Definition of the market risk premium

The „market risk premium“ is the difference between the expected return on the risky market portfolio and the risk-free interest rate. It is an essential part of the CAPM where it characterizes the relationship between the beta factor of a risky assets and ist expected return. Thus, the market risk premium is of major importance for company valuation and for asset allocation decisions.

Formally, the market risk premium is defined as

(1) ,

where represents the return on a risky but diversified market portfolio and represents the risk-free return. The market portfolio is usually represented by a country-wide share price index (e.g., S&P 500 for the U.S.), a worldwide share price index (such as the MSCI World or Dow Jones Global) or an even broader portfolio (e.g., including commodities and corporate bonds). The second term, the risk-free interest rate, should have the same/a similar duration, currency, and liquidity as the market portfolio.

Magnitude of the market risk premium

The market risk premium should be positive under the assumption that investors are risk averse. As to the specific magnitude and its volatility over time, several key results emerge from the academic literature:

  • The market risk premium is usually assumed to be between 3-7%, with most studies measuring the market risk premium separately for each country (see for example Dimson/Marsh/Staunton (2003)).
  • The market risk premium is not constant, but rather varies over time. In times of crises and times of high volatility, the market risk premium tends to be higher and in boom and times of low volatility, the market risk premium tends to be lower. (see for example Shiller (1981), Poterba/Summers (1988), Cochrane (2005)).
  • The market risk premium exhibits, similar to the risk-free rate, a term structure form. In times of low volatility, the term structure of the market risk premium is usually upward sloping whereas it is usually downward sloping in a volatile market environment (van Binsbergen/Brandt/Koijen (2012), Berg (2012)).

There does not exist an exact method to measure the market risk premium and different methodologies can lead to significantly different estimates. Furthermore, there is not yet an agreement in the academic literature as to whether changes in the market risk premium over time constitute an inefficiency of capital markets or whether these changes over time can be fully explained by rational factors.

Empirical measurement of the market risk premium

There are two main methodologies for determining the market risk premium

  • Historical averages

This methodology averages historical returns from stocks and risk-free investments over a time horizon of several decades. While straightforward to apply, this methodology has two main drawbacks: first, it relies on the assumption that the market risk premium is constant over time. If the market risk premium varies over time, then an increase in the market risk premium would lead to lower returns and thus – falsely – to a lower estimate of the market risk premium (and vice versa). Second, the standard error of the market risk premium estimates is rather high. Even with an estimation period of 100 years and a volatility of the stock price index of 20%, the standard error is still equal to .

  • Implied methods

Implied methods invert the standard discounted cash-flow valuation formlas. In the simplest case, the value of a stock can be determined based on next-years dividend , the dividend growth rate and the cost of capital via

(2) .

Therefore, the implied cost of capital can be determined as the sum of dividend yield and dividend growth

(3)

and the market risk premium can be determined accordingly as

(4) .

This methodology requires the existence of i) dividend and growth forecasts and ii) today’s value of the stock / market portfolio. Implied cost of capital methodologies usually rely on more sophisticated valuation formula than the one presented above. Popular methods include multi-period dividend discount models and residual income models (Malkiel (1979), Claus/Thomas (2001), Easton (2004)).

Bereiche, in denen die Marktrisikoprämie von Bedeutung ist

  • Unternehmensbewertung

Der Wert eines Unternehmens bestimmt sich unter der Voraussetzung ausschließlich finanzieller Ziele über den Barwert der mit dem Eigentum an dem Unternehmen verbundenen Nettozuflüsse an die Unternehmenseigner. Zur Ermittlung dieses Barwerts wird ein Kapitalisierungszinssatz verwendet, der die Rendite aus einer zur Investition in das zu bewertende Unternehmen adäquaten Alternativanlage repräsentiert (vgl. [[IDW]] Standard: Grundsätze zur Durchführung von Unternehmensbewertungen (IDW S 1) i.d.F. 2008 Tz. 4). Im Rahmen von Unternehmensbewertungen hat sich eine marktgestützte Ermittlung der Alternativrendite auf Basis des [[CAPM]] oder des Tax-Capital Asset Pricing Model (Tax-CAPM) etabliert.

Die Alternativrendite kann dabei als gewichtetes Mittel aus Eigen- und Fremdkapitalkosten, wobei diese jeweils im Rahmen des CAPM bestimmt werden können über

(5) .

  • Asset allocation

In der Asset Allocation ist die Marktrisikoprämie für die Entscheidung relevant, welcher Anteil des Vermögens in risikofreie Anlagen und welcher Anteil in risikoreiche Anlagen investiert werden sollte. Eine Marktrisikoprämie von Null bedeutete hierbei, dass risikoreiche Anlagen im Erwartungswert die gleiche Rendite aufweisen wie risikofreie Anlagen. Risikoaverse Anleger würden bei einer Marktrisikoprämie von Null ihr gesamtes Vermögen risikofrei anlegen, je höhere die Marktrisikoprämie ist, desto höher auch der Anteil, den Anleger bereit sind, in risikoreiche Anlagen zu investieren. Umgekehrt entsteht durch Angebot und Nachfrage in einem Kapitalmarkt, in dem der durchschnittliche Marktakteur risikoavers ist, automatisch eine positive Marktrisikoprämie.

Literature:

  • Berg, T., 2010, The Term Structure of Risk Premia: New Evidence from the Financial Crisis, ECB Working Pape No. 1165.
  • Binsbergen, J.H., Brandt, M.W. and R.S.J. Koijen, 2012, On the timing and pricing of dividends, American Economic Review, 102(4), 1596-1618.
  • Claus, J. and Thomas, J., 2001, Equity premia as low as three percent? Evidence from analysts’ earnings forecasts for domestic and international stock markets, Journal of Finance, 56(5), 1629-1666. Cochrane, J., 2005, Explaining the Variance of Price-Dividend ratios, Review of Financial Studies, 5, 243-280.
  • Dimson, E., Marsh, P. und M. Staunton, 2003, Global Evidence on the Equity Risk Premium, Journal of Applied Corporate Finance, 15, 27-38.
  • Easton, P., 2004, PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital, The Accounting Review, 79, 73-95.
  • IDW Standard: Grundsätze zur Durchführung von Unternehmensbewertungen (IDW S 1) i.d.F. 2008.
  • Malkiel, B.G., 1979, The capital formation problem in the United States, Journal of Finance, 34, 291-306.
  • Poterba, J.M and L.H. Summers (1988), Mean reversion in stock prices, Journal of Financial Economics 22, 27-59.
  • Shiller, R.J., 1981, Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?, American Economic Review, 71(3), 421-436.
  • Stehle, R., 2004, Die Festlegung der Risikoprämie von Aktien im Rahmen der Schätzung des Wertes von börsennotierten Aktiengesellschaften, Die Wirtschaftsprüfung, 906-927.