Market risk premium

The market risk premium is the difference between the expected return on a risky market portfolio and the risk-free interest rate . In the capital goods price model (CAPM), it is an essential component and, in conjunction with the beta factor, explains the expected return of a risky investment opportunity. It thus plays a central role in company valuation and in investment decisions ( asset allocation ).

Definition of the market risk premium

The market risk premium is formally defined as

{\ displaystyle MRP = E (r_ {M}) - r_ {f}}

where represents the return of a risky but broadly diversified market portfolio and the risk-free return. For the risky, broadly diversified market portfolio, common stock indices of a country (e.g. the DAX or CDAX in Germany ), a stock index with stocks from all over the world (e.g. MSCI World or Dow Jones Global Titans ) or even broader ones are used Portfolios (e.g. including commodities and bonds) in question. The second term, the risk-free interest rate, should be determined in the same currency, with the same or similar term and under comparable liquidity aspects as the market portfolio. (To determine the risk-free interest rate, see the base interest rate curve ). ${\ displaystyle \ textstyle r_ {M}}$ ${\ displaystyle \ textstyle r_ {f}}$

Amount of the market risk premium

The market risk premium is positive if one assumes risk-averse actors. There are various empirical studies on the amount and fluctuation over time. The following core results can be recorded:

The market risk premium is around 3–7%, with most studies measuring the market risk premium using national stock indices (see for Germany in particular Stehle and in an international comparison Dimson / Marsh / Staunton).
The market risk premium is not a constant variable, but fluctuates over time, i.e. H. with the degree of risk aversion of the market players. It tends to be higher in volatile times, after market crashes and recessions, and lower in times of low volatility, after sharp price increases and in boom times.
The market risk premium, like the risk-free interest rate, is time-dependent. In times of low volatility, it increases slightly with the term, while in volatile times the short-term market risk premium is significantly higher than the long-term premium.

There is no precise procedure for measuring the market risk premium; different methods sometimes lead to significantly different results. Furthermore, there is no consensus in the academic literature as to whether the volatility of the market risk premium represents an inefficiency of the markets or is fundamentally justified due to the greater uncertainty that prevails at certain times.

Empirical measurement of the market risk premium

In principle, there are two methods of measuring the market risk premium.

Historical mean values

In historical measurement, returns on stocks and risk-free investments are averaged over a time horizon of several decades. This method is relatively easy to use, but has two major disadvantages: On the one hand, it must be assumed that the market risk premium is constant. If the market risk premiums change over time, z. B. an increase in the market risk premium at lower prices and thus a lower historical market risk premium. On the other hand, the standard errors in the measurement are relatively high. For a period of 100 years and an average equity volatility of 20%, the result is e.g. B. still a standard error of . ${\ displaystyle \ textstyle {\ frac {20 \, \%} {\ sqrt {100}}} = 2 \, \%}$

Implicit procedures

Implicit procedures are based on an inversion of common evaluation procedures. In the simple case, the value of a share is derived from the dividend for the next year , the dividend growth rate and the cost of capital as ${\ displaystyle \ textstyle (D_ {1})}$ ${\ displaystyle \ textstyle (g)}$ ${\ displaystyle \ textstyle (k)}$

{\ displaystyle V = {\ frac {D_ {1}} {(kg)}}}

Thus, the implicit cost of capital can be determined as the sum of the dividend yield and dividend growth

{\ displaystyle k = {\ frac {D_ {1}} {V}} + g}

and correspondingly the market risk premium using the CAPM over

{\ displaystyle MRP = {\ frac {1} {\ beta}} \ cdot \ left ({\ frac {D} {V}} + g-r_ {f} \ right)}

.

Essential for this is the availability of i) dividend and growth forecasts and ii) the current value of the share / market portfolio. Most of the implicit methods use a more complex evaluation formula than the one shown above. In particular, multi-period dividend discount models and residual income models are used here.

