in the Eurozone, and the Bank of Japan (BOJ) – struggled toCentral banks’bring consumer price inflation up to their respective target levels
measures of inflation(typically around 2%). Central banks’ measures of inflation tend to focus
tend to focus on a
on a less-volatile indicator called “core” inflation, which excludes foodless-volatile indicatorand energy prices. In the aftermath of the 2008 Global Financial Crisisand the ensuing Euro Sovereign Debt Crisis – in an attempt drive
called “core” inflation,
inflation up to target levels and to support economic recovery – central
which excludes foodbanks kept their policy interest rates at near 0%, or even at negativeand energy prices.
levels, as in the case of the ECB and Bank of Japan. They also
implemented unconventional QE policies that led to a massive increasein central bank balance sheets due to large-scale purchases of assets, which comprised government
securities, mortgage-backed securities (MBS), and agency debt, while in some cases it even included
corporate debt and equity instruments (see Exhibit 1).

2

Data and Information for this Client Alert was collected through April 7, 2022.
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In 2020, another major shock shook global financial markets. The World Health Organization (WHO)announced on March 11, 2020 that it was changing its classification of COVID-19 to a “pandemic”. 3
COVID-19 led to the largest global recession since World War II. In response, major central banks
implemented QE and other crisis-related monetary policy measures last employed in the aftermath of the2008 Global Financial Crisis, as well as some new and untested measures. Some central banks introduced
QE policies for the first time in their history (e.g., Australia, Canada).
Exhibit 1: Total Assets Held by Major Central Banks: Federal Reserve, European Central Bank, Bank ofJapan, and Bank of England (In U.S. Dollars)
December 31, 2006 – End of March 2022
$30.0

USD 25.9 Trillion$25.0

Assets Held by Central Banks (in USD trillions)Bank of England

Bank of Japan
European Central Bank
$20.0

U.S. Federal Reserve

COVID-19 begins

$15.0

$10.0

$5.0

$0.0

Source of underlying data: Bank of England, FRED (Federal Reserve Bank of St. Louis). Analysis performed by Kroll.

In a period of approximately two years, the balance sheets of the Fed, ECB and the Bank of England grewat their fastest pace in history. Between February 29, 2020 and the end of March 2022, the size of the Fedbalance sheet more than doubled (from $4.2 trillion to $8.9 trillion), while both the ECB and the Bank ofEngland saw their respective balance sheets nearly double (approximately) in size (from $5.1 trillion to$9.7 trillion and $0.6 trillion $1.2 trillion, respectively).4 Prior to the pandemic, the Bank of Japan had thelargest balance sheet of the four major central banks (approximately $5.5 trillion), but afterwards both the
Fed and the ECB surpassed the Bank of Japan in balance sheet size (see Exhibit 1). 5

3

4
5

To simplify comparisons, when using monthly data in this document, dates up to and including February 29, 2020 are definedas “pre-pandemic”, and March 1, 2020 is used as the beginning of the pandemic.
Dates are as close to the end of March 2022 as possible.
As of February 29, 2020, the Fed, ECB, BOJ, and Bank of England had balance sheets of $4.2, $5.1, $5.4, and $0.6 trillion,
respectively. As of the end of March 2022, the Fed, ECB, BOJ, and Bank of England had balance sheets of $8.9, $9.7, $6.1, and$1.2 trillion, respectively.
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The sizable increases in these central banks’ balance sheets, along with various flight-to-quality episodes,
continued to exert a downward pressure on global long-term interest rates through early 2020 (see Exhibit2). At the onset of the pandemic, 10-year government bond yields reached record lows in 2020 in the U.S.,
Canada, and U.K., driven initially by flights to quality, but remained low as a result of the unprecedent levelof QE measures.6
Exhibit 2: Yields on 10-Year Government Bonds Issued by the U.S., Canada, U.K., Germany, and Japan
December 31, 2007 – March 31, 2022
6%

United States Treasury Constant Maturity - 10 Year
Canada Government Debt - 10 Year
5%

United Kingdom Government Debt - 10 YearGermany Government Debt - 10 Year
Japan Government Debt - 10 Year

4%

3%
2.40%
2.32%

2%
1.62%

1%
0.44%
0.21%

0%

-1%

Source of underlying data: Capital IQ.

