Cost of Capital: Applications and Examples, + Website, 5th Edition

APPENDIX 8A

Deriving ERP Estimates¹

Realized Risk Premium (ex post) Approach

Measuring Realized Risk Premiums

Realized Historical Stock and Bond Returns

Summarizing Realized Risk Premium Data

What Periodicity of Past Measurement?

Comparing Investor Expectations to Realized Risk Premiums

Arnott and Bernstein

Dimson, Marsh, and Staunton

Grinold, Kroner, and Siegel

Ibbotson and Chen

Using the Geometric Average for Compounding and the Arithmetic Average for Discounting

Compounding

Discounting

Is Bias Introduced by Using the Arithmetic Average as an ERP Estimate?

Implied ex ante ERP Estimates

Bottom-up Implied Estimates

Top-down Implied ERP Estimates

Top-down Risk Premium Estimates

Surveys

Using the Arithmetic Average Equivalent ERP for Discounting

REALIZED RISK PREMIUM (EX POST) APPROACH

Here we discuss in detail the following issues in applying the realized risk premium approach:

• What risk-free rate should be used to measure the realized premiums?
• What period should be used as the sample period?
• Should returns be measured over one-year holding periods or over longer holding periods?
• Is the arithmetic average or geometric average the more accurate method of summarizing realized return data over the sample period?

Measuring Realized Risk Premiums

The measure of the risk-free rate has generally not been controversial once the proper duration (long-term versus short-term) of the investment has been estimated, since the expected yield to maturity on appropriate U.S. government securities ...