Measuring the implied market risk premium (iMRP) in times of crisis and volatile equity markets


published on 20 February 2024 | reading time approx. 4 minutes

The market risk premium is one of the inputs to the Capital Asset Pricing Model (CAPM) used to determine the cost of equity. It represents the return that an investor expects to receive for assuming risk in addition to the return on a risk-free investment. The market risk premium can be derived from empirical market returns (as the historical market risk premium) or on a forward-looking basis as the implied market risk premium (iMRP). Both approaches are not without their problems. In times of crisis, equity markets regularly experience high volatility. This affects the calculation of the implied market risk premium.

From the Historical Market Risk Premium to a variety of methods

Until 2012, the analysis of historical market returns was the predominant approach for determining the market risk premium, as recommended by the IDW's Expert Committee for Business Valuation and Economics (FAUB). In Germany, this was based in particular on publications by Prof. Dr. Stehle of the Humboldt University in Berlin, who examined market returns from 1955 onwards. The method of calculating the historical market risk premium has been and continues to be the subject of theoretical debate. In particular, the following assump­tions are worthy of discussion and have a significant impact on the results of the study:

  • What stock market is being analysed?
  • What historical period is analysed?
  • How is the average return measured (arithmetic or geometric)?
  • How is the risk-free rate of return measured?
  • Should a discount for increased capital market efficiency be applied to historical returns?
  • Is the historical market risk premium time-varying (measured by the total market return approach) or time-stable (measured by the constant approach)?

However, the question of whether historical market risk premia can at all be used to estimate the future remains unanswered.

In the wake of the financial market crisis, FAUB raised the recommended range of the market risk premium in 2012. This was justified – only much later in 2019 – with a pluralistic approach that now includes both a his­to­ri­cal view and a forward-looking analysis. The forward-looking analysis is based on the implied market risk premium (iMRP).

Measurement of the implied market risk premium (iMRP)

The iMRP is based on average analyst estimates ("consensus estimates") of future earnings (net income) for publicly traded companies. Forecast periods of three years are generally used, as estimates beyond this time horizon generally do not provide sufficient coverage. Analysts' earnings forecasts (including payout ratios, where applicable) are used as the numerator in the valuation equation. The denominator of the valuation equation is filled with the cost of capital parameters of the base rate, beta factor, and growth discount. The base interest rate can be measured at the balance sheet date using the Svensson yield curve. The beta factor of the individual companies analysed can also be measured or is set to 1.0 as part of an overall market analysis. Appropriate assumptions are made regarding the inflation and growth discount. The valuation result is given and corresponds to the market capitalisation (equity value) on the valuation date.

The market risk premium remains in the valuation model as the last variable and thus as a residual variable. Solving the valuation equation for the market risk premium yields the implicit market risk premium, which, given all other input parameters, leads to the observable market capitalisation (equity value) at the valuation date. In practice, this is done iteratively in Microsoft Excel.

In practice, various models are used to determine the iMRP, which differ in particular in their approach to the valuation-relevant inflow (numerator). These include the dividend discount model, the residual profit model and the income capitalisation model. Rödl & Partner uses the following capitalized earnings value model in accor­dance with IDW S 1 to determine the implicit market risk premium. The capitalized earnings value method and the discounted cash flow method produce identical results under the same assumptions.

Formula: Valuation model for determining the implicit market risk premium before personal taxes

Pros and cons of the implicit market risk premium

The expected (future) cost of capital is determined using the CAPM. In the case of the historical market risk premium, it is assumed that returns measured over long historical periods are a reasonable estimate for the future. The iMRP, on the other hand, is an expected (i.e., forward-looking) market risk premium in the sense of the CAPM. From a model theory perspective, it is therefore preferable to the historical market risk premium.

However, the data basis for determining the iMRP is not unproblematic. While the historical market risk premium is based on actually realised – and thus objectively "existing" – market returns, the iMRP is based on subjective analyst estimates. Various studies have shown that, on average, analysts' forecasts are overly optimistic, especially for the second and third forecast years. This leads to distorted and generally too high implicit market risk premia.

Critics of iMRP also argue that different valuation models (e.g., capitalised earnings method, dividend discount model, cash flow method) produce different results.

Measuring the implicit market risk premium in times of crisis

In times of crisis, equity markets regularly experience high volatility. This has a significant impact on the measure­ment of the implicit market risk premium. Examples include the outbreak of the coronavirus pandemic in March 2020 and the outbreak of the Ukraine conflict in February 2022, both of which led to significant short-term declines in stock prices and thus market capitalisation.

However, analysts react to new macroeconomic conditions with a certain time lag and adjust their expectations downwards with a corresponding time lag. As a result, falling market capitalisations (valuation outcome) initially lead to rising implicit market risk premia (the denominator of the valuation formula) because of the lag in analyst estimates (the numerator of the valuation formula).

The iMRP after the outbreak of the Ukraine conflict

To illustrate the effect described above, we examined the implied market risk premia for various equity markets after the outbreak of the Ukraine conflict and how they have behaved since then through December 2023. To this end, we calculated the implied market risk premia for the DAX (local stock index), the S&P EUROPE 350 (European stock index) and the S&P Global 1200 (global stock index).

It can be seen that the implied market risk premiums are significantly higher between March 2022 and December 2022, and since October 22, 2019 have been almost consistently above the MRP range of 6.0 per cent to 8.0 per cent before personal taxes recommended by FAUB for use in company valuations. Only in calendar year 2023, after the equity markets had calmed down and analysts had adjusted their expectations, did the implied market risk premiums return to the MRP range recommended by FAUB. Accordingly, in a technical note dated March 20, 2022, FAUB stated that capital market data should be assessed on a long-term basis. Short-term fluctuations and possible exaggerations on the capital markets are to be classified as momen­tary and not necessarily long-term sentiment indicators. The increased uncertainty caused by the war in Ukraine must be taken into account in planning and should not be reflected in a general increase in risk premiums.

Chart: Implied Market Risk Premiums from March 2022 to December 2023

Source: iMRP Rödl & Partner


FAUB justifies its recommendation on the range of market risk premiums to be used for company valuations with a pluralistic approach. In addition to a historical view, it also provides for a forward-looking analysis. The latter is done by determining the implied market risk premium (iMRP) based on analyst estimates.

The iMRP is theoretically preferable due to its forward-looking nature but is susceptible to distortions in volatile equity markets and times of crisis. Analysts' estimates are regularly adjusted to changing macro­eco­nomic conditions with a certain time lag. This can lead to distorted results when measuring the implied market risk premium.

Therefore, implied market risk premia measured in times of crisis and volatile equity markets should not be used uncritically, but should be subjected to critical evaluation, if necessary by looking at longer time series.

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