More recently, as inflation pressures crept up, we observed a rise in government bond yields of major
developed countries (with the exception of Japan), although they are still relatively low by historicalstandards and, arguably, not fully reflective of higher inflation expectations. Japan is a unique case, as thecountry has suffered from deflationary pressures for decades. In 2016, the Bank of Japan announced anovel policy called “Quantitative and Qualitative Monetary Easing (QQE) with Yield Curve Control”, which
entailed targeting the nominal yield of 10-year Japanese government bonds to around 0.0%. Since then,the Japanese 10-year yield has hovered around 0.0%, as shown in Exhibit 2.

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German government debt as measured by month-end 10-year Bund data also declined and made local lows in 2020 (from-0.21% on December 31, 2019 to -0.65% on October 31, 2020), but the all-time low for the 10-year Bund as measured bymonth-end data was reached prior to the COVID-19 pandemic on August 31, 2019 (-0.74%).
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U.S. Risk-Free Rate and Inflation – Recent Trends and Challenges
Immediately after the outbreak of COVID-19, inflation dropped close to 0% in the U.S. and in other major
economies, as global demand for many categories of goods and services dropped abruptly.7 However, as
economies began to recover from the pandemic, a combination of factors has led to a surge in inflation in
2021 through the present. Initially, the Fed attributed the increase in U.S. inflation to temporary factors,
primarily driven by the low-price base of 2020 that resulted from the pandemic-related recession.
However, inflation proved to be more than transitory in the United States. Factors such as increased
consumer demand for goods and services (driven in part by pent-up demand coupled with unprecedented
levels of government fiscal stimulus), labor shortages, and global supply chain bottlenecks stemming fromCOVID-19 have all contributed to upward pricing pressures. More recently, both the U.S. consumer priceindex (CPI) inflation and the core inflation have reached near 40-year highs (see Exhibit 3).
Exhibit 3: 12-Month Percentage Change in U.S. CPI Inflation vs. U.S. Core Inflation
January 1982 – February 2022*

Source of underlying data: U.S. Bureau of Labor Statistics. CPI for All Urban Consumers (CPI-U), not-seasonally adjusted series.
*March 2022 data was unavailable when we issued our guidance effective April 7, 2022. Subsequently, the March 2022 CPI inflationand core inflation were published, reaching even higher levels of 8.5% and 6.5%, respectively.

What is different about the latest bout of inflation is that price increases are broad-based and not limited
to volatile items such as food and energy. Despite the relatively wide fluctuations in U.S. CPI inflation
observed after the 2008 Global Financial Crisis, U.S. core inflation generally hovered around the Fed’s 2.0%
target. That is no longer the case since mid-2021.8
This trend is not unique to the United States. Recent inflation figures for Canada, the U.K. and the Eurozone
are also at multi-decade highs, although still below the levels observed in the U.S.

