CAPM Alpha & BetaThe CAPM Alpha & Beta indicator is a crucial tool in finance and investment analysis derived from the Capital Asset Pricing Model (CAPM) . It provides insights into an asset's risk-adjusted performance (Alpha) and its relationship to broader market movements (Beta). Here’s a breakdown:
1. How Does It Work?
Alpha:
Definition: Alpha measures the portion of an investment's return that is not explained by market movements, i.e., the excess return over and above what the market is expected to deliver.
Purpose: It represents the value a fund manager or strategy adds (or subtracts) from an investment’s performance, adjusting for market risk.
Calculation:
Alpha is derived from comparing actual returns to expected returns predicted by CAPM:
Alpha = Actual Return − (Risk-Free Rate + β × (Market Return − Risk-Free Rate))
Alpha = Actual Return − (Risk-Free Rate + β × (Market Return − Risk-Free Rate))
Interpretation:
Positive Alpha: The investment outperformed its CAPM prediction (good performance for additional value/risk).
Negative Alpha: The investment underperformed its CAPM prediction.
Beta:
Definition: Beta measures the sensitivity of an asset's returns relative to the overall market's returns. It quantifies systematic risk.
Purpose: Indicates how volatile or correlated an investment is relative to the market benchmark (e.g., S&P 500).
Calculation:
Beta is computed as the ratio of the covariance of the asset and market returns to the variance of the market returns:
β = Covariance (Asset Return, Market Return) / Variance (Market Return)
β = Variance (Market Return) Covariance (Asset Return, Market Return)
Interpretation:
Beta = 1: The asset’s price moves in line with the market.
Beta > 1: The asset is more volatile than the market (higher risk/higher potential reward).
Beta < 1: The asset is less volatile than the market (lower risk/lower reward).
Beta < 0: The asset moves inversely to the market.
2. How to Use It?
Using Alpha:
Portfolio Evaluation: Investors use Alpha to gauge whether a portfolio manager or a strategy has successfully outperformed the market on a risk-adjusted basis.
If Alpha is consistently positive, the portfolio may deliver higher-than-expected returns for the given level of risk.
Stock/Asset Selection: Compare Alpha across multiple securities. Positive Alpha signals that the asset may be a good addition to your portfolio for excess returns.
Adjusting Investment Strategy: If Alpha is negative, reassess the asset's role in the portfolio and refine strategies.
Using Beta:
Risk Management:
A high Beta (e.g., 1.5) indicates higher sensitivity to market movements. Use such assets if you want to take on more risk during bullish market phases or expect higher returns.
A low Beta (e.g., 0.7) indicates stability and is useful in diversifying risk in volatile or bearish markets.
Portfolio Diversification: Combine assets with varying Betas to achieve the desired level of market responsiveness and smooth out portfolio volatility.
Monitoring Systematic Risk: Beta helps identify whether an investment aligns with your risk tolerance. For example, high-Beta stocks may not be suitable for conservative investors.
Practical Application:
Use both Alpha and Beta together:
Assess performance with Alpha (excess returns).
Assess risk exposure with Beta (market sensitivity).
Example: A stock with a Beta of 1.2 and a highly positive Alpha might suggest a solid performer that is slightly more volatile than the market, making it a suitable pick for risk-tolerant, return-maximizing investors.
In conclusion, the CAPM Alpha & Beta indicator gives a comprehensive view of an asset's performance and risk. Alpha enables performance evaluation on a risk-adjusted basis, while Beta reveals the level of market risk. Together, they help investors make informed decisions, build optimal portfolios, and align investments with their risk-return preferences.
Capm
Capital Asset Pricing Model (CAPM) [Loxx]Capital Asset Pricing Model (CAPM) demonstrates how to calculate the Cost of Equity for an underlying asset using Pine Script. This script will only work on the monthly timeframe. While you can change the default inputs, you should study what CAPM is and how this works before doing so. This indicator pulls various types of data from SPY from various timeframes to calculate risk-free rates, market premiums, and log returns. Alpha and Beta are computed using the regression between underlying asset and SPY. This indicator only calculates on the most recent data. If you wish to change this, you'll have to save the script and make adjustments. A few examples where CAPM is used:
Used as the mu factor Geometric Brownian Motion models for options pricing and forecasting price ranges and decay
Calculating the Weighted Average Cost of Capital
Asset pricing
Efficient frontier
Risk and diversification
Security market line
Discounted Cashflow Analysis
Investment bankers use CAPM to value deals
Account firms use CAPM to verify asset prices and assumptions
Real estate firms use variations of CAPM to value properties
... and more
Details of the calculations used here
Rm is calculated using yearly simple returns data from SPY, typically this is just hard coded as 10%.
