The document discusses the Capital Asset Pricing Model (CAPM). It begins by explaining how CAPM extends capital market theory to allow investors to evaluate risk-return tradeoffs for both diversified portfolios and individual securities. It does this by redefining risk as systematic risk rather than total risk, and measures systematic risk using beta coefficients. CAPM then expresses expected return as the risk-free rate plus an expected risk premium that is scaled according to a security's beta. The document then provides a conceptual overview of how CAPM was developed and how it calculates required rates of return for individual securities based on their beta and the expected market risk premium.

1. THE CAPITAL ASSET
PRICING MODEL

2. CAPITAL ASSET PRICING MODEL
Capital market theory represented a major step forward in how investors
should think about the investment process. The formula for the CML offers a
precise way of calculating the return that investors can expect for (1)
providing their financial capital (RFR), and (2) bearing σport units of risk
([E(RM) − RFR]/σM). This last term is especially significant because it expresses
the expected risk premium prevailing in the marketplace.
The capital asset pricing model (CAPM) extends capital market theory in a
way that allows investors to evaluate the risk-return trade-off for both
diversified portfolios and individual securities. To do this, the CAPM
redefines the relevant measure of risk from total volatility to just the no
diversifiable portion of that total volatility (i.e., systematic risk). This new risk
measure is called the beta coefficient, and it calculates the level of a
security’s systematic risk compared to that of the market portfolio. Using
beta as the relevant measure of risk, the CAPM then redefines the expected
risk premium per unit of risk in a commensurate fashion. This in turn leads
once again to an expression of the expected return that can be decomposed
into (1) the risk-free rate and (2) the expected risk premium.

4. A Conceptual Development of the
CAPM
As noted earlier, Sharpe (1964), along with Lintner (1965) and Mossin
(1966), developed the CAPM in a formal way. In addition to the
assumptions listed before, the CAPM requires others, such as that asset
returns come from a Normal probability distribution. Rather than a
mathematical derivation of the CAPM, we will present a conceptual
development of the model, emphasizing its role in the natural
progression that began with the Markowitz portfolio theory.

5. Recall that the CML expressed the risk-return trade-off for fully
diversified portfolios as follows:

6. When trying to extend this expression to allow for the evaluation of any
individual risky asset i, the logical temptation is to simply replace the
standard deviation of the portfolio (σpot) with that of the single security
(σi). However, this would overstate the relevant level of risk in the with
security because it does not take into account how much of that
volatility the investor could diversify away by combining that asset with
other holdings. One way to address this concern is to “shrink” the level
of σi to include only the portion of risk in Security i that is systematically
related to the risk in the market portfolio. This can be done by
multiplying σi by the correlation coefficient between the returns to
Security i and the market portfolio (riM). Inserting this product into the
CML and adapting the notation for the ith individual asset leaves:

7. Or

8. The CAPM redefines risk in terms of a security’s beta (βi), which
captures the no diversifiable portion of that stock’s risk relative to the
market as a whole. Because of this, beta can be thought of as indexing
the asset’s systematic risk to that of the market portfolio. This leads to
a very convenient interpretation: A stock with a beta of 1.20 has a level
of systematic risk that is 20 percent greater than the average for the
entire market, while a stock with a beta of 0.70 is 30 percent less risky
than the market. By definition, the market portfolio itself will always
have a beta of 1.00. Indexing the systematic risk of an individual
security to the market has another nice feature as well.

9. From Equation above, it is clear that the CAPM once again expresses
the expected return for an investment as the sum of the risk-free rate
and the expected risk premium. However, rather than calculate a
different risk premium for every separate security that exists, the CAPM
states that only the overall market risk premium (E(RM) − RFR) matters
and that this quantity can then be adapted to any risky asset by scaling
it up or down according to that asset’s riskiness relative to the market
(βi). As we will see, this substantially reduces the number of calculations
that investors must make when evaluating potential investments for
their portfolios.

10. Determining the Expected Rate
of Return for a Risky Asset
To demonstrate how you would compute expected or required rates of
return with the CAPM, consider the following example stocks,
assuming you have already computed betas:

11. Assume that we expect the economy’s RFR to be 5 percent (0.05) and
the expected return on the market portfolio (E(RM)) to be 9 percent
(0.09). This implies a market risk premium of 4 percent (0.04). With
these inputs, the SML would yield the following required rates of return
for these five stocks: