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CAPM - Professor Beason. This set of notes contains information about CAPM

Professor Beason. This set of notes contains information about CAPM
Course

Investments: Debt, Equity And Derivatives (FIN3144)

11 Documents
Students shared 11 documents in this course
Academic year: 2022/2023
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Virginia Polytechnic Institute and State University

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Capital Asset Pricing Model (CAPM)

● Definition: The Capital Asset Pricing Model (CAPM) is a financial model that helps investors understand how much risk is involved in an investment and the expected return on that investment. ● Assumptions: The CAPM assumes that investors are rational and aim to maximize their wealth, that markets are efficient, and that investors have homogeneous expectations about the future. ● Formula: The CAPM formula is used to calculate the expected return on an investment based on the level of systematic risk (also known as non-diversifiable risk) associated with the investment. The formula is:

Expected return = Risk-free rate + Beta x (Expected market return - Risk-free rate)

where:

● Risk-free rate: The expected return on a risk-free investment, such as a U. Treasury bond ● Beta: A measure of an investment's volatility in relation to the market as a whole. A beta of 1 indicates that the investment's price will move in line with the market, while a beta less than 1 means it is less volatile than the market, and a beta greater than 1 means it is more volatile. ● Expected market return: The expected return on the overall market ● Example: Assume the risk-free rate is 2%, the expected market return is 8%, and the beta of an investment is 1. The expected return on the investment would be:

Expected return = 2% + 1 x (8% - 2%) = 12%

Arbitrage Pricing Theory (APT)

● Definition: The Arbitrage Pricing Theory (APT) is a financial model that explains how the prices of assets are determined in financial markets. It suggests that the return on an asset is a linear function of various macroeconomic factors, such as inflation, industrial production, and the unemployment rate.

● Assumptions: The APT assumes that markets are efficient, that investors have homogeneous expectations about the future, and that investors are risk-averse and aim to maximize their wealth. ● Formula: The APT formula is used to calculate the expected return on an asset based on the asset's sensitivity to various macroeconomic factors. The formula is:

Expected return = a + b1 x Factor 1 + b2 x Factor 2 + ... + bn x Factor n

where:

● a: The expected return on a risk-free investment ● b1, b2, ..., bn: The sensitivity of the asset's return to each of the macroeconomic factors (also known as factor loadings) ● Factor 1, Factor 2, ..., Factor n: The macroeconomic factors that influence the asset's return ● Example: Assume the expected return on a risk-free investment is 2%, the sensitivity of an asset's return to inflation is 0, and the expected inflation rate is 3%. The expected return on the asset would be:

Expected return = 2% + 0 x 3% = 3%

Practice Problems:

  1. An investor is considering two investments: Investment A and Investment B. Investment A has a beta of 1 and is expected to return 8%, while Investment B has a beta of 0 and is expected to return 6%. The risk-free rate is 2%. Which investment has the higher expected return according to the CAPM?

Answer: Investment A has the higher expected return according to the CAPM. The expected return on Investment A is:

Expected return = 2% + 1 x (8% - 2%) = 12%

Practice Problems:

  1. An investor is considering an investment in a stock with a beta of 1. The investor's risk tolerance is low and they are looking for an investment with low risk. Is this stock a good fit for the investor's risk tolerance?

Answer: It is generally expected that stocks with higher betas will have higher levels of risk, as they are more volatile than the market as a whole. Therefore, an investment in a stock with a beta of 1 may not be suitable for an investor with a low risk tolerance.

  1. An investor is considering two investments: Investment A and Investment B. Investment A has a sensitivity of 0 to the inflation rate, while Investment B has a sensitivity of 1 to the inflation rate. The investor expects the inflation rate to increase by 2%. According to the APT, which investment is expected to have the higher return?

Answer: Investment B is expected to have the higher return according to the APT. The expected return on Investment A is:

Expected return = a + 0 x 2% = a + 1%

The expected return on Investment B is:

Expected return = a + 1 x 2% = a + 2%

Therefore, Investment B has a higher expected return of 2% compared to Investment A's expected return of 1%. It is also important to understand the limitations of the CAPM and APT.

Limitations of the CAPM and APT

● CAPM: One limitation of the CAPM is that it assumes that markets are efficient, which means that all available information is reflected in asset prices. However, this may not always be the case in real-world markets, as there may be instances of mispricing or irrational behavior.

● APT: Another limitation of the APT is that it assumes that all risks can be diversified away, which means that an investor can achieve the same level of return with lower risk by holding a well-diversified portfolio. However, this may not always be possible, as there may be certain types of risks that cannot be diversified away.

Despite these limitations, the CAPM and APT are widely used by investors and financial professionals as tools to understand risk and return in financial markets.

Practice Problems:

  1. An investor is considering an investment in a stock with a beta of 2. The investor is aware that the CAPM assumes that markets are efficient, but they believe that the stock is currently mispriced. Should the investor rely on the CAPM to make their investment decision?

Answer: It is important to recognize the limitations of the CAPM and to consider other factors in addition to the expected return calculated using the CAPM formula. If the investor believes that the stock is mispriced, they should consider other information and factors in addition to the expected return calculated using the CAPM in making their investment decision.

  1. An investor is considering an investment in a stock with a sensitivity of 1 to the unemployment rate. The investor is aware that the APT assumes that all risks can be diversified away, but they are concerned about the potential impact of the unemployment rate on their investment. Should the investor rely on the APT to make their investment decision?

Answer: It is important to recognize the limitations of the APT and to consider other factors in addition to the expected return calculated using the APT formula. If the investor is concerned about the potential impact of the unemployment rate on their investment, they may want to consider the potential impact of this risk in their investment decision, even if it cannot be fully diversified away.

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CAPM - Professor Beason. This set of notes contains information about CAPM

Course: Investments: Debt, Equity And Derivatives (FIN3144)

11 Documents
Students shared 11 documents in this course

University: Virginia Polytechnic Institute and State University

Was this document helpful?
Capital Asset Pricing Model (CAPM)
●Definition: The Capital Asset Pricing Model (CAPM) is a financial model that
helps investors understand how much risk is involved in an investment and the
expected return on that investment.
●Assumptions: The CAPM assumes that investors are rational and aim to
maximize their wealth, that markets are efficient, and that investors have
homogeneous expectations about the future.
●Formula: The CAPM formula is used to calculate the expected return on an
investment based on the level of systematic risk (also known as non-diversifiable
risk) associated with the investment. The formula is:
Expected return = Risk-free rate + Beta x (Expected market return - Risk-free rate)
where:
●Risk-free rate: The expected return on a risk-free investment, such as a U.S.
Treasury bond
●Beta: A measure of an investment's volatility in relation to the market as a whole.
A beta of 1 indicates that the investment's price will move in line with the market,
while a beta less than 1 means it is less volatile than the market, and a beta
greater than 1 means it is more volatile.
●Expected market return: The expected return on the overall market
●Example: Assume the risk-free rate is 2%, the expected market return is 8%, and
the beta of an investment is 1.5. The expected return on the investment would
be:
Expected return = 2% + 1.5 x (8% - 2%) = 12%
Arbitrage Pricing Theory (APT)
●Definition: The Arbitrage Pricing Theory (APT) is a financial model that explains
how the prices of assets are determined in financial markets. It suggests that the
return on an asset is a linear function of various macroeconomic factors, such as
inflation, industrial production, and the unemployment rate.

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