Rf is pulled from US 10 year bond yields
Beta and Alpha are pulled form monthly returns data of the asset and SPY
In the past, typically this data is purchased from investments banks whose research arms produce values for beta, alpha, risk free rate, and risk premiums. In 2022 ,you can find free estimates for each parameter but these values might not reflect the most current data or research.
History
The CAPM was introduced by Jack Treynor (1961, 1962), William F. Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics. Fischer Black (1972) developed another version of CAPM, called Black CAPM or zero-beta CAPM, that does not assume the existence of a riskless asset. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM.
Usage
The CAPM is used to calculate the amount of return that investors need to realize to compensate for a particular level of risk. It subtracts the risk-free rate from the expected rate and weighs it with a factor – beta – to get the risk premium. It then adds the risk premium to the risk-free rate of return to get the rate of return an investor expects as compensation for the risk. The CAPM formula is expressed as follows:
r = Rf + beta (Rm – Rf) + Alpha
Therefore,
Alpha = R – Rf – beta (Rm-Rf)
Where:
R represents the portfolio return
Rf represents the risk-free rate of return
Beta represents the systematic risk of a portfolio
Rm represents the market return, per a benchmark
For example, assuming that the actual return of the fund is 30, the risk-free rate is 8%, beta is 1.1, and the benchmark index return is 20%, alpha is calculated as:
Alpha = (0.30-0.08) – 1.1 (0.20-0.08) = 0.088 or 8.8%
The result shows that the investment in this example outperformed the benchmark index by 8.8%.
The alpha of a portfolio is the excess return it produces compared to a benchmark index. Investors in mutual funds or ETFs often look for a fund with a high alpha in hopes of getting a superior return on investment (ROI).
The alpha ratio is often used along with the beta coefficient, which is a measure of the volatility of an investment. The two ratios are both used in the Capital Assets Pricing Model (CAPM) to analyze a portfolio of investments and assess its theoretical performance.
To see CAPM in action in terms of calculate WACC, see here for an example: finbox.com
Further reading
en.wikipedia.org
Market Beta/Beta Coefficient for CAPM [Loxx]Market Beta/Beta Coefficient for CAPM is not so much an indicator as it is a value to be used in future indicators to forecast stock prices using the Capital Asset Pricing Model, CAPM. CAPM is used by the likes of value investors such as Warren Buffet and valuation/accounting/investment banking firms. More specifically, CAPM is typically used in Discounted Cashflow Analysis to value revenue generating assets.
What is Beta?
In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in small quantity. Thus, beta is referred to as an asset's non-diversifiable risk, its systematic risk, market risk, or hedge ratio. Beta is not a measure of idiosyncratic risk.
By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3.
How to calculate Beta
To calculate beta you typically choose 5 years of monthly data; typically SPY is used here
Calculate log returns of both the asset for which you are calculating Beta and the benchmark market data
Calculation the covariance between the asset and benchmark
Calculate the variance of the benchmark returns
Divide the covariance by the variance
Read more here:
en.wikipedia.org(finance)
en.wikipedia.org
einvestingforbeginners.com
Portfolio Metrics = α(Jensen's), β, CAPM(Ra), Sharpe, TreynorPortfolio Metrics...
Standard Deviation
Jensen's Alpha
Beta
Expected Return (CAPM, Ra)
Sharpe Ratio
Treynor Ratio
Cyclical vs. Defensive Sector Alphashows mean excess returns of defensive and cyclical sectors vs. S&P500
Alpha strategy - simple versionThis Strategy goes long when Sharpe Ratio is > 1 and Alpha against the S&P500 is generated. It exits when conditions break away. en.wikipedia.org(finance). Use on daily or 5min.
Betaen.wikipedia.org(finance)
Beta is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors.
The market portfolio of all investable assets has a beta of exactly 1 (here the S&P500). A beta below 1 can indicate either an investment with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market
Alpha strategyUSE ON DAILY TIMEFRAME TO DETECT MOMO STOCKS & ETFs AND TRADE THEM
This Strategy goes long when Sharpe Ratio is > 1 and Alpha against the S&P500 is generated. It exits when conditions break away. Strategy can be adapted to run intraday, it however needs different (lower) trigger levels.
examples to try this on: GER30, NAS100, JPN225, AAPL, IBB, TSLA, etc.
AlphaAlpha is a measure of the active return on an investment, the performance of that investment compared to the S&P500 index, where 0.01 = 1%
alpha < 0: the investment has earned too little for its risk (or, was too risky for the return)
alpha = 0: the investment has earned a return adequate for the risk taken
alpha > 0: the investment has a return in excess of the reward for the assumed risk