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8For example, in the U.S. the 12-month rolling inflation rate decreased from 2.3% at the end of February 2020 to 0.12% by theend of May 2020.
The personal consumption expenditures (PCE) price index is the Fed’s preferred measure of inflation. However, the upward
trends have been similar for PCE, CPI and core inflation measures.
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For example, in Canada consumer prices increased 5.7% year-over-year as of February 2022, the largest
gain in over 30 years.9 Similarly, in the U.K. CPI inflation rose by 6.2% in February 2022, the highest 12month inflation rate in the U.K.’s Office of National Statistics (ONS) series, which began in January 1997,
and the highest rate in 30 years using an historic modeled series. 10
In the Eurozone, statistics only begin in 1997, just prior to the creation of the euro on January 1, 1999.
Consumer price inflation in both the Eurozone and the European Union (EU) is measured using theHarmonized Index of Consumer Prices (HICP), which differs from indications using a national CPI index. 11
The objective of using a “harmonized” methodology is to ensure that data from all the countries in the EU
can be compared with each other. Harmonized inflation for the Eurozone reached 5.9% in February 2022,
the highest on record.12 Preliminary (flash) estimates for March 2022 pointed to an even-higher record of
7.5%.13 Notably, Germany – the largest economy in the Eurozone – saw February harmonized inflation
rise to 5.5%, but March preliminary estimates suggest a surge to 7.6%. Also, according to Germany’s
Federal Statistical Office (Destatis), German’s preliminary inflation estimates for March 2022 reached 7.3%
using a CPI-based measure, which would be a 40-year high, if confirmed.14
The recent Russia-Ukraine conflict has placed further pressure on an
already-strained global supply chain. Severe economic sanctions
imposed against Russia and the economic destruction in Ukraine havecontributed to a significant rise in the prices of oil, gas and othercommodities such as precious metals (e.g., palladium, platinum, silver,gold), base metals (e.g., aluminum, nickel) and agricultural products(e.g., fertilizer, wheat). Ukraine and especially Russia are large
producers of some of these commodities and the current conflict isfurther exacerbating global supply chain shortages and adding to
inflationary pressures. In the short run, the conflict may have a bigger
impact on inflation in Europe than in the U.S.

9

10

11
12

13

14

The recent RussiaUkraine conflict has
placed furtherpressure on an
already-strained
global supply chain.

Source: Statistics Canada, “Consumer Price Index, February 2022”, released on March 16, 2022 and accessible here:
https://www150.statcan.gc.ca/n1/daily-quotidien/220316/dq220316a-eng.htm. The last time Canada consumer prices
increased 5.7% or more on a year-over-year basis was August 1991 (6.0%). After the writing of this alert, the Canadian CPI
rose to an even higher 6.7% as of March 2022.
Source: Office for National Statistics, “Consumer price inflation, UK: February 2022”, released on March 23, 2022 and accessible
here: https://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/consumerpriceinflation/february2022. The March2022 CPI, which was released after the writing of this alert, climbed to 7.0%.
For more information, visit: https://ec.europa.eu/eurostat/web/hicp/faq.
Source: Eurostat database, “prc_hicp_manr” series, last updated on April 4, 2022. Accessible here:
https://ec.europa.eu/eurostat/web/hicp/data/database.
Preliminary indications may change when final figures are available. Source: Eurostat, “Flash estimate - March 2022 – Euro area
annual inflation up to 7.5%”, released on April 1, 2022 and accessible here:
https://ec.europa.eu/eurostat/documents/2995521/14442438/2-01042022-AP-EN.pdf/ba153bc6-c1aa-f6e5-785b21c83f5319e5.
Source: Destatis Statistisches Bundesamt, “Expected inflation rate for March 2022: +7.3%”, released on March 30, 2022 andaccessible here:
https://www.destatis.de/EN/Press/2022/03/PE22_137_611.html;jsessionid=FBAA821B9AED84449DC0763F90341B29.live
721. Also, see “German inflation rises more than expected in March”, Reuters, March 30, 2022,
https://www.reuters.com/world/europe/german-inflation-rises-more-than-expected-march-2022-03-30/.
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The question is whether these recent trends will change economists’ and market participants’ views on
long-term inflation expectations. Until recently, long-term U.S. inflation expectations remained anchoredat just above 2.0%. Exhibit 4 shows the 20-year “breakeven inflation”, which is defined as the expected
inflation implicit in the difference between nominal and inflation-indexed (i.e., real) yields for 20-year U.S.
government bonds. 15 This may be seen as a possible measure of investor expectations for long-term
inflation.
Using a breakeven inflation measure at the end of March 2022 implied an annualized average expected
U.S. inflation of approximately 2.8% over the next 20 years, which is higher than long-term expected
inflation from economic projections discussed in the next section.
Exhibit 4: Daily Breakeven Inflation Implied from 20-Year (Nominal) U.S. Treasury Constant-Maturity Bond
Yields and 20-Year Treasury Inflation-Protected Securities (TIPS) Yields
July 2004 – March 2022
3.5%
3.0%
2.8%

2.5%
2.2%

2.0%
1.5%
1.0%
Breakeven Inflation(20-Year U.S.Treasury minus 20-Year U.S. TIPS)
0.5%
0.0%

Long-Term Average: Breakeven Inflation
July 2004–March 2022 (2.2%)

Source of underlying data: Federal Reserve.

