Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Capital Asset Pricing Model (CAPM): Understanding Risk and Return in Finance, Study notes of Mathematical finance

Kansas City Kansas Community CollegeMathematical finance

The capital asset pricing model (capm) is a fundamental theory in modern finance that describes the relationship between the expected return of an asset and its risk. Developed in the 1960s by william sharpe, john lintner, and jan mossin, capm provides a framework for estimating the required rate of return for an asset, which is essential for investment decision-making, capital budgeting, and portfolio management. The assumptions, calculations, and implications of capm, including the risk-free rate, market portfolio, security market line, beta, and the efficient market hypothesis.

Typology: Study notes

2021/2022

Available from 05/29/2024

ryan-levin-1
ryan-levin-1 🇺🇸

4 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
The Capital Asset Pricing Model (CAPM) is a fundamental theory in modern
finance that describes the relationship between the expected return of an
asset and its risk. It was developed independently by William Sharpe, John
Lintner, and Jan Mossin in the 1960s, building upon the work of Harry
Markowitz on modern portfolio theory. Here's a detailed explanation of
CAPM:
1. **Assumptions:**
- Investors are risk-averse and aim to maximize their expected utility of
wealth.
- Investors have homogeneous expectations about asset returns, risks,
and correlations.
- Investors can borrow and lend at the risk-free rate.
- There are no market imperfections, such as taxes, transaction costs, or
restrictions on short-selling.
- All assets are publicly traded and perfectly divisible.
2. **The Risk-Free Rate and the Market Portfolio:**
- The risk-free rate (Rf) is the return on a risk-free asset, such as a
government bond.
- The market portfolio (Rm) represents the portfolio of all risky assets in
the market, weighted by their market capitalization.
3. **The Security Market Line (SML):**
- The SML is the graphical representation of the CAPM, which shows the
relationship between the expected return of an asset and its risk.
- The SML is a linear function with the following equation:
E(Ri) = Rf + βi * (E(Rm) - Rf)
where:
- E(Ri) is the expected return of asset i
- Rf is the risk-free rate
- βi is the beta of asset i, which measures the sensitivity of the asset's
returns to the market returns
pf3
pf4

Partial preview of the text

Download Capital Asset Pricing Model (CAPM): Understanding Risk and Return in Finance and more Study notes Mathematical finance in PDF only on Docsity!

The Capital Asset Pricing Model (CAPM) is a fundamental theory in modern finance that describes the relationship between the expected return of an asset and its risk. It was developed independently by William Sharpe, John Lintner, and Jan Mossin in the 1960s, building upon the work of Harry Markowitz on modern portfolio theory. Here's a detailed explanation of CAPM:

  1. Assumptions:
    • Investors are risk-averse and aim to maximize their expected utility of wealth.
    • Investors have homogeneous expectations about asset returns, risks, and correlations.
    • Investors can borrow and lend at the risk-free rate.
    • There are no market imperfections, such as taxes, transaction costs, or restrictions on short-selling.
    • All assets are publicly traded and perfectly divisible.
  2. The Risk-Free Rate and the Market Portfolio:
    • The risk-free rate (Rf) is the return on a risk-free asset, such as a government bond.
    • The market portfolio (Rm) represents the portfolio of all risky assets in the market, weighted by their market capitalization.
  3. The Security Market Line (SML):
    • The SML is the graphical representation of the CAPM, which shows the relationship between the expected return of an asset and its risk.
    • The SML is a linear function with the following equation: E(Ri) = Rf + βi * (E(Rm) - Rf) where:
      • E(Ri) is the expected return of asset i
      • Rf is the risk-free rate
      • βi is the beta of asset i, which measures the sensitivity of the asset's returns to the market returns
  • E(Rm) is the expected return of the market portfolio
  1. Beta (β):
  • Beta (β) is a measure of the systematic risk of an asset, which represents the asset's sensitivity to market movements.
  • Beta is calculated as the covariance of the asset's returns and the market returns, divided by the variance of the market returns.
  • A beta of 1 indicates that the asset's returns move in line with the market.
  • A beta greater than 1 indicates that the asset is more volatile than the market (aggressive).
  • A beta less than 1 indicates that the asset is less volatile than the market (defensive).
  1. The Efficient Market Hypothesis (EMH):
  • CAPM assumes that the market is efficient, meaning that all available information is already reflected in asset prices.
  • In an efficient market, investors cannot consistently earn above- average returns by trading on publicly available information.
  1. Implications and Applications:
  • CAPM provides a framework for estimating the required rate of return for an asset, which is essential for investment decision-making, capital budgeting, and portfolio management.
  • It helps investors understand the relationship between risk and return, and how to construct efficient portfolios.
  • CAPM is widely used in financial analysis, asset valuation, and performance evaluation.
  1. Limitations and Criticisms:
  • CAPM relies on several simplifying assumptions that may not hold true in the real world, such as the existence of a risk-free asset and the ability to borrow and lend at the risk-free rate.
  1. Calculating Expected Returns:
    • Company A: E(Ra) = 2% + 0.8 * 5% = 6%
    • Company B: E(Rb) = 2% + 1.5 * 5% = 9.5% Interpretation:
  • Company A: Despite its lower beta and lower expected return, it's considered less risky. Investors are compensated for the lower risk with a lower expected return.
  • Company B: The higher beta reflects the higher risk associated with this company. Investors are compensated for this risk with a higher expected return. Real-World Implications:
  • Investment Decisions: CAPM helps you understand the risk-return trade-off and make informed investment decisions. If you're risk-averse, you might prefer Company A, even with its lower expected return. If you're comfortable with higher risk, Company B might be more appealing.
  • Performance Evaluation: CAPM can be used to evaluate the performance of investments. If a stock's actual return is higher than its expected return based on CAPM, it might be considered outperforming.
  • Capital Budgeting: Companies use CAPM to determine the required rate of return for their projects. This helps them decide whether to invest in projects that are expected to generate returns exceeding the cost of capital. Important Note: This is a simplified example. In reality, CAPM is just one tool among many used in investment analysis. Other factors, such as company fundamentals, industry trends, and macroeconomic conditions, also play a crucial role in investment decisions.