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Which implied ERP calculation to use? (3 of 3)

Unfortunately even though I would like to use an implied equity risk premium, the valuation experts (Damodaran, McKinsey’s Koller et al) use different methods to arrive at an approximate implied ERP. I have compared both methods per below with open data sources, so anybody can reproduce this.

Damodaran’s implied ERP

Damodaran has put his spreadsheets online and calculates an updated number regularly. Using the spreadsheet and choosing a 12 months trailing dividend the ERP is 6.59%

In his spreadsheet Damodaran uses analyst forecasts for growth, current dividends and a yearend current S&P number.

I think using analyst estimates is a weakness. Evidence enough analysts often aren’t good in forecasting. (who is?)

Fortunately in his ERP paper Damodaran shows the implied ERP’s based on analyst forecasts have predictive power. So all is not lost, but I still would like to improve on this method.

Koller et al.’s implied ERP

Koller et al. say they use a current year earnings yield calculated according to their value driver formula. Ke=E x (1- g/ROE)/P+g.

E = current year earnings, g = 3.5% gdp growth, ROE is an historical aggregate 13.5 % for the S&P and P = median 12 month trailing S&P price.

Koller et al. mention that they found from 1962 to 2008, a stable real average market return of 7% (excl. inflation) without much volatility. See picture:

Source: Valuation: Measuring and Managing the Value of Companies, 5th edition Koller, Wessels and Goedhart

So to determine a current ERP it’s just subtracting the real risk free rate (I use 10y TIPS) from the stable historical implied ERP of 7%. Easy!

But when I apply this basic exercise, the outcome is 7.5%. [7% – (- 0.47%) ], because the 10y TIPS rate is negative.

An ERP of 7.5% is:

  • not within the 4.5%-5.5% range that Koller et al have indicated
  • higher than ’08’s ERP: 5% (7.8% Market Return – 1.8% 10y TIPS)

To triangulate both outcomes I’ve used the value driver formula with current market data as input:

  • 12 month trailing median Price = 1308 (S&P 500)
  • 12 month trailing Earnings = 88.6
  • E (Rm) = 8.5%
  • 10 yr T Bond = 1.65%
  • Resulting in an ERP of 6.8%

Conclusion

  • All three results are within a 1% range (6.6% – 7.5%)
  • No confirmation for the negative outcome of the Campbell/ Shiller dividend yield model
  • Results are 2% higher than Koller et al’s range (e.g. upper limit vs upper limit)
  • In ’08 the movement was within their range, with an ERP of 5%
  • Q: is 2012 so exceptional?

For pricing purposes I’d go for a mixed approach using McKinsey’s value driver formula assumptions (RoE 13.5%, 3.5% growth), a current quote for the S&P and 12 month trailing EPS, stripping out dependency on analyst forecasts, but incorporating current market prices.

When I test this approach, the result is an ERP of 6.6%. Pretty close to Damodaran’s number and it also works for ’08.

I also would like to use McKinsey’s long term real market returns (7%), for intrinsic value calculations but when I approximate their technique with my open source data my real returns are volatile. Perhaps due to different sources of inflation data. I can only find realized inflation rates while I should incorporate expected inflation. To be continued.

The sources I used:
Damodaran: http://pages.stern.nyu.edu/~adamodar/
TIPS & Bonds: http://online.wsj.com/mdc/public/page/2_3020-tips-20120629.html?mod=mdc_pastcalendar
Valuation: 4th and 5th edition, Koller, Wessels Goedhart
Realized inflation: ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt
S&P 500 weekly price history: http://finance.yahoo.com/q?s=%5EGSPC
S&P trailing earnings: http://www.multpl.com/s-p-500-earnings/


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