15

Breakeven inflation is a measure of market expected inflation calculated as the difference between nominal and inflation-indexed
government securities. It is sometimes referred to as market implied inflation or market expected inflation.
8

There are some shortcomings in using breakeven inflation as a proxy for long-term inflation expectations.16
Changes (sometimes significant) in breakeven inflation rates are not uncommon in times of crises. Thisphenomenon was observed in the U.S. in the aftermath of the 2008 Global Financial Crisis and at the onset
of COVID-19 outbreak in March 2020, where the 20-year breakeven inflation reached lows of 0.7% and0.9%, respectively. In addition, several academic studies have pointed out that the breakeven inflation is
an imperfect measure of expected inflation because it ignores the presence of inflation risk premia in
nominal yields (which can be negative or positive) and illiquidity premia common in inflation-indexedbonds. Inflation risks and illiquidity premia vary over time.17 Nonetheless, it is informative that marketbased inflation expectations rose gradually since the low in March 2020 – at the height of the COVID-19
crisis – and were back to the long-term average of 2.2% in January 2021. Since Russia’s invasion of Ukraine
on February 24, 2022, market expectations of U.S. long-term inflation have accelerated.

Methods of Estimating a Normalized Risk-free Rate
During periods in which risk-free rates appear to be abnormally low due to flightto-quality or massive central bank monetary interventions, valuation analysts may
want to consider normalizing the risk-free rate.
By “normalization” we mean estimating a risk-free rate that more likely reflects the sustainable average
return on long-term bonds issued by governments considered “safe” (typically, those rated AAA by major
rating agencies).
Estimating a normalized risk-free rate can be accomplished in a number of ways, including (i) simple
averaging, and (ii) various “build-up” methods.
The first method of estimating a normalized risk-free rate entails calculating averages of yields to maturity
on long-term government securities over various periods. This method’s implied assumption is thatgovernment bond yields revert to a longer-term mean.
Exhibit 5 illustrates how the 20-year U.S. Treasury yield – a typical proxy for the risk-free rate in U.S. dollars– and its 10-year trailing (moving) average have evolved from December 2007 through March 2022.
During this period, the 20-year yield surpassed its 10-year moving average only twice: briefly in September
2018, and then again in March 2022.

16

17

Refer to the following research highlighting the shortcomings of using breakeven inflation as an indication of long-term inflation:
Bauer, Michael D., and Glenn D. Rudebusch (2015), “Optimal Policy and Market-Based Expectations”, FRBSF Economic Letter2015-12 (April 13); and Christensen, Jens H.E. and Jose A. Lopez (2016), “Differing Views on Long-Term Inflation Expectations”,
FRBSF Economic Letter 2016-11 (April 4).
For an overview of this concept and a summary of academic literature addressing this issue, see for example Church, Jonathan,“Inflation expectations and inflation realities: a comparison of the Treasury Breakeven Inflation curve and the Consumer Price
Index before, during, and after the Great Recession”, BLS Monthly Labor Review, December 2019, available here:
https://www.bls.gov/opub/mlr/2019/article/pdf/inflation-expectations-and-inflation-realities.pdf. Or review a more formal
research paper by the same author: “Market-Based Inflation Expectations and Inflation Realities: A Comparison of the Treasury
Breakeven Inflation (TBI) Rate Curve and the Consumer Price Index before, during, and after the Great Recession”, BLS Working
Paper 511, February 2019, available here: https://www.bls.gov/osmr/research-papers/2019/pdf/ec190010.pdf.
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Exhibit 5: Spot and 10-Year Moving Average of Yields on U.S. 20-Year U.S. Government Bonds
December 31, 2007 – March 31, 2022
2008
Financial
CrisisCOVID-19
Recession

6.0%

5.0%

10-year moving average

4.0%

March 31, 2022
2.6%

3.0%

2.0%

2.5%

December 31, 2008
3.1%

1.0%

0.0%

March 25, 2020
1.2%
(Kroll increases U.S. ERP
from 5.0% to 6.0% )December 09, 2020
1.5%
(Kroll decreases U.S. ERP
from 6.0% to 5.5%)

Source of underlying data: Capital IQ, NBER.

