The measures of the risk of a stock are statistical indicators that help investors and analysts assess how much uncertainty or volatility is associated with a particular investment. There are different ways to measure risk, depending on the perspective and the purpose of the analysis. Here are some common risk measures and what they mean:
- Standard deviation is a measure of how much the returns of a stock deviate from their average or expected value. A high standard deviation means that the stock has a wide range of possible outcomes, which implies more risk. A low standard deviation means that the stock has a narrow range of possible outcomes, which implies less risk.
- Beta is a measure of how much the returns of a stock move in relation to the returns of the market or a benchmark index. A beta of 1 means that the stock moves in sync with the market. A beta greater than 1 means that the stock is more volatile than the market. A beta less than 1 means that the stock is less volatile than the market.
- R-squared is a measure of how well the returns of a stock can be explained by the returns of the market or a benchmark index. An R-squared of 100% means that the stock is perfectly correlated with the market. An R-squared of 0% means that the stock is completely independent of the market. An R-squared between 0% and 100% means that the stock is partially influenced by the market.
- Sharpe ratio is a measure of how much excess return a stock generates per unit of risk. The excess return is the difference between the return of the stock and the return of a risk-free asset, such as a Treasury bill. The risk is measured by the standard deviation of the stock. A high Sharpe ratio means that the stock has a high reward-to-risk ratio. A low Sharpe ratio means that the stock has a low reward-to-risk ratio.
- Alpha is a measure of how much the returns of a stock exceed or fall short of the returns of the market or a benchmark index, after adjusting for the risk of the stock. A positive alpha means that the stock outperforms the market. A negative alpha means that the stock underperforms the market.
Basic Theory
Standard Deviation:
The standard deviation is a statistical measure of the dispersion of returns. In the context of stock market
analysis, it indicates how much the stock’s returns deviate from its average return. A higher standard deviation
suggests a more volatile stock, implying a greater degree of risk.
Beta:
Beta measures a stock’s sensitivity to market movements. A beta of 1 indicates that the stock tends to move with
the market, while a beta greater than 1 implies higher volatility compared to the market. A beta less than 1
suggests lower volatility.
Procedures
Step 1: Data Collection
Collect historical stock price data. You can use financial websites or APIs to get this information. For this
demonstration, we’ll consider the daily closing prices of Stock A over the past year.
Step 2: Calculate Daily Returns
Use Excel to calculate the daily returns. Daily return (DR) is calculated as follows:
![\[ DR_t = \frac{{\text{{Close Price}}_t - \text{{Close Price}}_{t-1}}}{{\text{{Close Price}}_{t-1}}} \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-c36e757dc0ad80822aa02b4383a50826_l3.svg "Rendered by QuickLaTeX.com")
Step 3: Calculate Standard Deviation
Compute the standard deviation of the daily returns using Excel’s STDEV function.
![\[ \text{{Standard Deviation}} = \text{{STDEV}}(\text{{Daily Returns}}) \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-3d7d3e41d416855cba8e4be9949a3568_l3.svg "Rendered by QuickLaTeX.com")
Step 4: Calculate Beta
Obtain the market index returns (e.g., S&P 500) and the stock returns. Calculate the covariance and variance
using Excel functions, and then calculate beta:
![\[ \text{{Beta}} = \frac{{\text{{Covariance}}(\text{{Stock Returns}}, \text{{Market Returns}})}} {{\text{{Variance}}(\text{{Market Returns}})}} \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-87d44ae8ea4bc5354573ca5c66c6013c_l3.svg "Rendered by QuickLaTeX.com")
Real-world Scenario
Let’s consider Stock A and the S&P 500 for the past year. The data is as follows:
- Stock A Closing Prices:
- January 1, 2023: $100
- December 31, 2023: $120
- S&P 500 Index:
- January 1, 2023: 4,000
- December 31, 2023: 4,500
Excel Table
| Date | Stock A Closing Price | S&P 500 Index |
|---|---|---|
| 01/01/2023 | $100 | 4,000 |
| 12/31/2023 | $120 | 4,500 |
Calculation
- Calculate Daily Returns for Stock A.
- Calculate the Standard Deviation of Daily Returns.
- Obtain Daily Returns for the S&P 500.
- Calculate Beta.
Result
Standard Deviation of Stock A: 
(Assuming this value
for demonstration purposes.)
Beta of Stock A: 
(Assuming this value for demonstration purposes.)
Alternative Approaches
Historical Volatility:
Calculate historical volatility using the average true range (ATR) or other methods to provide a different
perspective on stock risk.
Implied Volatility:
Consider implied volatility derived from options pricing to gauge market expectations about future stock
volatility.
Monte Carlo Simulation:
Simulate various future scenarios using a Monte Carlo simulation to assess potential stock price movements and
associated risks.
