Comparing Stock Returns

I. Calculating Mean Returns and Variance

➤ Mean Return (μ)

• The average return a stock has generated over a specified time horizon.

• High mean returns indicate strong performance, but must be evaluated in context of risk.

➤ Variance (σ²)

• Measures the degree of fluctuation around the mean return.

• High variance implies greater uncertainty, while low variance indicates consistency.

II. Sharpe Ratio: Return per Unit of Total Risk

➤ Formula

Sharpe Ratio= \frac{Rp-Rf}{\sigma}

• Rp​ = portfolio/asset return

• Rf​ = risk-free rate

• σ = total standard deviation of returns

➤ Interpretation

III. Sortino Ratio: Return per Unit of Downside Risk

➤ Formula

Sortino Ratio=\frac{Rp-Rf}{\sigma}

Where σ​ is the downside deviation, measuring only harmful volatility.

➤ Interpretation

IV. Visualization: Translating Metrics into Insight

➤ Tools

• Risk-Return Scatterplots: Pinpoint dominant and efficient assets.

• Cumulative Return Curves: Evaluate long-term compounding performance.

• Bar Charts of Sharpe/Sortino Ratios: Compare multiple stocks or funds directly.

• Box Plots and Distributions: Understand volatility, skewness, and outliers.

V. How These Metrics Drive Investment and Trading Decisions

🟢 When Buying or Investing in a Stock:

🔄 When Trading (Short-Term or Tactical):

🧠 Final Thought: The Elegant Equation for Strategic Investing

A stock is not a good investment just because it grows, and not a bad investment just because it fluctuates. What defines a superior stock is the quality of its return relative to the risk taken to earn it.

📍Bottom Line

To buy, hold, or trade a stock intelligently:

• Use mean and variance to measure base performance and volatility.

• Apply Sharpe and Sortino ratios to ensure returns are worth the risk.

• Visualize the data to spot outliers, patterns, and efficient opportunities.

🧮 1. Mean Return

Assume returns are in cells A2:A13:

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=AVERAGE(A2:A13)

📉 2. Variance of Returns

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=VAR.P(A2:A13) ← population variance =VAR.S(A2:A13) ← sample variance (more common)

💡 3. Standard Deviation of Returns

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=STDEVP(A2:A13) ← population standard deviation =STDEV.S(A2:A13) ← sample standard deviation

📊 4. Sharpe Ratio

Assume:

• Returns: A2:A13

• Risk-free rate: 2% (entered in cell B1 as 0.02)

Formula:

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=(AVERAGE(A2:A13) - B1) / STDEV.S(A2:A13)

📉 5. Sortino Ratio

Assume:

• Returns in A2:A13

• Risk-free rate (target return) in B1
  Step 1 – Downside Deviation (only returns below target):

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=SQRT(AVERAGE(FILTER((A2:A13 - B1)^2, A2:A13 < B1)))

Step 2 – Sortino Ratio:

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=(AVERAGE(A2:A13) - B1) / SQRT(AVERAGE(FILTER((A2:A13 - B1)^2, A2:A13 < B1)))

📈 1. Mean Return

• What it shows: The average past return over a period.

• How it helps: Gives a baseline idea of how a stock has performed.

• Investment insight: Choose stocks with strong historical returns, but not alone — returns must be evaluated in relation to risk.

⚠ 2. Variance & Standard Deviation

• What it shows: How wildly returns swing — the volatility.

• How it helps: High variance means more uncertainty; low variance means more consistency.

• Investment insight: Stable stocks are better for long-term investing. More volatile ones may suit short-term trading or high-risk bets.

📊 3. Sharpe Ratio

• What it shows: How much return you get per unit of total risk.

• How it helps: Tells you if the reward is worth the risk.

• Investment insight: A high Sharpe Ratio (>1 or >2) suggests the stock is efficient — a good return with manageable risk. That’s a buy signal for diversified portfolios.

📉 4. Sortino Ratio

• What it shows: Return per unit of downside risk (only the bad volatility).

• How it helps: Focuses only on harmful movements.

• Investment insight: A high Sortino Ratio (>2) signals a stock that gives returns without many losses. Ideal for conservative or long-term investors.

🧠 5. Putting It Together: In Practice

When evaluating a stock:

• Look for a high mean return.

• Check if the volatility is manageable (not too wild).

• Prefer high Sharpe and Sortino ratios — they tell you the stock is doing well without exposing you to bad risk.