The late 2018 and the current environment share some common traits. Back in September 2018, the factthat the spot yield rose above its 10-year moving average was initially a sign that investors expected longterm interest rates to start moving upwards, closer to historical levels. As background, after a nearly 10year period with only one interest rate hike (December 2015), the Fed had finally embarked on a path ofmonetary policy normalization: between December 2016 and December 2018, the Fed raised the target
range for its benchmark short-term interest rate (the federal funds rate) eight times, to arrive at a target
range between 2.25% and 2.50%. 18 In addition, the Fed had begun unwinding its portfolio of U.S.
Treasuries, MBS, and agency debt. This gradual unwinding process, known as “quantitative tightening” (or“QT”) began in October 2017.19

18

19

The Fed kept a zero-interest-rate policy (dubbed “ZIRP” in the financial press) for seven years, from December 2008 until
December 2015. For a history on Fed interest rate rates, visit: https://www.federalreserve.gov/monetarypolicy/openmarket.htm.
For a timeline of the QT program, refer to Engemann, Kristie M, “What Is Quantitative Tightening?”, July 17, 2019, Open Vault
Blog, Federal Reserve Bank of St. Louis. Available here: https://www.stlouisfed.org/open-vault/2019/july/what-is-quantitativetightening.
10However, shortly after equity markets had peaked in September 2018, the 20-year yield started to decline
again, ending the year at 2.9% – below its 10-year moving average (at the time) of approximately 3.1%.
With the Fed’s rise of its benchmark policy rate and consequent upward pressure on short term rates, thespread between short and long-term rates started to compress. This flattening of the yield curve stoked
renewed fears that it could potentially be a signal or precursor to a U.S. recession. Equity markets reacted
badly, and the S&P 500 index ended 2018 with a negative 6.2% price return. The Fed reversed course on
its path to normalization and later in 2019 decreased its benchmark policy rate three times. In addition, theFed halted the QT of its balance sheet in August 2019, earlier than previously announced. When the Fed
began implementing its QT run-off, the total assets on its balance sheet were around $4.5 trillion in size(see Exhibit 1). Between October of 2017 and August 2019, the Fed only managed to decrease its balance
sheet to $3.8 trillion, before it ended its QT program.
For the second time since the 2008 Global Financial Crisis, the Fed is embarking in the process ofnormalizing its monetary policy by raising its benchmark policy rate and by reducing the size of its balance
sheet, which stood at nearly $9.0 trillion at the end of March 2022. The significant difference from 2018 is
the impact that the 40-year high inflation levels will have on the pace and path of normalization. For the
12 months ending December 2018, CPI inflation was 1.9% compared to 7.9% in February 2022, which
gives the Fed a lot less room to maneuver.
Inflation has continued to surprise on the upside, which has led to a significant shift in monetary policy
stance since December 2021. In early 2022, some Fed officials began speaking publicly about the need tobe more aggressive in normalizing the interest rate policy, in response to unexpectedly high inflation
readings. On January 12, 2022, James Bullard, President of the Federal Reserve Bank of St. Louis, indicatedin an interview that a more hawkish path for monetary policy wasneeded relative to his recent expectations, meaning that more interest
Inflation has
rates were needed and faster than previously projected. 20 At the end
continued to surpriseof its January 25–26 meeting, the Federal Open Market Committee(FOMC) stated that a rate hike in March was likely (with more wereon the upside, which
expected to come) and announced the end of QE expansion of its
has led to a significant
balance sheet (due to high inflation). 21 Since then, other Fed officials
shift in monetary
have followed suit with progressively more hawkish statements. For
policy stance since
perspective, Exhibit 6 shows (i) the median personal consumer
December 2021.
expenditures (PCE) inflation projected for 2022, (ii) projected numberof rises for the federal funds rate in 2022, and (iii) Fed balance sheet
policy, as provided at the FOMC meetings of December 2021 and March 2022. As of December 2021,
FOMC members generally expected four 0.25% rate rises in 2022 and that the target federal funds ratewould reach 0.9% by the end of 2022. By March 2022 FOMC members had significantly changed their

