How stretched are equity prices? Evidence from option-implied estimates of equity risk premia

Published on 14 January 2025

In 2024 Q4, as part of its assessment of developments in financial markets, the Financial Policy Committee (FPC) considered a new option-implied measure of the equity risk premium (ERP) alongside existing measures of risk premia. The new measure suggests that UK and euro-area equity risk premia remain low historically, in line with other ERP metrics. For the US market, the new ERP measure appears less compressed relative to existing measures, consistent with market expectations of strong earnings growth – especially in the US tech sector. US equity valuations therefore appear slightly less stretched by this metric, but this is predicated on strong future earnings growth actually materialising.

As part of its financial stability risk assessment, the FPC regularly considers risk premia across financial markets – the amount of expected compensation investors require above risk-free interest rates for being exposed to risky assets. When risk premia are compressed that implies investor risk appetite is high or that risks to future returns, including future earnings and macroeconomic conditions, are perceived to be low. As a result, we observe risky asset prices that are high relative to expected future earnings for a given interest rate environment.

In its latest Financial Stability Report (FSR), the Committee noted that risk premia across a number of markets continued to appear compressed by historical standards, including in equity markets, and continued to judge risk premia and valuations therefore remained vulnerable to a shift in risk appetite, particularly in the context of elevated global risks. US equity prices in particular have been rising strongly for an extended period, with market intelligence suggesting that higher US equity valuations have been driven in part by investor optimism over the potential impact of artificial intelligence (AI) and other technological developments on productivity and earnings. Having timely and accurate measures of risk premia is important in helping the FPC to form such judgements.

Following recent advances in the academic literature (see Martin (2017), Chabi-Yo and Loudis (2020)), Bank staff have introduced a new ERP metric that uses option prices to estimate statistics from option-implied future return distributions (the variance, skewness, and kurtosis) over a fixed time horizon (typically one year). Under no-arbitrage pricing conditions this approach provides an estimate of the ERP. This type of estimate has been shown to be an accurate predictor of realised excess returns, especially over shorter time frames (Martin (2017)).

Sources: CME, EUREX, ICE (LIFFE) and Bank calculations.
(a) The measure used follows the lower-bound ERP estimate of Chabi-Yo and Loudis (2020) over a one-year time horizon, and uses options on the FTSE 100, S&P 500, and EUROSTOXX 50 for the UK, US, and euro area respectively.

We observe that the UK and euro-area option-implied ERP measures are compressed relative to their historical levels, in-line with estimates of the excess CAPE^{^{footnote [1]}} yield, another metric used by the Bank to assess the extent to which risk premia appear compressed (Charts 1 and 2).^{^{footnote [2]}} However, under the option-implied measure, the level of the US ERP is slightly less compressed both relative to its historical levels, as well as relative to UK and euro-area markets.

The US option-implied ERP estimate is also noticeably less compressed than the excess CAPE yield on a historical percentiles’ basis (Chart 2). This is influenced by the historical distribution of the option-implied ERP, where we observe a small number of extremely large observations and a significant ‘bunching’ of observations around current levels, which results in a highly right-skewed distribution (see Chart 1). As such, large changes in historical percentile positions can be driven by relatively small changes in the ERP estimate, especially in the lower to middle part of the distribution.

Sources: Bloomberg Finance L.P., CME, EUREX, ICE (LIFFE) and Bank calculations.
(a) The whiskers reflect the minimum and maximum value of the ERP estimates between the June 2024 FSR and the November 2024 FSR.
(b) Note that the option-implied measure uses different equity indices than the CAPE for the UK (FTSE 100) and euro area (Eurostoxx 50) for liquidity and data availability reasons. The Excess CAPE yield uses the FTSE all share and Stoxx Europe 600 in line with previous FPC communications. Both measures use data from the S&P 500 (US), and any percentile changes due to the use of different indices are minimal.
(c) Daily data updated to 14 November 2024.
(d) Data shown as a percentile of five-day rolling average since May 2006.

What explains the difference between the option-implied and CAPE yield measures of ERP?

The key difference between the option-implied and excess CAPE yield ERP models is in the way future expected earnings are reflected. Whereas the excess CAPE yield measure compares current equity prices to inflation-adjusted past earnings as a proxy for future earnings, in forward-looking option-implied metrics, future expected earnings will be reflected implicitly in the market prices of equity options.^{footnote [3]} Furthermore, option-implied statistics are inherently volatile, whereas the excess CAPE is a cyclically adjusted measure that smooths out temporary spikes.

If current market expectations of future earnings exceed past average earnings, for example due to technological innovations such as AI, this may lead to a divergence between the two ERP estimates, and could explain the difference for US equity ERP estimates seen in Chart 2. This is more likely to be the case in high-growth sectors such as information technology, which account for a much larger share of US equity market capitalisation, when compared to euro-area and UK equity markets.

As discussed above, US ERP measured using forward-looking option-implied metrics look closer to historical averages than when measured by the excess CAPE yield – in turn implying that valuations look less stretched by historical standards once the market expectations of future growth in US equities are taken into account. But this conclusion depends crucially on whether these market expectations of future growth are justified and not overly optimistic. And market expectations could change quickly, for example in response to the crystallisation of global risks.

This post was prepared with the help of Alex Kontoghiorghes, Sofia Carollo, Pietro Sparago and Jakob Schedlbauer.

This analysis was presented to the Financial Policy Committee in 2024 Q4.

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Cyclically adjusted price-to-earnings ratio.
CAPE-based metrics have been shown to be good forecaster of longer-term excess returns in equity markets, such as over a 10-year horizon (Shiller, Black and Jivraj (2020)).
The assumption that options pricing adequately reflects market expectations of future returns in equity markets underlies the use of option-implied ERP estimates. While the option markets for the equity indices are typically highly liquid, investor segmentation between option and equity index markets or pricing frictions specific to derivative markets are a possibility. If such irregularities were to exist and occur consistently, this could lead to a persistently biased option-implied ERP estimate.