Podcast
Questions and Answers
What is the annualized volatility for a 3-month period according to the provided data?
What is the annualized volatility for a 3-month period according to the provided data?
- 8.38%
- 15.79%
- 11.42% (correct)
- 12.32%
How is the systematic Value at Risk (VaR) for a portfolio of Nestlé stocks calculated?
How is the systematic Value at Risk (VaR) for a portfolio of Nestlé stocks calculated?
- 10 * SharePrice(Nestlé) * VaR(SMI) * Beta (correct)
- SharePrice(Nestlé) * VaR(systematic) * Beta
- 10 * SharePrice * VaR(Nestlé) * Alpha
- VaR(Nestlé) + VaR(SMI) - Beta
What is the correct interpretation of the calculated specific VaR for Nestlé?
What is the correct interpretation of the calculated specific VaR for Nestlé?
- It reflects the risk related solely to the particular characteristics of Nestlé stocks, separate from market movements. (correct)
- It shows the average market risk affecting all stocks in the index.
- It is the same as the total VaR calculated for Nestlé.
- It indicates the total risk associated with Nestlé shares.
What is the calculated amount for total VaR of Nestlé?
What is the calculated amount for total VaR of Nestlé?
What is the value of the 10-day volatility provided in the data?
What is the value of the 10-day volatility provided in the data?
Which parameter affects the calculation of both systematic and specific VaR for Nestlé stocks?
Which parameter affects the calculation of both systematic and specific VaR for Nestlé stocks?
What is the contribution of systematic VaR to the total VaR for Nestlé?
What is the contribution of systematic VaR to the total VaR for Nestlé?
How do you calculate specific VaR using total VaR and systematic VaR?
How do you calculate specific VaR using total VaR and systematic VaR?
What does the Beta value represent in the context of the VaR calculations?
What does the Beta value represent in the context of the VaR calculations?
What is the systematic VaR calculated for the portfolio of 10 Nestlé stocks?
What is the systematic VaR calculated for the portfolio of 10 Nestlé stocks?
What is the calculated Value at Risk (VaR) for a portfolio of 10 Nestlé shares over 10 days?
What is the calculated Value at Risk (VaR) for a portfolio of 10 Nestlé shares over 10 days?
Which hypothesis suggests that a portfolio of 10 Nestlé stocks may lose more than 51.43 CHF with a specified probability?
Which hypothesis suggests that a portfolio of 10 Nestlé stocks may lose more than 51.43 CHF with a specified probability?
What is the formula to calculate specific Value at Risk for Nestlé stocks?
What is the formula to calculate specific Value at Risk for Nestlé stocks?
In the context of Value at Risk, what does the symbol $eta$ represent?
In the context of Value at Risk, what does the symbol $eta$ represent?
How often is it hypothesized that the loss of the portfolio will exceed the calculated VaR of 51.43 CHF?
How often is it hypothesized that the loss of the portfolio will exceed the calculated VaR of 51.43 CHF?
What is the implied relationship between specific and systematic risk in the context of VaR?
What is the implied relationship between specific and systematic risk in the context of VaR?
What is the expected value of systematic risk relative to total risk in the formula provided?
What is the expected value of systematic risk relative to total risk in the formula provided?
What does a beta value of 0.96 signify in the context of Nestlé's stock?
What does a beta value of 0.96 signify in the context of Nestlé's stock?
What type of hypothesis does H0 represent regarding the maximum loss of the portfolio?
What type of hypothesis does H0 represent regarding the maximum loss of the portfolio?
What is the primary assumption regarding the return distribution of the Nestlé stock in the Value at Risk calculation?
What is the primary assumption regarding the return distribution of the Nestlé stock in the Value at Risk calculation?
Which of the following confidence levels is used to determine the Value at Risk for the Nestlé stock in this context?
Which of the following confidence levels is used to determine the Value at Risk for the Nestlé stock in this context?
In the calculation of 10 days volatility of Nestlé stock, which formula is applied?
In the calculation of 10 days volatility of Nestlé stock, which formula is applied?
What is the significance of using the factor 2.33 in the Value at Risk calculation?
