Equity Risk Premium

The Equity Risk Premium (ERP) is one of the most important metrics in finance.  Some of its main uses include the valuation of companies, capital expenditure planning, asset allocation and setting a 'fair' rate of return for regulated industries.  As the ERP is used in a number of important financial decisions, it is the subject of much debate in academic literature and the finance industry.  The Auckland Centre for Financial Research (ACFR) has recently collected new data in New Zealand which we hope will provide useful insights to the ERP.


The ERP is a long-term estimate of the future excess return, or premium, investors expect to be compensated for risking their money in stocks rather than risk-free assets.  It is a measure of the average return of an entire equity market in excess of a risk-free asset (usually government bonds).  As the return from an entire equity market is used, the ERP is a market consensus in that it does not rely on the perceptions of one or a number of persons but all investors in an equity market.  This makes it a neutral estimate which can be used as a benchmark for more detailed analysis of the equity market (Ibbotson, 2011).

View Ibbotson (2011)

Many academics and practitioners use long-term historical data on equity returns and government bond yields to calculate the ERP.  The ERP is the average return of an equity market minus the average yield of a chosen government bond.  Other methods of calculating the ERP include model or consensus based and are discussed later.

ACFR research on the ERP in New Zealand

We have recently collected the longest series of historical New Zealand data available, the only data set of its kind.  This data consists of equity prices, dividend yields, inflation rates and 10-year government bond yields from 1899 to 2016.  The development of the New Zealand stock market is in itself interesting.  Yearly data is presented below to give the reader an idea of the equity returns, bond yields and inflation rates since 1899:

The difference in returns and yields of stocks and bonds respectively is striking.  10-year government bonds have never produced a negative yield and have remained relatively steady over 117 years.  Equities on the other hand have shown extreme volatility through market booms and busts.  It is clear from this graph why investors demand a return premium for putting money into risky equities rather than bonds and will continue to do so in the future.

The following table shows the average yearly figures for equity returns, dividend yields, capital gains, 10-year government bond yields and inflation rates over the 117 year sample collected by the ACFR:



Standard deviation



Equity returns (nominal, HPR)





Capital gain





Dividend yield





Inflation rate





Real Equity returns





10-year Gov. bond yields





We use nominal equity returns and 10-year government bond yields to calculate an ERP estimate of 4.76%.

Historical ERP advantages

1. Historical returns provide an unbiased measure of the ERP.  Rather than using predictions or 'experience' in deriving the ERP, which can be influenced by natural human biases, we can observe investors actual expectations of equity returns over bond yields.

2. The longer the data series, the more accurate the ERP.  The greater the number of booms and busts of the business cycle included in the sample, the more realistic the ERP.  Human expectations over the short term are volatile, it is only by using long term data that we can truly see the view of investors return requirement of equity.  Also, using long-term data allows one to be more confident on the future ERP from a statistical viewpoint.

Dimson et al (2003) provide an example to highlight the danger of using recent stock market performance to estimate the ERP.  In the U.S., they show that returns averaged 17.6% p.a. in the 1990’s and point out that investors believed this performance could be extrapolated into the future.  Then, the dotcom bubble burst in 2000.  Stock returns were, on average, negative from 2000-2002, whereas bonds did generally well.  Therefore, if the 1990’s were used to extrapolate into the future, the ERP would have been artificially high; if the 2000-2002 period were used to extrapolate into the future, this would imply that investors would be demanding a negative return for taking on risk.

View Dimson et al (2003)

We can highlight the same point made by Dimson et al (2003) using our own data.  We shall take the extremely volatile period of the 1980's, calculate the ERP and compare with the realised ERP of the 1990's and 2000's.  The ERP, if calculated using only 1980's data, is 14.78%.  The realised ERP in the 1990's was 3.34% and 1.99% in the 2000's.  Clearly, investor expectations over the short period of the 1980's was not representative of expectations in the 1990's and 2000's.  Trying to predict investor expectations using short-term data is extremely difficult.

Model or consensus based estimates of the ERP

The most common method for calculating the ERP is to use long-term historical data as this data shows exactly how much excess return investors have demanded in equity over bonds.  Interestingly, organisations use a range of ERP values, some use historical data but many use models such as the dividend growth model or residual income model or consensus based views to 'estimate' the ERP.  Below is a sample of ERP values used by various organisations:


Model/consensus based?


