Investment Risk Management

📈 Monthly Returns

  • Definition: The percentage change in a stock's value from the start to the end of each month.

  • Formula:

Purpose: Breaks down performance over shorter periods to detect seasonal trends, momentum, or volatility patterns.

Kid-Friendly Notes

What it is:
“How much money the stock made or lost each month.”

📉 Standard Deviation (σ)

  • Definition: Measures how much monthly returns deviate from the average return.

  • Indicates:

    • High σ = High risk/volatility.

    • Low σ = Stable returns.

Strategic use: Investors may prefer lower σ for long-term holdings, higher σ if seeking aggressive gains with controlled exposure.

Kid-Friendly Notes

What it is:
“How bumpy the ride is.”

If a stock goes up and down a lot, it’s like a rollercoaster. That’s high risk. If it moves just a little, like a merry-go-round, that’s low risk.

📊 Task 3: Calculating Beta (β)

📐 Beta (β)

  • Definition: A stock’s sensitivity to movements in the overall market (systematic risk).

  • Formula: β = Covariance (stock, market) / Variance (market)

📌 Interpretation:

  • β=1: Stock moves in line with the market.

  • β>1: More volatile than the market.

  • β<1: Less volatile (defensive).

  • β<0: Moves opposite to the market.

🧠 Strategic use:

  • Use high-beta stocks in bull markets for leverage.

  • Use low-beta stocks in downturns for protection.

  • Beta informs portfolio diversification and asset allocation.

    Kid-Friendly Notes

    What it is:
    “How much a stock moves when the whole market moves.”

    The market is like a dog pulling a leash. Some stocks run fast with it (high beta), some walk slowly (low beta), and some even go backward (negative beta).

📐 Task 4: Calculating Treynor Ratio

📊 Treynor Ratio (TR)

  • Definition: Measures return per unit of systematic risk (beta).

  • Formula:

📌 Interpretation:

  • High TR → Better risk-adjusted return for market risk.

  • It complements Sharpe Ratio, but focuses only on systematic risk, not total risk.

🧠 Strategic use:

  • Ideal for comparing well-diversified portfolios.

  • Helps assess performance of fund managers who take systematic risk.

    Kid-Friendly Notes

    What it is:
    “How many points you score for each level of danger from the market.”

    You’re in a video game. If you earn lots of coins without facing too many monsters (market risk), you’re really good at playing. That’s a high Treynor Ratio.

📉 Task 5: Calculating Value at Risk (VaR)

🧮 Value at Risk (VaR)

  • Definition: The maximum expected loss over a period, at a given confidence level.

  • Formula (Parametric Method): VaR=Z×σ×t​

  • Where:

    • Z-score for confidence level (e.g. 1.65 for 95%)

    • σ = standard deviation of returns

    • t = time horizon

📌 Interpretation:

  • E.g. “At 95% confidence, we won’t lose more than $X in a day.”

  • Types: Parametric (normal), Historical, Monte Carlo

🧠 Strategic use:

  • Essential for capital allocation, stress testing, and regulatory compliance.

  • Helps managers cap tail risk and plan for worst-case scenarios.

    Kid-Friendly Notes

    What it is:
    “How much money you might lose on a really bad day.”

    You have $100. VaR tells you, “You might lose $5 tomorrow — but only if things go really wrong.” It’s like checking the weather for money storms.

🧠 Summary: Decision-Making Framework

Metric

Purpose

Use For

Mean Return

Measures average gain

Return expectation

Std. Deviation

Measures total risk

Volatility assessment

Beta (β)

Sensitivity to market

Portfolio construction

Sharpe Ratio

Return per total risk

Comparing diversified assets

Sortino Ratio

Return per downside risk

Managing drawdowns

Treynor Ratio

Return per market risk

Evaluating fund managers

VaR

Worst-case loss estimation

Risk control & capital planning

✅ Monthly Returns

excel

複製編輯

=(B2 - B1) / B1

(Assumes B1 and B2 are consecutive monthly closing prices)

📉 Standard Deviation of Returns

excel

複製編輯

=STDEV(C2:C13)

(Assumes C2:C13 contains monthly return values)

📐 Beta (β)

excel

複製編輯

=SLOPE(C2:C13, D2:D13)

(C2:C13 = stock returns, D2:D13 = market returns)

🏆 Treynor Ratio

excel

複製編輯

=(AVERAGE(C2:C13) - RiskFreeRate) / Beta

Replace RiskFreeRate and Beta with actual values or cell references

🚨 Value at Risk (VaR) – Parametric (95%)

excel

複製編輯

=NORM.S.INV(0.05) * STDEV(C2:C13)

(Negative number = expected loss)

📊 Sharpe Ratio

excel

複製編輯

=(AVERAGE(C2:C13) - RiskFreeRate) / STDEV(C2:C13)

📉 Sortino Ratio

excel

複製編輯

=(AVERAGE(C2:C13) - RiskFreeRate) / STDEVP(FILTER(C2:C13, C2:C13 < RiskFreeRate))

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