BLOCK 4 2

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Questions and Answers

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?

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?

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?

51.43 CHF Signup and view all the answers

What is the value of the 10-day volatility provided in the data?

2.42% Signup and view all the answers

Which parameter affects the calculation of both systematic and specific VaR for Nestlé stocks?

Beta value Signup and view all the answers

What is the contribution of systematic VaR to the total VaR for Nestlé?

41.41 CHF Signup and view all the answers

How do you calculate specific VaR using total VaR and systematic VaR?

Total VaR - Systematic VaR Signup and view all the answers

What does the Beta value represent in the context of the VaR calculations?

The sensitivity of a stock's returns to market returns. Signup and view all the answers

What is the systematic VaR calculated for the portfolio of 10 Nestlé stocks?

41.41 CHF Signup and view all the answers

What is the calculated Value at Risk (VaR) for a portfolio of 10 Nestlé shares over 10 days?

51.43 CHF Signup and view all the answers

Which hypothesis suggests that a portfolio of 10 Nestlé stocks may lose more than 51.43 CHF with a specified probability?

Hypothesis H1 Signup and view all the answers

What is the formula to calculate specific Value at Risk for Nestlé stocks?

VaR Nestle(specific) = VaR 2Nestle(total) − VaR systematic Signup and view all the answers

In the context of Value at Risk, what does the symbol $eta$ represent?

Market correlation factor Signup and view all the answers

How often is it hypothesized that the loss of the portfolio will exceed the calculated VaR of 51.43 CHF?

Once every 1,000 days Signup and view all the answers

What is the implied relationship between specific and systematic risk in the context of VaR?

Specific and systematic risk are uncorrelated. Signup and view all the answers

What is the expected value of systematic risk relative to total risk in the formula provided?

It is subtracted from total risk. Signup and view all the answers

What does a beta value of 0.96 signify in the context of Nestlé's stock?

The stock is less volatile than the market. Signup and view all the answers

What type of hypothesis does H0 represent regarding the maximum loss of the portfolio?

The portfolio will certainly lose no more than 51.43 CHF. Signup and view all the answers

What is the primary assumption regarding the return distribution of the Nestlé stock in the Value at Risk calculation?

It is normally distributed. Signup and view all the answers

Which of the following confidence levels is used to determine the Value at Risk for the Nestlé stock in this context?

99% Signup and view all the answers

In the calculation of 10 days volatility of Nestlé stock, which formula is applied?

Volatility = Daily Return x Sqrt(10/252) Signup and view all the answers

What is the significance of using the factor 2.33 in the Value at Risk calculation?

It is the number of standard deviations to reach the 99% percentile. Signup and view all the answers

What is the current price of a Nestlé share as given in the example?

76.50 CHF Signup and view all the answers

When calculating the Value at Risk (VaR) for the portfolio of Nestlé stocks, what is the holding period typically assumed?

10 days Signup and view all the answers

What is the calculated Value at Risk (VaR) for 1 CHF of the Nestlé stock at a confidence level of 99%?

0.0672 CHF Signup and view all the answers

What is the formula for calculating Value at Risk (VaR) for Nestlé stock as per the example?

VaR = Price x Volatility x Z-Score Signup and view all the answers

Which of the following does NOT contribute to the calculation of Value at Risk (VaR) for Nestlé stock?

Historical performance over one year Signup and view all the answers

Why is it essential to determine a confidence level when calculating Value at Risk?

To quantify potential maximum loss within a specific probability. Signup and view all the answers

What is the resulting Value at Risk (VaR) for the position after implementing a 100% hedge against the SMI market?

30.50 CHF Signup and view all the answers

Which of the following does NOT contribute to the residual VaR calculation?

Risk-free rate Signup and view all the answers

What does the term 'aggregate residual VaR' refer to in the context of a portfolio?

Combination of systematic and specific risks Signup and view all the answers

What is the impact of hedging SMI futures on the Value at Risk of Nestlé shares?

It reduces the VaR but does not eliminate all residual risk Signup and view all the answers

In relation to VaR, what does 'stock beta' specifically measure?

The volatility of the stock relative to the market Signup and view all the answers

What does the phrase 'To aggregate does not mean simple addition' imply in the context of VaR?

Risk correlations must be taken into account. Signup and view all the answers

After hedging, if the net VaR of the investment is 30.50 CHF, what can we infer about the effectiveness of the hedge?

The hedge only partially reduced risk. Signup and view all the answers

Which component is essential in calculating the historical simulation of VaR?

Past price movements of the asset Signup and view all the answers

What type of risk does the residual VaR represent after hedging?

Both systematic and specific risks Signup and view all the answers

What is a primary goal of using VaR in portfolio risk management?

To quantify the potential maximum loss over a specific time period Signup and view all the answers

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.

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: σ²_total = β²σ²_systematic + σ²_specific
Formula for specific VaR: σ_specific = √σ²_total - β²σ²_systematic

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.