20

21

Derby, Michael, “Fed's Bullard: Four Interest Rate Rises in 2022 Now Appear Likely”, January 12, 2022, The Wall Street
Journal. Accessible here: https://www.wsj.com/articles/fed-s-bullard-four-interest-rate-rises-in-2022-now-appear-likely11642017785.
The Fed has the responsibility for setting monetary policy in the United States. To do so, the Fed controls the three tools ofmonetary policy: open market operations, the discount rate, and reserve requirements. The Board of Governors of the Federal
Reserve System is responsible for setting the discount rate and reserve requirements, while the FOMC is the committee charged
under U.S. law with overseeing the nation’s open market operations (i.e., the Fed's buying and selling of U.S. Treasury securities).
To learn more about the FOMC, visit: https://www.federalreserve.gov/monetarypolicy/fomc.htm.
11

outlook, and generally expected eight 0.25% rate rises in 2022, with the year-end 2020 target federal
funds rate reaching 1.9%, a full 100 basis points (b.p.) above the median expectations just three months
earlier.
Exhibit 6: FOMC Projected 2022 PCE Inflation, Projected Number of Federal Funds Rate Hikes in 2022,
and Balance Sheet Impact of QE vs QT Announcements
December 2021 vs. March 2022 Meeting
Projected
2022 PCE
Inflation(Median)Number of
0.25%
Rate Rises in
2022 (Median) *December 14-15, 202122

2.6%

4

Quantitative Easing 23•
Monthly purchases to decelerate beginning inJanuary 2022 to:o U.S. Treasury securities = $40 billiono Agency debt / MBS = $20 billion•
Increases in the Fed’s balance sheet holdings likely
to cease by mid-March, a few months sooner than
had been anticipated at the previous FOMC
meeting

March 15-16, 202224

4.3%

8

Quantitative Tightening 25•
Fed will begin reducing holdings of U.S. Treasury
securities and agency debt / MBS, at a pace to beannounced in a coming meeting.
•
FOMC meeting participants agreed that a more
rapid pace of balance sheet runoff is appropriate
relative to the QT program implemented in 2017–2019.

FOMC Meeting

QE/QT Announcements –Balance Sheet Impact* Number of rate rises could be smaller, should the Fed decide to increase rates by larger increments at each meeting (e.g., 0.50%).

While there have been several economists and analysts predicting that the Fed’s current accelerated plansto raise rates will lead to a recession (or to a period of ‘stagflation’, where the economy experiencessluggish or no growth, accompanied by high inflation), the central bank seems to have little choice if it
wants to bring inflation under control.