The Treasury






Commerce Commission (Powerco)






Model or consensus based estimates of the ERP are subject to human behavioral biases.  These biases have been well documented in financial literature.  Together, these biases can lead to a subjective view of the ERP.  That is, subjective to the person making a judgement or deciding on inputs to a model.  The subjectivity is usually based on recent events and/or developments (within the last 20-30 years) in financial markets.  This is not nearly enough time to be confident on investors expectations of excess stock returns over bonds.

Dividend growth model

Residual income model

Consensus based views

The ERP outside of New Zealand

The equity return and bond yield data we collect provides a good measure of the ERP for the New Zealand market.  It is, however, useful to look at the ERP in various equity markets around the world.  As financial markets have become more accessible, most investors will hold a portion of their portfolio in foreign assets and so need an understanding of expected excess equity returns over bonds in various countries and a world ERP.

Dimson et al (2011) has collected long-term historical data (1900-2010) for 19 countries and calculated an ERP for each and a 'world' ERP as an average of the 19 countries.  The majority of the 19 countries are European with the European ERP calculated as 5.20%.  In the Australasian/Asia region, Australia has an ERP of 7.80% and Japan is 9.10%.  The U.K. has an ERP of 5.20%, United States has an ERP of 6.40% and the 'world' ERP is calculated as 5.00%.

View Dimson et al (2011)

Tax-adjusted market risk premium

The discussion on the calculation of the ERP thus far has ignored the influence of taxes.  In New Zealand, investors are taxed on dividends and interest payments through resident withholding tax.  New Zealand also has the advantage of imputation credits that avoids double taxation of company profits distributed as dividends to investors.

View IRD information on imputation credits

The ERP can be transformed to take account of the following:

1. Tax paid on dividend income less imputation credits (which will reduce the average market return for equity).

2. Tax paid on interest income (which will reduce the return on risk-free government bonds).

As tax is a practical consideration for investors expectations of excess equity returns over bonds, a tax-adjusted ERP provides a more 'realistic' measure.  Lally and Marsden (2004) have conducted research on a tax-adjusted ERP in New Zealand with data from 1931-2002.  They calculate a tax-adjusted ERP of 7.20% for the period they consider.

View Lally and Marsden (2004)

While a tax-adjusted ERP is a useful measure, its calculation produces a number of challenges regarding the tax rate to use (data on imputation credits is publicly available from the NZSE).  As the ERP measures the excess return of the average market return, an average market rate of tax is needed.  This means that the composition of market participants and their tax rates must be known or estimated with reasonable precision.  This information is generally not available for New Zealand over long time periods (or even at all), and means that a number of assumptions must be made when estimating a tax-adjusted ERP which leaves the result open to criticism.

Generally, when tax is considered in the calculation the ERP will increase compared to estimating without tax.  The reason for this is because of imputation credits in New Zealand. As dividends are taxed at a much lower (effective) rate than interest income, the average market return of equity is reduced by a small amount whereas the yield on risk-free bonds is reduced by a much greater amount.  As the ERP calculation is average market return on equity minus average government bond yield and bond yields are reduced by a larger amount than average equity market returns, the ERP increases with tax considerations.

ERP components

Arithmetic vs geometric mean returns

The first component in the ERP is an average of market equity returns which provides an estimate of expected future returns.  The expected market return is usually calculated in two ways: arithmetic or geometric mean.  The arithmetic mean is a simple average and the geometric mean is a calculation of the compound rate of growth.  Statistically speaking, the arithmetic mean has an upward bias when used to estimate expected returns, the geometric mean has a downward bias when used to estimate expected returns.  The difference between the statistically 'correct' estimate of expected returns and the arithmetic and geometric mean varies depending on the investment horizon (Jacquier et al, 2003).

View Jacquier et al (2003)

Risk-free rate: Bills vs bonds

The second component in the ERP is a risk-free asset, usually government bills or bonds.  Government bills/bonds are used rather than corporate paper/bonds as the former is considered risk-free.  If a government lacks the funds to repay a bond/bill issue they can simply print more money.  Also, the likelihood of default is low for most developed countries.

The difference between bills and bonds is the maturity.  Bills have shorter maturities than bonds which means they have less risk.  This is due to the fact that as maturity increases, the chance of default increases and hence risk increases.  As bills have less risk they have a lower return than bonds.  Therefore, the choice between bills and bonds will affect ERP estimation.  Essentially, the risk-free rate should reflect the investment horizon that the ERP is applied to.  For valuation and capital budgeting projects a long-term risk-free rate should be used such as government bonds, for shorter horizons, bills should be used (Damodaran, 1999).

View Damondaran (1999)


For more information on the ERP and the latest research conducted by the Auckland Centre for Financial Research please contact Professor Bart Frijns via email: bart.frijns@aut.ac.nz