CAPM

Demonstrating the Capital Asset Pricing Model (CAPM) in R Understanding CAPM

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between systematic risk and expected return for a financial asset. It’s often used to price assets and evaluate investment performance.  

R Code Implementation

library(quantmod)

## Ładowanie wymaganego pakietu: xts

## Ładowanie wymaganego pakietu: zoo

## 
## Dołączanie pakietu: 'zoo'

## Następujące obiekty zostały zakryte z 'package:base':
## 
##     as.Date, as.Date.numeric

## Ładowanie wymaganego pakietu: TTR

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

library(PerformanceAnalytics)

## 
## Dołączanie pakietu: 'PerformanceAnalytics'

## Następujący obiekt został zakryty z 'package:graphics':
## 
##     legend

Get historical data for a stock and a market index (e.g., S&P 500)

getSymbols(c("AAPL", "^GSPC"), from = "2018-01-01", to = "2023-12-31")

## [1] "AAPL" "GSPC"

Calculate daily returns

stock_returns <- na.omit(ROC(AAPL[,6]))
market_returns <- na.omit(ROC(GSPC[,6]))

Calculate beta (systematic risk)

beta <- CAPM.beta(Ra = stock_returns, Rb = market_returns)

Assume a risk-free rate (e.g., 3-month Treasury bill rate)

risk_free_rate <- 0.03

Calculate the expected return using CAPM

expected_return <- risk_free_rate + beta * (mean(market_returns) - risk_free_rate)

Print the results

cat("Beta:", beta, "\n")

## Beta: 1.217629

cat("Expected Return:", expected_return * 100, "%")

## Expected Return: -0.6068119 %

Explanation:

Data Acquisition: - getSymbols: Fetches historical price data for the stock (AAPL) and the market index (S&P 500).

Return Calculation:

• ROC: Calculates the rate of change (return) for both the stock and the market index.

Beta Calculation:

• CAPM.beta: Calculates the beta of the stock, which measures its systematic risk relative to the market.

Expected Return Calculation:

• The CAPM formula is used to calculate the expected return based on the risk-free rate, beta, and market risk premium.

Result Printing:

• The calculated beta and expected return are printed to the console.

Note:

The risk-free rate can be obtained from various sources, such as Treasury yields or other risk-free assets. The CAPM is a simplified model and may not perfectly predict future returns. It’s important to consider other factors, such as company-specific risks and market conditions, when making investment decisions. (more advanced techniques like time-varying beta and factor models.)