Markets versus textbooks: Calculating today’s cost of equity

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So much for “transitory.” It turns out that inflation ran on the express tracks after all, and interest rates, though historically still low, were sharply ramped up. What does that mean for the cost of equity? The textbook answer would have it that higher interest rates translate seamlessly to a higher cost of equity. Declining stock returns throughout 2022 seem to bolster the case. Hearken back to your introductory course on finance, and it all looks fairly straightforward: start with ten-year government bond yields as the risk-free rate, and add a market premium. The market uses ten-year Treasuries as its risk-free proxy—right?

Actually, no. Our research shows that during approximately the past 15 years, the cost of equity has been decoupled from government bond rates; monetary policy has manipulated long-term rates to such an extent that Treasury yields no longer reflect what the market actually applies. By our analysis, even as central banks significantly ratcheted up rates in 2022, the cost of equity increased, but modestly, reflecting only slightly higher expectations of long-term inflation. Perhaps that’s because the cost of equity over the past 15 years did not decline to reflect the low cost of government debt.

Present, past, and future: The trouble with a textbook approach

No one knows for sure what the actual duration and magnitude of inflation will be. Multiple forces are at work, including (1) supply and demand disruptions due to the COVID-19 pandemic and the Ukraine war; (2) the reluctance of many people to return to the workforce1Gone for now, or gone for good? How to play the new talent game and win back workers,” McKinsey Quarterly, March 9, 2022.; (3) a prolonged period of aggressive fiscal spending, particularly in response to the pandemic, that has contributed to unprecedented peacetime government deficits; and (4) extraordinarily expansive monetary policies since the Great Recession of 2007–08 that have resulted in historically low interest rates. Moving forward, it’s unclear what additional steps governments will take to address inflation. Lack of clarity invites greater uncertainty.

It’s important to keep in mind that expected real interest rates on ten-year US government bonds are about 1 percent,2 which is still very low by historical standards, and that investors currently expect long-term inflation to be modest, at about 2.5 percent.3 By comparison, expectations about long-term inflation reached and exceeded 10 percent in the 1970s and early 1980s.4

You may have heard that rapidly rising interest rates over 2022 have significantly increased the cost of equity. Starting with a historical market-risk premium of about 5 percent, and using a beta of 1, the argument ultimately boils down to the effect of higher Treasury yields. If those yields really were a proxy for the risk-free rate, the cost of equity would change a lot, in line with the pronouncements of the Federal Reserve and other central banks.5The real cost of equity,” McKinsey on Finance, October 1, 2002.

A textbook analysis maintains that lower interest rates during the COVID-19 pandemic were largely responsible for higher TSR in 2020–21, and that higher interest rates over the course of 2022 from a more hawkish Fed drove down TSR during that year. But that approach considers only one period, in isolation. And facts don’t support the often-quoted assertion that rates were lower at the end of 2021 than 2019. While interest rates declined in 2020 as the Fed took aggressive monetary-easing actions, interest rates were back at their starting levels by the end of 2021—before the stock market began to turn down: the yield on ten-year Treasury bonds was 1.8 percent at the end of 2019 and returned to 1.8 percent at the end of 2021. The S&P 500 index during that period increased from 3,240 to 4,766, up 47 percent. From the end of 2021 until October 2022, the yield on ten-year Treasuries increased from 1.8 percent to 4.1 percent, while the stock market declined by 18 percent. It doesn’t seem logical to attribute the decline in the stock market during 2022 to the increase in interest rates; other factors must have been driving up the market from 2019 to 2021, because interest rates at the beginning and end of the period were flat.

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It turns out that while textbook answers may be fine for classrooms, classrooms are not real life. Consider price-to-earnings (P/E) ratios. In practice, the cost of equity is a major driver of P/Es; if the cost of equity really varies significantly, we would expect P/E ratios to move substantially as well. Yet over the course of about 15 years, as government yields were reduced to unprecedented lows and then increased to much higher levels, median P/E ratios have remained remarkably constant—and firmly within historical bounds.

