# 1.3.1 Estimating the future equity risk premium

There are three ways to estimate the future equity risk premium:

- using historical data and assuming that the past equity risk premium is a good indicator of the future equity risk premium
- asking experts for their opinion of the future equity risk premium
- estimating the implied future equity risk premium from today’s stock market index value using the dividend valuation model (DVM).

## Using historical data

This method takes into account past returns on equities and risk-free assets and looks at the actual difference. It assumes that the average equity risk premium that was earned in the past is the same as investors expect to earn in the future. There is an assumption that the actual equity risk premium earned reflects what investors expected the equity risk premium to be before investing. In other words, the extra 6% or 7% that investors earned in the past by investing in equities rather than risk-free assets is assumed to be a reliable indicator of what investors expect today for the future.

When looking at the past, it is essential to get enough data points for statistical reliability. For example, taking ten years of annual data would not give a reliable estimate of the future equity risk premium, as we have seen already. A 100-year period, that Dimson et al. (2002) use, gives a much more reliable estimate of the average historic equity risk premium from which to derive an expected future equity risk premium.

## Stop and reflect

Why is the historical equity risk premium approach not appropriate for estimating the equity risk premium for markets such as India or China?

It is not appropriate because there is not enough reliable historical data for such markets.

One advantage of looking at the historic equity risk premium and not just historic equity returns, is that, by doing so, the effects of inflation are neutralised. Both historic bond yields and historic equity returns will have included an allowance for inflation and so, by taking the difference between these two numbers, the equity risk premium becomes inflation neutral. Including data from the 1970s, for example, when inflation was very high, should not distort the results.

## Expert opinion

Another way of estimating the expected future risk premium is to ask the experts. For example, what do fund managers or academics think that the equity risk premium should be in order to compensate investors for the extra risk of investing in equities when compared with the risk-free asset? Such experts should know about the historic returns for estimating the future equity risk premium, but they may also have additional insights as to possible special factors to allow for in the future (e.g. the impact of the 2008–9 global financial crisis).

In 2010, a global survey of 3,861 analysts, company managers and university professors gave the replies shown in Table 1 when they were asked for the equity risk premium relative to bonds that they used in their calculations of present value of future cash flow. Note that their equity risk premium expectations are below estimates derived from long-run historical data. For example, the UK equity risk premium forecasts in Table 1 are between 5.0% and 5.6% which is less than the 6% historic equity risk premium for the UK (calculated on 100 years of historical data).

Group | Average ERP | |||

USA and Canada | Europe | UK | Other (emerging markets) | |

601 analysts | 5.1% | 5.0% | 5.2% | 6.3% |

1,749 corporate managers | 5.3% | 5.7% | 5.6% | 7.5% |

1,511 professors | 6.0% | 5.3% | 5.0% | 7.8% |

## Stop and reflect

Why do you think there is much similarity in the estimates for developed markets? Why do you think the estimate is higher for other (emerging market) countries?

The lack of difference in the equity risk premium estimates for the major stock markets is probably due to the globalisation of US finance texts and hence of views on the equity risk premium.

The higher equity risk premium applied by emerging market country managers and analysts may be due to the less developed corporate governance, stock market regulation, accounting disclosure and legal protection for minority investors in those markets.

## The dividend valuation model

The third method of calculating the equity risk premium is to estimate the *implied* equity rate of return embedded in the *current* market price, given the *forecast* dividends to be paid on shares. To do this, the dividend valuation model is used. Dividends are the payments made to share investors by companies – usually once or twice a year.

The dividend valuation model (DVM) simply defines the price P_{i} of a share i to be the present value of all future dividends discounted by the required rate of return for that particular share. Since companies have an unlimited life, provided they are not liquidated, an infinite stream of dividends, D_{n}, from year 1 to infinity, ∞, can be assumed. So:

- where
- P
_{i}= current price of share i - D
_{n}= dividend expected in year n on share i - E(R
_{i}) = expected return on share i given its risk - (∑ means the summation of all terms with n varying from n = 1 to n = ∞ (infinity).)

This is a simple present value equation that does not depend on any unrealistic assumptions to be valid. Its disadvantage, however, is that no one really has any idea what the likely dividends are going to be for any company, given the uncertainties of the real world.

A simplified version of the DVM, sometimes known as the Gordon growth model after Gordon (1959), assumes for simplicity that dividends will grow at a constant rate, g. Although unrealistic, the advantage of the Gordon growth model is that the formula simplifies dramatically to:

- where
- P
_{i }= current price of share i - D
_{1}= dividend expected in year 1 on share i - E(R
_{i}) = expected return on share i given its risk - g = expected constant annual growth rate of share i’s dividends
- Multiplying through by E(R
_{i}) – g, dividing by P_{i}, and taking g to the right-hand side of the equation gives:

This can be interpreted as saying that the required rate of return on a share is the sum of the dividend yield (with next year’s dividend rather than last year’s) and the expected growth rate, g, on the dividends. Therefore, the cost of equity capital for a share or market can be estimated by inputting the expected dividend for next year and dividing by the current share price (or, taking the expected dividend yield), and then adding the expected constant growth rate for dividends beyond next year. This growth rate can either be estimated by assuming that the historic growth rate over, say, the last five years will continue indefinitely, or can be derived from consideration of a likely real rate of growth (which could be assumed to be the long-term real growth rate of the economy) plus a long-term forecast inflation rate.

Note that the Gordon growth model formula (1959) was obtained by using the idea of a geometric progression; that is, a progression where each term grows by a constant factor. In the case of the Gordon growth model, the factor includes (1 + g) which is what the dividends grow by each year.

### Example

A share has an expected dividend next year of 3p, a current share price of 100p and its historic growth rate in dividends has been 8% per year.

The cost of equity capital can be estimated as:

E(R_{i}) = D_{1}/P_{i} + g = (3/100) + 8% = 3% + 8% = 11%

if it is assumed that dividend growth in the future will be the same as in the past.

Alternatively, suppose the long-term inflation forecast is 5% annually and the company is expected to grow in line with the economy, which is expected to grow 2.5% in real terms every year. The Fisher equation provides a formula for the relationship between nominal and real growth for interest rates, which can be applied to the nominal growth rate as:

1 + nominal growth rate = (1 + real growth rate)(1 + expected inflation)

So,

Substituting into the Gordon growth model, the cost of equity capital for this company can be estimated as:

E(R_{i}) = D_{1}/P_{i} + g

= 3% + 7.625% = 10.6%, rounded to one decimal place.

Note that many investors approximate the above version of the Fisher equation by simply adding the real growth and expected inflation components. In this case, it would be 2.5% + 5% = 7.5% rather than 7.625% for g.

This formula can also be applied to the market as a whole to estimate the equity risk premium implied by current market prices and dividend forecasts. In December 2010, the UK market, as measured by the FTSE All-Share Index, had an overall dividend yield of 3% and, by consensus, the expected growth rate of UK dividends for that index was 7.5% (equivalent to approximately 2.5% real growth in dividends and 5% expected inflation). If the government bond yield at the time was 4.0%, what was the expected equity risk premium?

Using the formula E(R_{M}) = D_{1}/P_{M} + g_{M} where D_{1}/P_{M }is next year’s dividend yield for the market as a whole and g_{M }is the growth rate expectation for the market as a whole, gives D_{1}/P_{M} = 3% x (1.075) = 3.225% and g_{M} = 7.5% and so E(R_{M}) = 10.725%. Deducting 4.0% for the risk-free rate gives an equity risk premium *implied *by the market of 6.725%, above the historic estimate of 6% (assuming a bond benchmark) and the expert forecasts of 5.0% to 5.6%.