22

23

24

25

Source: “Summary of Economic Projections”, December 15, 2022, released as part of the December 14-15, 2022 FOMC
meeting. Economic projections are based on individual assumptions provided by Fed members and Federal Reserve Bank
presidents.
“Minutes of the Federal Open Market Committee”, December 14-15, 2021. Available here:
https://www.federalreserve.gov/monetarypolicy/fomcminutes20211215.htm.
Source: “Summary of Economic Projections”, March 16, 2022, released as part of the March 15-16, 2022 FOMC meeting.
Economic projections are based on individual assumptions provided by Fed members and Federal Reserve Bank presidents.
Available here: https://www.federalreserve.gov/monetarypolicy/files/fomcprojtabl20220316.pdf.
“Minutes of the Federal Open Market Committee”, March 15-16, 2022. Available here:
https://www.federalreserve.gov/monetarypolicy/fomcminutes20220316.htm.
12Economists and professional forecasters have revised their expectations for long-term yields accordingly.
Exhibit 7 displays how year-end consensus expectations for the 10-year U.S. Treasury yield have shiftedfrom pre-COVID (in December 2019, shown by the dark blue line), through the height of the pandemic
when we lowered our U.S. normalized risk-free rate (in June 2020, shown by the magenta line), until March2022 (in the green line). In March 2022, the average expectations for the 10-year Treasury yield reached3.1% in 2027. Historically, the 20-year U.S Treasury yield has (on average) exceeded the 10-year yield.
Economists call this difference a term premium. Based on the latest consensus forecasts in Exhibit 7, thiswould imply that by 2027 the 20-year would be expected to exceed 3.1%.
Exhibit 7: Comparison of (Average) Projected 10-Year U.S. Government Bond Yields
December 2019, June 2020, and March 2022

3.5%

3.1%

3.0%
2.5%
2.0%

December 31, 2019

1.5%
June 30, 2020

1.0%
March 25, 2022

0.5%
0.0%
2020

2021

2022

2023

2024

2025

2026

2027

Sources of Underlying Data: Blue Chip Economic Indicators, Blue Chip Financial Forecasters, Consensus Economics, Livingston
Survey, and Survey of Professional Forecasters.

If we use a long-term moving average for the yield on 20-year U.S. Treasury bonds to estimate thenormalized risk-free rate as of March 31, 2022, the trailing (or moving) 10-year average was 2.5% (seeExhibit 5). In contrast, the corresponding spot yield on March 31, 2022 was 2.6%. However, based on thedevelopments described above, this method likely underestimates the future 20-year yield. Taking the
average over the last 10 years is a simple way of “normalizing” the risk-free rate. An issue with using
historical averages, though, is selecting an appropriate comparison period that can be used as a reasonableproxy for the future.
The second method of estimating a normalized risk-free rate entails using a simple build-up method,where the components of the risk-free rate are estimated and then added together. Conceptually, the riskfree rate (in nominal terms) can be (loosely) illustrated as the return on the following two components:

Risk-Free Rate = Real Rate + Expected Inflation

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Academic researchers and economic analysts have proposed a number of explanations for the secular (i.e.,
not cyclical or temporary) decline in global real interest rates, which they argue precedes the onset of the2008 Global Financial Crisis. The following are some of the most-often-cited factors:••••

Lower global long-run output and productivity growth
Shifting demographics (aging population leading to slower labor force expansion)
Global “savings glut”
Safe asset shortage (increased demand for safe-haven assets, accompanied by a declining supply)

More recently, some economists and analysts have posited that the post-pandemic recovery may havereversed some of these trends, at least temporarily (e.g., there is less support for a global savings glut
explanation). Whether this will have an ultimate impact on reversing the downward trends in real rates
remains to be seen.
In Exhibit 8, we display the spot 20-year U.S. Treasury yield and its long-term (10-year) trailing averageas of March 31, 2022. We also summarize long-term real rate estimates and inflation expectations for theUnited States at the end of March 2022, based on data assembled from a variety of sources. Both methods
were used to arrive at our concluded normalized U.S. risk-free rate as of March 31, 2022.
Exhibit 8: Long-Term, Spot and Normalized Risk-Free Rates for the United States as of March 31, 2022
Method 1: Long-Term Average
20-Year U.S. Government Securities: 26- Spot Rate
- Long-Term (10-year) Trailing Average Yield

