**You haven’t checked your result with prospective estimates implied by the market**

Your ERP estimate could be out of line with prospective views of the ERP if you haven’t sense-checked it against plausible estimates from the market as a whole.

Historical estimates of the ERP are determined by looking at realised excess returns of equities over risk-free bonds over some periods of time. Prospective estimates consider current market prices (measured by a broad index), the current dividend yield on this index and expectations of earnings growth. It isn’t possible for long-term earnings growth of listed companies to outperform economic growth forever, since then the earnings of listed shares would eventually be larger than the entire economy. There are also reasons to believe that unlisted companies may grow faster than listed companies on average, in which case the earnings growth of listed companies may well be below that of the overall economy.

As an example, let’s take the current dividend yield of the JSE All Share Index = 2.4%.

Then, consider a long-term real economic growth forecast of 3%. This is above what we are achieving at the moment, and above recent history. However, there is reason to believe that with our state of development and population growth, this should be achievable in the long run.

We’ll also use a long-run inflation assumption of 4.5%, although this makes little difference since we are considering most of the calculations in real terms. It helps to understand the scenario a little better though if the figures include inflation. We’ll assume a real return on risk-free bonds of 3%, which is more or less where index linked bonds trade.)

The Dividend Discount Model (DDM also known as the Gordon Growth Model) equates price, dividends, growth and required return as follows:

P = D1 / (r-g)

Where D1 is the next dividend (so the current dividend inflated on average for 6 months assuming uniform declaration of dividends over the year, which isn’t quite right but is an acceptable approximation.

R is the required return (risk-free + equity risk premium). Risk-free is 3% + 4.5% = 7.5% in line with long-dated government bonds.

g will be the expected economic growth rate of inflation (4.5%) + real economic growth of 3% = 7.5%.

We can use some basic algebra to change the DDM to be r = (D1/P)+g which shows that the required return is the forward dividend yield plus growth in dividends. The ERP is thus (D1/P+g) – risk-free.

*These assumptions result in an ERP of only 2.5%, which is actually below my own view of a reasonable range for an ERP of 3% to 5%. You could argue that the market might be fairly expensive at the moment, which would result in a low estimate of the ERP.*

Let’s have a look at what parameters we would need to establish and ERP of 8%, which is what many people use. We can’t change the market dividend yield, real interest rates or break even inflation since they are derived directly from observable market prices. The only parameter we can reasonably change is expected real growth in GDP.

*We have to expect 8.4% real GDP growth on average for several years in order to justify an ERP of 8%. Hardly reasonable for South Africa.*

The DDM isn’t the only model that can be used. More sophisticated models could allow for a few years of explicit projections of economic growth (which can be reasonably reliable given real GDP growth is a mean-reverting autoregressive time series) and can improve the accuracy.

I’ve attached a little spreadsheet for you to play around with your own parameters and see what ERP you think is implied by the market.

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