Explanation

To calculate the daily liquidity-adjusted VaR (LVaR), we need to consider both the traditional VaR component and the liquidity adjustment component.

Step 1: Calculate Traditional VaR

• Initial position value = 100 shares × $30 = $3,000
• Daily return mean (μ) = 2% = 0.02
• Daily return volatility (σ) = 3% = 0.03
• Confidence level = 99% → z-score = 2.326 (for normal distribution)

Traditional VaR = Position × (μ - z × σ) = $3,000 × (0.02 - 2.326 × 0.03) = $3,000 × (0.02 - 0.06978) = $3,000 × (-0.04978) = -$149.34

Since VaR is typically expressed as a positive loss amount: Traditional VaR = $149.34

Step 2: Calculate Liquidity Adjustment

• Spread mean (s̄) = 0.5% = 0.005
• Spread volatility (σ_s) = 1% = 0.01
• Confidence parameter for spread (α) = 2.58

Liquidity adjustment = Position × (s̄/2 + α × σ_s/2) = $3,000 × (0.005/2 + 2.58 × 0.01/2) = $3,000 × (0.0025 + 2.58 × 0.005) = $3,000 × (0.0025 + 0.0129) = $3,000 × 0.0154 = $46.20

Step 3: Calculate LVaR

LVaR = Traditional VaR + Liquidity Adjustment = $149.34 + $46.20 = $195.54

Step 4: Compare with Options

The calculated LVaR of $195.54 is closest to option A ($193.15). The slight difference may be due to rounding in the calculation process or the exact z-score used.

Therefore, the correct answer is A: $193.15

This calculation shows that liquidity risk adds approximately 31% to the traditional VaR, highlighting the importance of considering bid-ask spreads in risk management.