Investment Theory and Risk Management, + Website

Appendix 19.1: CAPM

CAPM as a Basis for Deriving IRR, PME, and Risk-Adjusted Returns

I am going to derive all the performance measures from the basic CAPM relationship.

Basic CAPM:

Assume risk-free rate is zero for now and rewrite the asset's return as:

Solve this for P₀ to get the pricing form of the CAPM:

This is a simple two-period discount model. Generalize the future price as a stream of cash flows (dividends) in discrete time.

If we set t = 1 and assume the market rate is constant at r_m, then this looks like the simple textbook dividend discount model, but with a CAPM discount factor, that is a function of the asset's β with the market return, plus Jensen's index (α).

The discount factor is the risk-adjusted market rate of return plus the alpha. Equivalently, we can express this as a future value by multiplying both sides by (1 + α + βr_m)^T to get:

Finally, we can rewrite this in ...