R fo Financial Analysis: A Comprehensive Guide by Schwartz Alice & Van Der Post Hayden

Author:Schwartz, Alice & Van Der Post, Hayden
Language: eng
Format: epub
Publisher: Reactive Publishing
Published: 2023-12-18T00:00:00+00:00

```r

library(PerformanceAnalytics)

# Historical stock and market returns

stock_returns <- c(0.12, 0.18, 0.14, 0.15, 0.10)

market_returns <- c(0.10, 0.15, 0.13, 0.12, 0.09)

risk_free_rate <- 0.03

# Calculate excess returns

excess_stock_returns <- stock_returns - risk_free_rate

excess_market_returns <- market_returns - risk_free_rate

# Compute beta for the stock

stock_beta <- cov(excess_stock_returns, excess_market_returns) / var(excess_market_returns)

# Calculate expected returns using CAPM

expected_stock_returns <- risk_free_rate + (stock_beta * (mean(excess_market_returns)))

# Compute Jensen's Alpha

jensen_alpha <- mean(excess_stock_returns) - expected_stock_returns

```

This snippet employs the `PerformanceAnalytics` package to ascertain the alpha of a stock, using historical data to evaluate its performance against the broader market. A positive alpha indicates that the portfolio manager has added value, generating returns greater than those warranted by the market risk taken.

Beyond Alpha: A Constellation of Metrics**

While alpha offers insights into risk-adjusted performance, it doesn't stand alone. Other metrics like the Sharpe ratio, Sortino ratio, and Treynor ratio complement alpha, each bringing a unique perspective to the analysis. For example, the Sharpe ratio measures return per unit of total risk (standard deviation), while the Sortino ratio considers only downside risk. The Treynor ratio, much like alpha, evaluates returns based on market risk (beta), but unlike alpha, it does not subtract the expected CAPM return, providing a different angle on risk-adjusted performance.

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