E[r i ] = r f + β i (E[r m ] r f. Investment s risk premium is proportional to the expectation of the market risk premium: er mt = r mt r ft

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1 The Equity Premium Equity Premium: How much more return an investor requires to hold a risky equity relative to a risk free investment. Equity Market Premium: The amount of extra return an investor needs to hold a diversified equity portfolio of all available stocks listed in a given market.

2 When we want to calculate the required return of an investment, typically think in terms of starting with the risk free rate, and adding a premium reflecting the risk of the invesment. For example, in the CAPM we estimate E[r i ] = r f + β i (E[r m ] r f Investment s risk premium is proportional to the expectation of the market risk premium: er mt = r mt r ft The risk adjustment is made by scaling up by the beta (β i ) of the investment. Need an estimate of the expected market risk premium.

3 Need an estimate of the expected market risk premium. There are three different approaches to doing such an estimation. Survey evidence Implied expected market premium in current prices. The historical experience (historical average)

4 Surveying investors Possibilities: What are individual investors expectations of returns? What about market professionals? Concentrate on the latter, market professionals

5 Surveying market professionals US: Merril Lynch survey of institutional investors Year Expectation about market risk premium % 2008 (mar) 4.1% % 2012 (jan) 4.08% 2013 (jan) 4.8%

6 Surveying market professionals Graham and Harvey (2013) survey of US CFOs numbers for cost of capital for their firm Year Expectation about market risk premium 2012 (jan) 3.95% 2013 (jan) 3.83%

7 Surveying market professionals Time series of Graham and Harvey (2013) survey of US CFOs

8 Surveying market professionals A worldwide survey: Fernandez, Aguirreamalloa, and Linares (2013)

9 Surveying market professionals A worldwide survey: Fernandez et al. (2013)

10 Surveys problematic: Tend to respond too much to recent stock price movements. Sensitive to how question is asked. Sensitive to who gets surveyed. Do not find much predictive power

11 Implied equity premia Simple example: Value = Expected dividends next period Required return on equity Expected growth rate in dividends Possible to estimate three of the variables in the model Value (current level of market) Expected dividends next period Expected growth rate in dividends Given these, then one backs out the implicit Required return on equity.

12 Implied equity premia Example (from Damodaran (2013), The current level of the S&P 500 is 900. The expected dividend yield on the index for the next period is 3%. The expected growth rate in earnings and dividends in the long term is 6%. Then, it is a matter of solving for r in 900 = 900 3% r 0.06 r = 9%. If the current risk free rate is 5%, we would estimate the risk premium as mrp = 9% r f = 9% 5% = 4%.

13 Implied equity premia Time series of estimates of US impied risk premia (Damodaran, 2013)

14 Estimating the historical equity market risk premium Calculate er mt = r mt r ft r mt is typically the return of a broad stock market index, such as S&P 500. r ft is the return on risk free borrowing, typically estimated as the interest rate on long term government bonds.

15 Estimating the historical US equity market risk premium Use the data provided by Damodaran on his homepage to illustrate the typical calculation. The time series of the actual annual returns. Return on stocks, bills and bonds Return S&P500 T Bill T bond

16 Calculate the difference S&P 500 T bonds Return

17 Take the historical average. In this picture we illustrate the evolution of the estimate of the average using a longer and longer time period. S&P 500 T bonds Return Stock Bond Arith mean Geom mean

18 Longer time series of US stock returns (Goyal and Welch, 2008). erm rfree logreturn erm Rf Cumulative mean Rolling mean(20y)

19 Going beyond the US Possible issue with focusing on the US: the economy in the world that ex post has turned out to be the most succesful. After the US civil war ( ) there has been no war on US soil. Most other economies in the world has suffered through periods of war and unrest. Using only US data can then introduce a survivorship bias in the estimation (Brown, Goetzmann, and Ross, 1995). We should therefore look beyond the US. The best known world wide evidence on world-wide equity returns is that provided by Elroy Dimson and coauthors (Dimson, Marsh, and Staunton, 2011).

20 Worldwide Equity Premia Source: (Dimson et al., 2011).

21 The Norwegian Equity Premium Norway is a case study of the problems in predicting the equity premium. Reliable Norwegian Equity data is primarily post Calculate the historical risk premium as the difference between the return on a stock market index and the risk free rate, proxied by NIBOR Index Period Average Annual Excess Return EW ( ) VW ( ) OBX ( ) 6.29 TOT ( ) (from Ødegaard (2016).) The indices to use are EW (equally weighted) and VW (value weighted), total return indices. Hard to argue for an equity market risk premium of this magnitude.

22 The Norwegian Equity Premium Instead: Survey of Norwegian financial analysts estimates of the market premium at the end of 2013.

23 The Norwegian Equity Premium Implicit Risk premium Norway An alternative estimate for Norway is had by imlicit estimates: For the largest stocks in Norway, estimate the stock required return, and then back out the average market risk premium.

24 The Equity Premium Puzzle What is the equity premium puzzle? Consisely: The claim that the equity premium (the difference between the return on holding equity and risk free bonds) is too high to be explained by reasonable levels of risk aversion. Is it really a puzzle? Short answer: For the purposes of doing valuation Don t Worry, (be happy).

25 The Equity Premium Puzzle A slightly longer answer. The Equity Premium Puzzle is really only of concern in the context of macroeconomic modelling. In this type of modelling we posit the existence of one (representative) economic decision maker, and vary the preference parameters of this single decision maker. The equity premium puzzle as formulated by Mehra and Prescott (1985) is that to generate an equity premium as high as the one observed (6% in the US) the preferences of the representative consumer needs to have a very high degree of risk aversion. By simple introspection we don t believe that this is a reasonable degree of risk aversion for the typical decision maker in the typical economy.

26 The Equity Premium Puzzle The equity premium puzzle: dictonomy between the preferences of the representative consumer what is viewed as reasonable preferences for the typical investor. But is this a meaningful comparison? When we write the utility in terms of consumption in a macro model, we have in mind the total consumption in the economy, which is then distributed to all individual consumers in the economy. Under very special assumptions, the prefererences of all individuals in the economy can be aggregated into a representative consumer. The equity premium puzzle: Is only a puzzle in the context of a macro-model of the equity market where the utility functions of all individuals in the economy satisfy aggregation. Without aggregation we are no longer sure the equity premium is a puzzle.

27 Predictability of market risk premium Another input to our thinking about the equity risk premium is whether it is predictable. If we are trying to estimate the expected market risk premium, and it is predictable, the predicability should be used in generating the expection.

28 S J Brown, W N Goetzmann, and S A Ross. Survival. Journal of Finance, 50: , Aswath Damodaran. Equity risk premiums (erp): Determinants, estimation and implications the 2013 edition. Working Paper, New York University, March Elroy Dimson, Paul Marsh, and Mike Staunton. Equity premia around the world. Working Paper, London Business School, July Pablo Fernandez, Javier Aguirreamalloa, and Pablo Linares. Market risk premium and risk free rate used for 51 countries in Working Paper, IESE Business School, Amit Goyal and Ivo Welch. A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies, 21(4): , John R Graham and Campbell R Harvey. The equity risk premium in Working Paper, Duke University, R Mehra and E Prescott. The equity puzzle. Journal of Monetary Economics, 15:145 61, Bernt Arne Ødegaard. Empirics of the Oslo Stock Exchange: Basic, descriptive, results, Working Paper, University of Stavanger, January 2016.