Areas where the market risk premium is important

Company valuation

The value of a company is determined, assuming exclusively financial goals, via the present value of the net inflows to the company owners associated with ownership of the company. To determine this present value, a capitalization interest rate is used that represents the return on an alternative investment that is adequate for investing in the company to be valued (see IDW Standard: Principles for carrying out company valuations). In the context of company valuations, a market-based determination of the alternative return based on the CAPM or the Tax-Capital Asset Pricing Model (Tax-CAPM) has become established. The alternative return can be expressed as a weighted average of equity and debt costs, whereby these can be determined in the context of the CAPM over . ${\ displaystyle \ textstyle k = r_ {f} + \ beta \ cdot MRP}$

Asset allocation

In asset allocation , the market risk premium is relevant for deciding which portion of the asset should be invested in risk-free assets and which portion should be invested in high-risk assets. A market risk premium of zero means that risky investments have the same expected return as risk-free investments. With a market risk premium of zero, risk-averse investors would invest all their assets risk-free; the higher the market risk premium, the higher the proportion that investors are willing to invest in risky assets. Conversely, supply and demand in a capital market in which the average market player is risk-averse automatically creates a positive market risk premium.

literature

Tobias Berg: The Term Structure of Risk Premia: New Evidence from the Financial Crisis . Ed .: European Central Bank (= Working Paper Series . No. 1165 ). March 2010 (English, online [PDF; 980 kB ]).
Jules H. van Binsbergen, Michael W. Brandt, Ralph SJ Koijen: On the Timing and Pricing of Dividends . In: American Economic Review . tape 102 , no. 4 , June 2012, p. 1596–1618 , doi : 10.1257 / aer.102.4.1596 (English, version previously published in October 2010 by the National Bureau of Economic Research, Cambridge, Massachusetts [PDF; 572 kB ]).
James Claus, Jacob Thomas: Equity Premia as Low as Three Percent? Evidence from Analysts' Earnings Forecasts for Domestic and International Stock Markets . In: Journal of Finance . tape 56 , no. 5 , October 2001, p. 1629-1666 , JSTOR : 2697733 (English).
John H. Cochrane: Explaining the Variance of Price-Dividend Ratios . In: Society for Financial Studies (Ed.): Review of Financial Studies . tape 5 , no. 2 , 1992, p. 243–280 (English, version previously published in November 1989 by the National Bureau of Economic Research, Cambridge, Massachusetts [PDF; 429 kB ]).
Elroy Dimson, Paul Marsh, Mike Staunton: Global Evidence on the Equity Risk Premium . In: Journal of Applied Corporate Finance . tape 15 , no. 4 , August 2003, p. 27-34 (English).
Peter D. Easton: Pe ratios, Peg ratios, and Estimating the Implied Expected Rate of Return on Equity Capital . In: Accounting Review . tape 79 , January 2004, p. 73-95 (English).
IDW Standard: Principles for conducting company evaluations (IDW S 1) i. d. F. 2008.
Burton G. Malkiel: The Capital Formation Problem in the United States . In: Journal of Finance . tape 34 , 1979, pp. 291-306 , doi : 10.1111 / j.1540-6261.1979.tb02092.x .
James M. Poterba, Lawrence H. Summers: Mean reversion in stock prices . In: Journal of Financial Economics . tape 22 , no. 1 , 1988, p. 27–59 (English, version previously published in August 1987 by the National Bureau of Economic Research, Cambridge, Massachusetts [PDF; 286 kB ]).
Robert J. Shiller: Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? In: American Economic Review . tape 71 , no. 3 , 1981, p. 421–436 (English, version previously published in February 1980 by the National Bureau of Economic Research, Cambridge, Massachusetts [PDF; 441 kB ]).
Richard Stehle: The determination of the risk premium of shares in the context of estimating the value of listed stock corporations . In: The auditing . 2004, p. 906-927 .

Individual evidence

↑ Stehle (2004)
↑ Dimson / Marsh / Staunton (2003)
↑ Shiller (1981), Poterba / Summers (1988), Cochrane (2005)
^ Van Binsbergen / Brandt / Koijen (2012), Berg (2012)
^ Malkiel (1979), Claus / Thomas (2001), Easton (2004)
↑ IDW Standard: Principles for carrying out company valuations (IDW S 1) i. d. F. 2008 No. 4

Web links

[1] Stehle (2004)

[2] Dimson / Marsh / Staunton (2003)

[3] Shiller (1981), Poterba / Summers (1988), Cochrane (2005)

[4] Van Binsbergen / Brandt / Koijen (2012), Berg (2012)

[5] Malkiel (1979), Claus / Thomas (2001), Easton (2004)

[6] IDW Standard: Principles for carrying out company valuations (IDW S 1) i. d. F. 2008 No. 4