Learn About Measurement Of Risk From Stock Market Course

3.1 Volatility

One of the clearest ways to understand risk in investments is through volatility, which represents the degree of uncertainty in future outcomes. Investors usually form an expectation about returns, but the actual results often differ. This gap between expected return and realized return is where volatility comes into play.

Volatility essentially measures how much the price of a security fluctuates around its average or expected level. A stock that moves steadily within a narrow band is considered less volatile, while one that swings sharply up and down is highly volatile. Greater volatility means greater uncertainty, and therefore, higher risk.

Examples

• Adani Group stocks (2023): After the Hindenburg Research report alleged governance issues, Adani stocks saw extreme volatility. Prices crashed by over 50% in weeks, then partially recovered as investor confidence slowly returned.
• Zomato IPO (2021): The food delivery giant’s shares surged initially but later experienced sharp swings as investors debated profitability in the tech-driven startup space.
• Banking sector (2020 pandemic): During COVID-19 lockdowns, bank stocks like SBI and ICICI Bank dropped steeply due to fears of rising NPAs, then rebounded strongly as the economy reopened.
• Rupee vs Dollar (2022–23): Currency volatility impacted IT exporters positively (Infosys, TCS gained from a weaker rupee) but hurt import-heavy industries like oil and aviation.

Investor Insight

• High volatility= greater uncertainty, often linked to external shocks (policy changes, global crises, corporate scandals).
• Low volatility= more predictable returns, often seen in stable sectors like FMCG or utilities.
• Measuring past volatility helps investors gauge the riskiness of a security, though it does not guarantee future stability.

3.2 Standard Deviation

Risk in finance is essentially the uncertainty of returns. Two investments may have the same average return, but if one fluctuates more than the other, it is considered riskier. Standard deviation captures this variability.

Let’s compare Company X and Company Y. Both have similar expected returns, but their spreads differ.

Step 1: Returns Data

Arithmetic Mean:

• Company X → 62/5 =12.4%
• Company Y → 52/5 =10.4%

Both companies have comparable average returns, but the spread of Company X is wider.

Step 2: Probability Distribution & Variance

Company X

Expected Return (E) = 12.25% Variance = 0.002821 Standard Deviation = √0.0002821=5.3%

Company Y

Expected Return (E) = 11% Variance = 0.000236 Standard Deviation = √0.000236 =1.5%

Step 3: Comparison

3.3 Beta

Beta (β) is a measure of systematic risk — the risk that arises from overall market movements and cannot be diversified away. It shows how sensitive a stock or portfolio is compared to the market index (such as Nifty 50 or S&P 500). Investors use Beta to understand whether a stock will amplify market movements or dampen them.

Key Characteristics of Beta

• β = 1→ The stock moves exactly in line with the market.
• β < 1→ The stock is less volatile than the market (defensive).
• β > 1→ The stock is more volatile than the market (aggressive).
• β < 0→ The stock moves in the opposite direction of the market (hedge asset).

Real-World Examples

Illustration in Practice

Suppose the Nifty 50 rises by 10%:

• A stock with β = 1.3 (Infosys) is expected to rise by 13%.
• A stock with β = 0.7 (NTPC) may rise only 7%.
• A stock with β = -0.2 (Gold ETF) might fall by 2%, providing diversification.

This demonstrates how Beta captures both the direction and magnitude of a stock’s movement relative to the market.

Beta and CAPM (Capital Asset Pricing Model)

Beta is central to CAPM, which estimates the expected return on equity:

Where:

• K_e= Cost of equity (expected return)
• R_f= Risk-free rate (e.g., government bonds)
• R_m= Market return
• β= Stock’s sensitivity to market

Example with Current Numbers

Suppose:

• Risk-free rate (R_f) = 6%
• Market return (R_m) = 12%
• Stock Beta (β) = 1.2

K_{e = 6% +1.2 * (12% -6%)=6%+7.2% =13.2%}

Thus, the investor should expect 13.2% return for taking on the extra risk.

Expanded Insights

Industry Differences

• Utility companies (like NTPC) usually have low betas because their revenues are stable and less dependent on economic cycles.
• Technology firms (like Infosys) often have high betas because their earnings are more sensitive to innovation cycles and market sentiment.

Portfolio Impact

• A portfolio’s overall Beta is the weighted averageof the Betas of its individual stocks.
• Adding a low-beta stock reduces portfolio risk, while adding a high-beta stock increases it.

Negative Beta Assets

• Assets like gold or insurance products sometimes show negative betas, meaning they move opposite to the market.
• These are valuable for diversification, especially during downturns.

3.4 Alpha

Alpha (α) is a measure of how much an investment has outperformed or under-performed compared to what was expected, given its risk level. It is widely used to evaluate the skill of fund managers or the effectiveness of active investment strategies. While Beta explains how much a stock moves with the market, Alpha shows whether the investment has delivered returns beyond those justified by its risk exposure.

Key Points

• Alpha > 0→ The investment has outperformed expectations.
• Alpha < 0→ The investment has under-performed relative to its benchmark.
• Alpha = 0→ The investment performed exactly as expected, given its risk.
• Active Return vs Excess Return→ Active return is measured against a benchmark index (e.g., Nifty 50), while excess return is measured against the risk-free rate.

Formula for Alpha

α=R-R_{f –} β (R_m -R_f)

Where:

• R= Portfolio return
• R_f= Risk-free rate
• β= Systematic risk of the portfolio
• R_m= Market return (benchmark index)

Example with Current Context

Suppose:

• Portfolio return (R) = 22%
• Risk-free rate (R_f) = 6%
• Beta (β) = 1.1
• Market return (R_m) = 14%

α = (0.22-0.06)-1.1 (0.14-0.06)

α =0.16 -0.088=0.072 or 7.2%

This means the portfolio outperformed the benchmark by 7.2% after adjusting for risk.

Formula: Alpha = R − [Rf + β×(Rm − Rf)]

Alpha vs Beta – Comparison