2.6%
2.5%

Method 2: Fisher Equation

Range

Median

-1.1% to 2.0%

0.6%

1.9% to 3.0%

2.5%

0.9% to 5.0%

NMF

2.9%

3.1%

Estimated Long-term Real Risk-Free Rate
Expected Long-term Inflation

28

Range of Estimates
Midpoint
Concluded Normalized Risk-free Rate

26
27
28

27

3.0%

Source of underlying data: Capital IQ.
For a list of the academic paper references used to arrive at the real rate estimates, please click here.
Source of underlying data: Blue Chip Economic Indicators (March 10, 2022); Blue Chip Financial Forecasts (March 1, 2022 andDecember 1, 2021); "Consensus Forecasts – Surveys of International Economic Forecasts", Consensus Economics (Survey
Dates: October 11, 2021 and March 14, 2022); “Comparative World Overview Tables”, IHS Markit (March 15, 2022); “The
Livingston Survey”, Federal Reserve Bank of Philadelphia (December 17, 2022); “Country Economic Forecast – United States”,
Oxford Economics (March 9, 2022); “Survey of Professional Forecasters – First Quarter 2022”, Federal Reserve Bank ofPhiladelphia (February 11, 2022), Federal Reserve Bank of Cleveland (March 2022); “Aruoba Term Structure of Inflation
Expectations”, Federal Reserve Bank of Philadelphia (March 2022); the University of Michigan Inflation Expectations (March
2022).
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The U.S. long-term inflation expectations (using Method 2) represent a higher range relative to prior Kroll
analyses. In particular, the median long-term inflation expectation is now a full 50 b.p. higher at 2.5%
compared to the median of 2.0% estimated back in June 2020 when we lowered our U.S. normalized riskfree rate. Based on recent market evidence of a higher long-term inflation expectations for the U.S.,
we increased our concluded U.S. normalized risk-free rate from 2.5% to 3.0% for valuation dates as ofApril 7, 2022 and thereafter, until further guidance is issued. This rate is to be used with a Recommended
U.S. ERP of 5.5%, implying a base U.S. cost of equity capital of 8.5% (= 3.0% + 5.5%). However, given
how fast U.S. inflation expectations are rising, the current guidance could be changed again in the near
future.
We performed a similar analysis (Methods 1 and 2) to arrive at normalized risk-free rates as of March 31,
2022 for Canada, Germany and the U.K., but long-term expected inflation for these countries has not
moved upwards sufficiently to support an increase in their respective normalized risk-free rates at thistime. As result, we have reaffirmed the normalized risk-free rates for Germany at 1.5%, and for the U.K.
and Canada at 2.5% as of April 7, 2022 and thereafter, until further guidance is issued. However, longerterm impacts of the Russia-Ukraine war and the continued global supply bottlenecks and labor shortages
on prices may cause long-term inflation projections for these countries to increase. At that point, which
could be in the near future, we would revise our normalized risk-free rate for these countries. We willclosely monitor developments in this area.

Conclusion
There are several risk factors and sources of uncertainty that may impact the shape of the global economic
recovery and the pattern of behavior by financial markets over the next few months:
•
•
•
•
•
•
•

Geopolitical risks
Resurgence of COVID-19 cases
Inflationary pressures
Global supply chain disruptions
Labor shortages
Rising interest rates
Unwinding of fiscal stimulus to deal with government deficits created by COVID-19

Based on market conditions prevailing at the end of March 2022, we found sufficient support for an
increase of the U.S. normalized risk-free rate from 2.5% to 3.0%, when developing USD-denominateddiscount rates as of April 7, 2022 and thereafter, until further guidance is issued. This rate is to be usedwith a reaffirmed Kroll Recommended U.S. ERP of 5.5%, implying a base U.S. cost of equity capital of
8.5% (= 3.0% + 5.5%). However, given how fast U.S. inflation expectations are rising and how financial
markets are behaving, the current guidance could be changed again in the near future.

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Authors

Contributors

Carla S. Nunes, CFA

Anas Aboulamer, Ph.D.

Managing Director

Director+1 215 430 6149

+1 416 361 2572

Carla.Nunes@kroll.com

Anas.Aboulamer@kroll.com

Jim Harrington

Kevin Latz

Director

Senior Associate+1 312 697 4938

+1 312 980 9515

James.Harrington@kroll.com

Kevin.Latz@kroll.com
Molly Jennerman
Senior Associate+1 414 225 1030
Molly.Jennerman@kroll.com
Kevin Madden
Director+1 312 697 4964
Kevin.Madden@kroll.com

About Kroll
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