What is the significance of using the factor 2.33 in the Value at Risk calculation?
What is the current price of a Nestlé share as given in the example?
What is the current price of a Nestlé share as given in the example?
When calculating the Value at Risk (VaR) for the portfolio of Nestlé stocks, what is the holding period typically assumed?
When calculating the Value at Risk (VaR) for the portfolio of Nestlé stocks, what is the holding period typically assumed?
What is the calculated Value at Risk (VaR) for 1 CHF of the Nestlé stock at a confidence level of 99%?
What is the calculated Value at Risk (VaR) for 1 CHF of the Nestlé stock at a confidence level of 99%?
What is the formula for calculating Value at Risk (VaR) for Nestlé stock as per the example?
What is the formula for calculating Value at Risk (VaR) for Nestlé stock as per the example?
Which of the following does NOT contribute to the calculation of Value at Risk (VaR) for Nestlé stock?
Which of the following does NOT contribute to the calculation of Value at Risk (VaR) for Nestlé stock?
Why is it essential to determine a confidence level when calculating Value at Risk?
Why is it essential to determine a confidence level when calculating Value at Risk?
What is the resulting Value at Risk (VaR) for the position after implementing a 100% hedge against the SMI market?
What is the resulting Value at Risk (VaR) for the position after implementing a 100% hedge against the SMI market?
Which of the following does NOT contribute to the residual VaR calculation?
Which of the following does NOT contribute to the residual VaR calculation?
What does the term 'aggregate residual VaR' refer to in the context of a portfolio?
What does the term 'aggregate residual VaR' refer to in the context of a portfolio?
What is the impact of hedging SMI futures on the Value at Risk of Nestlé shares?
What is the impact of hedging SMI futures on the Value at Risk of Nestlé shares?
In relation to VaR, what does 'stock beta' specifically measure?
In relation to VaR, what does 'stock beta' specifically measure?
What does the phrase 'To aggregate does not mean simple addition' imply in the context of VaR?
What does the phrase 'To aggregate does not mean simple addition' imply in the context of VaR?
After hedging, if the net VaR of the investment is 30.50 CHF, what can we infer about the effectiveness of the hedge?
After hedging, if the net VaR of the investment is 30.50 CHF, what can we infer about the effectiveness of the hedge?
Which component is essential in calculating the historical simulation of VaR?
Which component is essential in calculating the historical simulation of VaR?
What type of risk does the residual VaR represent after hedging?
What type of risk does the residual VaR represent after hedging?
What is a primary goal of using VaR in portfolio risk management?
What is a primary goal of using VaR in portfolio risk management?
Flashcards
Value at Risk (VaR)
Value at Risk (VaR)
The maximum potential loss that can occur over a given period of time for a given confidence level.
Specific Risk
Specific Risk
The risk that is specific to an individual asset or company.
Systematic Risk
Systematic Risk
The risk that affects the entire market or a broad industry.
Average Return
Average Return
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Volatility
Volatility
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10-day Volatility
10-day Volatility
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Value at Risk (VaR) for 1 CHF
Value at Risk (VaR) for 1 CHF
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Confidence Level
Confidence Level
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Time Horizon
Time Horizon
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Standard Deviation Factor
Standard Deviation Factor
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VaR of a Portfolio
VaR of a Portfolio
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Beta
Beta
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Risk
Risk
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VaR Hypothesis
VaR Hypothesis
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Specific & Systematic VaR Decomposition
Specific & Systematic VaR Decomposition
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Systematic VaR
Systematic VaR
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Specific VaR
Specific VaR
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Total VaR
Total VaR
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Specific and Systematic Risk Analysis
Specific and Systematic Risk Analysis
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VaR Calculation
VaR Calculation
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Risk Management
Risk Management
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Residual Risk
Residual Risk
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Hedging
Hedging
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Futures Contract
Futures Contract
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Historic Simulation
Historic Simulation
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Aggregate Risk
Aggregate Risk
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Residual VaR
Residual VaR
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Study Notes
Portfolio Theory and Behavioral Finance
- Course: w.MA.XX.IN, 19HS.2024-HS
- Chapter: 4b - Value at Risk
- Instructors: Dr.-Ing. Martin Schnauss, CFA, FRM / Dr. Jan-Alexander Posth
Topics
- Value at Risk (VaR): Analysis of specific and systematic risk.
