Financial Risk Manager Part 2

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Explanation:

Explanation

To calculate the 1-day 99% VaR of the portfolio, we need to map the portfolio to a position in the underlying stock TUV using delta approximation:

Delta Analysis:

Deep in-the-money call options: delta ≈ 1
Deep out-of-the-money call options: delta ≈ 0
Forward contracts: delta = 1

Net Portfolio Delta (D_p):

5,000 deep ITM calls × delta 1 = 5,000
20,000 deep OTM calls × delta 0 = 0
10,000 forwards × delta 1 = 10,000
Total D_p = 15,000

VaR Calculation Parameters:

Confidence level (99%): α = 2.326
Stock price: S = USD 52
Portfolio delta: D_p = 15,000
Annual volatility: σ = 0.12
Trading days: 252
Time horizon: 1 day

1-day VaR Formula:

VaR = α × S × D_p × σ × √(1/252)

VaR = α × S × D_p × σ × √(1/252)

Calculation:

VaR = 2.326 × 52 × 15,000 × (0.12/√252)
    = 2.326 × 52 × 15,000 × (0.12/15.8745)
    = 2.326 × 52 × 15,000 × 0.00756
    = 2.326 × 52 × 113.4
    = 2.326 × 5,896.8
    = USD 13,714.67

VaR = 2.326 × 52 × 15,000 × (0.12/√252)
    = 2.326 × 52 × 15,000 × (0.12/15.8745)
    = 2.326 × 52 × 15,000 × 0.00756
    = 2.326 × 52 × 113.4
    = 2.326 × 5,896.8
    = USD 13,714.67

The portfolio is approximately gamma neutral, so delta approximation is appropriate. The closest amount to USD 13,714.67 is USD 13,715.

Explanation:

Explanation

To calculate the 1-day 99% VaR of the portfolio, we need to map the portfolio to a position in the underlying stock TUV using delta approximation:

Delta Analysis:

Deep in-the-money call options: delta ≈ 1
Deep out-of-the-money call options: delta ≈ 0
Forward contracts: delta = 1

Net Portfolio Delta (D_p):

5,000 deep ITM calls × delta 1 = 5,000
20,000 deep OTM calls × delta 0 = 0
10,000 forwards × delta 1 = 10,000
Total D_p = 15,000

VaR Calculation Parameters:

Confidence level (99%): α = 2.326
Stock price: S = USD 52
Portfolio delta: D_p = 15,000
Annual volatility: σ = 0.12
Trading days: 252
Time horizon: 1 day

1-day VaR Formula:

VaR = α × S × D_p × σ × √(1/252)

VaR = α × S × D_p × σ × √(1/252)

Calculation:

VaR = 2.326 × 52 × 15,000 × (0.12/√252)
    = 2.326 × 52 × 15,000 × (0.12/15.8745)
    = 2.326 × 52 × 15,000 × 0.00756
    = 2.326 × 52 × 113.4
    = 2.326 × 5,896.8
    = USD 13,714.67

VaR = 2.326 × 52 × 15,000 × (0.12/√252)
    = 2.326 × 52 × 15,000 × (0.12/15.8745)
    = 2.326 × 52 × 15,000 × 0.00756
    = 2.326 × 52 × 113.4
    = 2.326 × 5,896.8
    = USD 13,714.67

The portfolio is approximately gamma neutral, so delta approximation is appropriate. The closest amount to USD 13,714.67 is USD 13,715.

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A fund manager owns a portfolio of options on TUV, a non-dividend paying stock. The portfolio is made up of 5,000 deep in-the-money call options on TUV and 20,000 deep out-of-the-money call options on TUV. The portfolio also contains 10,000 forward contracts on TUV. Currently, TUV is trading at USD 52. Assuming 252 trading days in a year, the volatility of TUV is 12% per year, and that each of the option and forward contracts is on one share of TUV, which of the following amounts would be closest to the 1-day 99% VaR of the portfolio?

Real Exam

Community

LLeetQuiz

USD 11,557

9.4%

USD 12,627

12.5%

USD 13,715

71.9%

USD 32,000

6.3%