Explanation

When LVaR (Liquidity-adjusted Value at Risk) is expressed as asset VaR plus the cost of liquidation under normal time, the ratio LVaR/VaR represents how much larger the liquidity-adjusted risk measure is compared to the standard VaR.

Let's analyze each option:

A. It should fall in proportion with the assumed spread - This is incorrect. When the spread increases, the liquidation cost component of LVaR increases, making LVaR larger relative to VaR. Therefore, the ratio LVaR/VaR should increase, not fall, with higher spreads.

B. It should fall as the confidence level increases - This is incorrect. As confidence level increases, both VaR and LVaR increase, but the liquidation cost component remains relatively constant. The ratio typically becomes closer to 1 at higher confidence levels since the liquidation cost becomes a smaller proportion of the total risk measure.

C. It should rise as the holding period increases - This is CORRECT. As the holding period increases:

• VaR increases proportionally to the square root of time (√T)
• The liquidation cost component remains relatively constant (or may increase at a different rate)
• Therefore, the ratio LVaR/VaR = (VaR + liquidation cost)/VaR = 1 + (liquidation cost/VaR)
• Since VaR increases with √T while liquidation cost remains relatively stable, the ratio liquidation cost/VaR decreases, making the overall ratio approach 1 from above

Actually, let me correct this analysis. When holding period increases, VaR increases (√T scaling), but the liquidation cost component typically remains more stable. Therefore, LVaR/VaR ratio should actually decrease as holding period increases, not rise.

The correct answer should be that the ratio should fall as the holding period increases, but since option C says "rise" and that's incorrect, and options A and B are also incorrect, there appears to be an issue with the question options.

Based on standard LVaR theory:

• LVaR = VaR + 0.5 × spread × position
• LVaR/VaR = 1 + (0.5 × spread × position)/VaR
• As holding period increases, VaR increases (√T), so the ratio decreases
• As confidence level increases, VaR increases, so the ratio decreases
• As spread increases, the ratio increases

Therefore, none of the given options are correct based on standard LVaR formulation.