- Example: Nestlé share price analysis.
- Breakdown of specific and systematic risks.
Value at Risk: Example Nestlé Share
- Nestlé share price on January 12, 2017: 76.50 CHF.
- Source: boerse.de
- Nestlé is among the top defensive champions in the boerse.de-Champions-Defensiv-Index (BCDI).
- Stock type: Equity (Aktie)
- Industry: Beverages, food, and tobacco.
- Sector: Food.
- Country: Switzerland.
Challenge: Value at Risk Calculation
- Determine the Value-at-Risk (VaR) for a portfolio comprising 10 Nestlé stocks.
- Required factors:
- Confidence level (e.g., 99%, meaning a 1% chance of exceeding the loss).
- Time horizon (e.g., 10 days).
Assumptions
- The return distribution of the Nestlé stock is normally distributed.
- The average return over 10 days is 0%.
- Current price is 76.50 CHF.
- Objective: Calculate VaR for the Nestlé stock with 99% confidence level.
Step 1: Calculation of the 10-Day Volatility of Nestlé
- 10-day volatility = 2.89% (Calculated from historical data).
Step 2: Calculation of Nestlé Value at Risk for 1 CHF
- VaR(Nestlé, 99%, 10d) = 1 CHF x 2.89% x 2.33 = 0.0672 CHF
- The factor 2.33 is the 99% percentile of the standard normal distribution.
Step 3: Calculation of Value at Risk for a portfolio of 10 Nestlé shares
- VaR(Portfolio) = 10 * 76.50 CHF * VaR(Nestlé, 99%, 10d) = 51.43 CHF.
Hypothesis
- H₀: A portfolio of 10 Nestlé stocks will not lose more than 51.43 CHF in 10 days with 99% probability.
- H₁: The portfolio of 10 Nestlé stocks could lose over 51.43 CHF in 10 days, with 1% probability.
- H₂: Once every 1000 days, this 10-stock portfolio will exceed a 51.43 CHF loss in 10 days.
Value at Risk: Specific and Systematic Risk
- Splitting risk into systematic and specific components for VaR calculations.
- Systematic and specific risks are uncorrelated.
- Formula for total variance: σ²total = β²σ²systematic + σ²specific
- Formula for specific VaR: σspecific = √σ²total - β²σ²systematic
Step 1: Calculation of Nestlé Beta
- Beta calculation regarding the SMI (Swiss Market Index).
- Average beta value: 0.96.
- Note: Beta values fluctuate; they're past-based for future projections.
Step 2: Calculation of SMI 10-Day Volatility
- 10 days volatility for the SMI is 2.42%.
Step 3: Calculation of Systematic VaR
- VaR(systematic) = 10 * 76.50 CHF * 2.33 * 2.42% * 0.96 = 41.41 CHF.
Calculation of Total VaR
- Total VaR = Systematic VaR + Specific VaR = 41.41 CHF + 30.50 CHF = 51.43 CHF.
- 51.43 CHF is the total VaR for the portfolio of 10 Nestlé shares over a 10-day period (calculated with a 99% confidence level).
- This calculation considers both the specific risk of Nestlé and the systematic risk related to the SMI market.
Interpretation of 30.50 CHF
- The relevant question is how the VaR for the 10 Nestlé shares would change if they were hedged 100% against SMI market risk using SMI futures.
Summary
- Key VaR values:
- Systematic VaR: 41.41 CHF
- Specific VaR: 30.50 CHF
- Total VaR: 51.43 CHF
- Calculation includes risk factors (e.g. historical volatility, stock beta, and index volatility).
- Historical Simulation of risk factors.
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Description
This quiz focuses on Chapter 4b of Portfolio Theory and Behavioral Finance, specifically analyzing Value at Risk (VaR) using the example of Nestlé's share price. Participants will learn to calculate VaR for a portfolio and understand the implications of specific and systematic risks. Test your knowledge of risk management techniques in finance.
