The Capital Asset Pricing Model (CAPM) measures the relationship between the expected return and the risk of investing in security. This model is used to analyze securities and price them given the expected rate of return and cost of capital involved.

1. Capital Asset Pricing Model
Dr. Asif Hasan

2. Definition
The Capital Asset Pricing Model (CAPM)
measures the relationship between the
expected return and the risk of investing in
security.
This model is used to analyze securities and
price them given the expected rate of return
and cost of capital involved.
The (capital asset pricing model) CAPM
formula is represented below
Expected Rate of Return = Risk-Free
Premium + Beta * (Market Risk Premium)
Ra = Rrf + βa * (Rm – Rrf)

3. Component of CAPM

4. CAPM Assumptions
• All investors are risk-averse by nature.
• Investors have the same time period to evaluate information.
• There is unlimited capital to borrow at the risk-free rate of return.
• Investments can be divided into unlimited pieces and sizes.
• There are no taxes, inflation, or transaction costs.
• Risk and return are linearly related.

5. CAPM &Security Market Line
In the following chart, you can see that
the CML is now called the security
market line (SML). Instead of expected
risk on the x-axis, the stock’s beta is
used. As you can see in the illustration,
as beta increases from 1 to 2, the
expected return is also rising.
The CAPM and the SML make a connection
between a stock’s beta and its expected risk.

6. Example
• Imagine an investor is contemplating a stock valued at Rs.100
per share today that pays a 3% annual dividend. Say that this stock has a
beta compared with the market of 1.3, which means it is more volatile than
a broad market portfolio (i.e., the S&P 500 index). Also, assume that the
risk-free rate is 3% and this investor expects the market to rise in value by
8% per year.
• The expected return of the stock based on the CAPM formula is 9.5%:
• 9.5%=3%+1.3×(8%−3%)

7. The CAPM and the Efficient Frontier

8. Example of Efficient Frontier

9. Advantages of the CAPM
• It considers only systematic risk, reflecting a reality in which most investors have
diversified portfolios from which unsystematic risk has been essentially eliminated.
• It is a theoretically-derived relationship between required return and systematic risk
which has been subject to frequent empirical research and testing.
• It is generally seen as a much better method of calculating the cost of equity than the
dividend growth model (DGM) in that it explicitly considers a company’s level of
systematic risk relative to the stock market as a whole.
• It is clearly superior to the WACC in providing discount rates for use in investment
appraisal.

10. Limitations of CAPM
• Assumptions may not hold: CAPM relies on certain assumptions, such as the efficient
market hypothesis, which may not always hold true in real-world scenarios. Therefore,
the model may not be an accurate representation of the market and may lead to poor
investment decisions.
• 2. Limited in scope: CAPM only takes into account market risk and assumes that all
investors have access to the same information. This means that it may not fully capture
other factors that can impact the value of an investment.
• 3. Relies on historical data: CAPM relies on historical data to estimate market risk and
return, which may not always be a reliable predictor of future performance.

11. Arbitrage Pricing Theory/Model(APT)
• Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea
that an asset's returns can be predicted using the linear relationship between the asset’s
expected return and a number of macroeconomic variables that capture systematic risk.
• Formula for the Arbitrage Pricing Theory Model

12. How the Arbitrage Pricing Theory Works?
• The arbitrage pricing theory was developed by the economist Stephen Ross in
1976, as an alternative to the capital asset pricing model (CAPM).
• Unlike the CAPM, which assume markets are perfectly efficient, APT assumes
markets sometimes misprice securities, before the market eventually corrects and
securities move back to fair value.
• Using APT, arbitrageurs hope to take advantage of any deviations from fair market
value.

13. How the Arbitrage Pricing Theory Works? Continued…..
• APT factors are the systematic risk that cannot be reduced by the diversification of
an investment portfolio.
• The macroeconomic factors that have proven most reliable as price predictors
include unexpected changes in inflation, gross national product (GNP), corporate
bond spreads and shifts in the yield curve.
• Other commonly used factors are gross domestic product (GDP), commodities
prices, market indices, and exchange rates.

14. Example
• The following four factors have been identified as explaining a stock's return and its
sensitivity to each factor and the risk premium associated with each factor have been
calculated:
• Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
• Inflation rate: ß = 0.8, RP = 2%
• Gold prices: ß = -0.7, RP = 5%
• Standard and Poor's 500 index return: ß = 1.3, RP = 9%
• The risk-free rate is 3%
• Using the APT formula, the expected return is calculated as:
• Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

15. Fama French Three Factor Model
• In asset pricing and portfolio management the Fama–French three-factor model is
a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe
stock returns.
• The Fama-French model aims to describe stock returns through three factors: (1) market
risk,
• (2) the outperformance of small-cap companies relative to large-cap companies, and
• (3) the outperformance of high book-to-market value companies versus low book-to-
market value companies.
• The rationale behind the model is that high value and small-cap companies tend to
regularly outperform the overall market.

16. The Fama-French Three-
Factor Model Formula
The mathematical representation
of the Fama-French three-factor
model is:
• Market Risk Premium
• SMB (Small Minus Big)
• HML (High Minus Low)

17. 1. Market Risk Premium
• Market risk premium is the difference between the expected return of the market and the risk-free
rate. It provides an investor with an excess return as compensation for the additional volatility of
returns over and above the risk-free rate.
2. SMB (Small Minus Big)
• Small Minus Big (SMB) is a size effect based on the market capitalization of a company. SMB
measures the historic excess of small-cap companies over big-cap companies. Once SMB is
identified, its beta coefficient (β) can be determined via linear regression. A beta coefficient can
take positive values, as well as negative ones.
• The main rationale behind this factor is that, in the long-term, small-cap companies tend to see
higher returns than large-cap companies.

18. Continued………..
3. HML (High Minus Low)
• High Minus Low (HML) is a value premium. It represents the spread in returns
between companies with a high book-to-market value ratio (value companies) and
companies with a low book-to-market value ratio. Like the SMB factor, once the
HML factor is determined, its beta coefficient can be found by linear regression.
The HML beta coefficient can also take positive or negative values.
• The HML factor reveals that, in the long-term, value stocks (high book-to-market
ratio) enjoy higher returns than growth stocks (low book-to-market ratio).

19. Task
• Read the application of CAPM and Fama French Model.