The consistency of median P/E ratios is yet another indication that markets no longer apply government bond yields as a proxy for the risk-free rate. Valuing a company by using a 6.6 percent cost of equity implies that even modestly growing companies would have P/E multiples of 25-fold or higher. Mathematically, every 1 percent decrease in the cost of equity for the S&P 500 index should increase the P/E of the index by roughly 20 to 25 percent. Given the low interest rates over the past 15 years, the typical large company should have traded in the well-above 20-fold P/E range since the Great Recession. But that hasn’t been the case. Median large companies have consistently traded in the 15-fold to 17-fold P/E range since the financial crisis—despite low interest rates during the entire period.

An evidence-based approach to the cost of equity

One helpful way to explore further is to infer an actual cost of equity from market valuations. We conducted an analysis to reverse engineer P/E multiples, applying time-tested assumptions about profit growth and ROIC, and derived a narrow band of costs of equity that markets have been applying for years. Under this approach, we observe that the real cost of equity has remained stable over the past six decades—in the 6.5–7.0 percent range. The only meaningful changes in expected returns over time have been on a nominal basis (Exhibit 1).

The only meaningful changes in expected returns over time have been on a nominal basis.

The results of this analysis are consistent with a long-term view of median P/Es of large companies, which has also been stable—in the 15-fold to 17-fold range—for decades (Exhibit 2).

Median P/E ratios are remarkably consistent.

Facts being stubborn things, it’s fair to dig more deeply into 2022 market dynamics. If the cost of equity didn’t rise in lockstep with interest rates and therefore push stock prices down, what actually was the reason for lower returns? While a portion of the decline has been due to economic concerns, the largest contributor, by our analysis, has been the reversal of massive valuation increases that a handful of companies (mostly in the technology sector) enjoyed in 2020 and 2021. We draw this conclusion by examining the gap between the “official” P/E ratio of large stocks (a weighted average that was heavily weighted by the Big Tech companies in 2020 and 2021) and the P/E of the median company. Large, outperforming companies carried so much weight in the index and had such high multiples that the weighted average P/E rose significantly in 2020 and 2021. Yet throughout 2020 to 2022, the median P/E multiple remained constant. More recently, we’ve seen that the weighted average P/E is reverting to the median.

Today’s cost of equity

To estimate the current cost of equity, we convert the real expected return into a nominal return, by adding an estimate of inflation that is consistent with reasonable cash flow projections. This can be done by using the spread between the yield on inflation-protected bonds (TIPS) and standard, non-inflation-protected government bonds. As of today, this approach brings the nominal cost of equity to approximately 9.5 percent (7.0 percent real return plus 2.5 percent expected inflation, based on the TIPS spread). That’s only about 0.2 percent higher than at the start of 2022.

This approach has proved effective throughout the period of low interest rates that started with the Great Recession. Valuation models based on low interest rates over the past 15 years, on the other hand, have not led to sensible results. If the cost of equity had truly declined along with falling interest rates in the past decade and a half, we should have seen a dramatic increase in P/E multiples. For example, a 3 percent drop in the cost of equity should have increased the P/E ratio from a typical trading range of 15–16 times to over 25 times. However, no such increase occurred. As government-pronounced rates declined from 4–5 percent in 2006 to 1–2 percent in 2012, P/E ratios remained within their consistent band.

We can also triangulate this approach by using a synthetic estimate for the risk-free rate rather than government bond yields. To build a synthetic risk-free rate, add the expected inflation rate (about 2.5 percent) to a long-term average real interest rate (2 percent); this results in a synthetic risk-free rate of about 4.5 percent. Adding a 5 percent market-risk premium leads to an expected market return of approximately 9.5 percent, which is entirely consistent with an expected cash-flow-based approach.

Calculating today’s cost of equity is not a rote exercise, and the most fundamental assumption of all—that markets use government bond yields as a proxy for the risk-free rate—does not withstand closer scrutiny. But then, why should it? Complicated challenges are seldom settled by fiat.

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