Is higher historical stock volatility associated with higher annualized return?

Investors often assume that taking higher risks generates higher rewards.

However, is this relationship actually supported by historical stock market data?

Our Objective

• Analyze S&P 500 stocks from 2021-2025.
• Calculate stock returns and risk.
• See if higher risk does mean higher returns.

The S&P 500 is an index that tracks the top 500 leading US companies.

Why We Are Using It?

• It helps measure the overall performance of the U.S stock market.
• Allows us to study hundreds of individual stocks.
• Helps us compare stock risk and returns from 2021 - 2025.

• I used S&P 500 stock data from Yahoo Finance
• The data covers from January 2021 - December 2025
• I analyzed 487 stocks that had enough data for the full period
• Annual return measures the average return per year
• Volatility measures how much daily returns changed

Sources Yahoo Finance data through tidyquant

Stock Volatility (Risk)

• Measures how much a stock’s returns fluctuate.
• Higher volatility is where a stock’s price swings rapidly up and down.
• Lower volatility is when a price is relatively stable.

Stock Return:

• Measures how much money an investment gains or loses.
• Higher returns mean better performance.

Stock returns measure how much an investment gains/loses over time

Return Formula

\[ R_{annual} = \left[\left(\frac{P_{end}}{P_{start}}\right)^{1/T} - 1 \right] \times 100 \] Where:

• \(T\) = Number of years between the starting and ending dates.

• \(P_{start}\) = Starting stock price.

• \(P_{end}\) = Ending stock price.

• \(R_{annual}\) = Percentage stock return.

Volatility measures how much a stock’s returns change over time

Standard Deviation Formula: \[ V = s \times \sqrt{252} \] Where:

• \(s\) = Standard deviation of daily returns
• \(252\) = Approximate trading days in a year
• \(V\) = Annualized volatility

top10 <- stock_calculations %>%
slice_max(volatility, n = 10)

cor(stock_calculations$volatility,
    stock_calculations$annual_return)

Insight: CVNA (Carvana) has the highest annualized volatility at approximately 111.2%, followed by BE (Bloom Energy), and SMCI (Super Micro Computer)

Insight: Among the ten most volatile stocks, annualized returns ranged from approximately -23% to 57%. High volatility did not consistently produce high returns

Insight: Across 487 S&P 500 stocks with enough historical data, risk and return showed a weak positive relation (r = 0.144)

Correlation: 0.144

R-squared: \[ R^2 = 0.144^2\approx .021 \] Volatility explains only about 2.1% of the differences in annual returns

Conclusion:

• There is a weak positive relationship between risk and return.
• Higher volatility does not guarantee higher returns.
• Stocks with similar risk can have very different returns.