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Answer: USD 2,076
## Explanation To calculate the liquidity-adjusted daily 95% VaR, we need to consider both the market risk component and the liquidity risk component. ### Step 1: Calculate Market Risk VaR - Position value = 1,000 shares × USD 80 = USD 80,000 - Daily volatility = 1.54% - 95% VaR z-score = 1.645 - Market Risk VaR = Position value × Volatility × z-score = USD 80,000 × 0.0154 × 1.645 = USD 2,026.64 ### Step 2: Calculate Liquidity Risk Component - Bid-ask spread = USD 0.10 - Spread cost = 0.5 × Spread × Position size = 0.5 × USD 0.10 × 1,000 = USD 50 ### Step 3: Calculate Total Liquidity-Adjusted VaR - Liquidity-adjusted VaR = Market Risk VaR + Liquidity cost = USD 2,026.64 + USD 50 = USD 2,076.64 Therefore, the estimated liquidity-adjusted daily 95% VaR is approximately **USD 2,076**, which corresponds to option B. **Key Points:** - The liquidity adjustment accounts for the cost of liquidating the position in an illiquid market - The bid-ask spread represents the transaction cost when buying or selling - The 0.5 multiplier accounts for the fact that we only incur half the spread when liquidating (selling at the bid price) - The normal distribution assumption allows us to use the standard z-score of 1.645 for 95% confidence level
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You are a manager of a renowned hedge fund and are analyzing a 1,000 share position in an undervalued but illiquid stock BNA, which has a current stock price of USD 80 (expressed as the midpoint of the current bid-ask spread). Daily return for BNA has an estimated volatility of 1.54%. The average bid-ask spread is USD 0.10. Assuming returns of BNA are normally distributed, what is the estimated liquidity-adjusted daily 95% VaR, under normal market?
A
USD 1,389
B
USD 2,076
C
USD 3,324
D
USD 4,351
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