A large institutional fund needs to estimate the total liquidity cost associated with unwinding 60% of its illiquid fixed-income portfolio under stressed market conditions over a 5-day liquidation horizon. The risk manager has gathered the following data:
* Current market value of the illiquid portfolio: $800 million
* 1-day 99% VaR for the entire portfolio: $20 million
* Average daily trading volume for these securities: $120 million
* Market Impact Cost (MIC) Rule: If the daily liquidation amount exceeds 50% of the average daily trading volume, an additional market impact of 1.25% of the *excess daily liquidation amount* is incurred. This impact is applied cumulatively over the liquidation period.
* Current bid-ask spread: 75 basis points (0.75%) on the *entire amount liquidated*.
* Liquidation horizon: 5 trading days
* Funding cost of holding the portfolio: 5 bps per day
* Haircut on secured lending against these assets: 1.5%
Assuming the square root of time rule for VaR scaling is appropriate for market risk over the liquidation period, what is the total estimated liquidity cost?
A.$32.68 million
B.$50.57 million
C.$36.43 million
D.$30.43 million
Rationale:
The total estimated liquidity cost comprises three components: the market risk (VaR) of the liquidated portion, the market impact cost (MIC), and the bid-ask spread cost.
1. **Amount to be Liquidated**: 60% of the current market value = 0.60 * $800 million = $480 million.
2. **Daily Liquidation Amount**: Over a 5-day horizon, the daily liquidation amount is $480 million / 5 days = $96 million per day.
3. **Market Impact Cost (MIC)**:
* First, determine the threshold for market impact: 50% of the average daily trading volume = 0.50 * $120 million = $60 million.
* Since the daily liquidation amount ($96 million) exceeds this threshold, a market impact cost is incurred.
* The excess daily liquidation amount = $96 million (daily liquidation) - $60 million (threshold) = $36 million.
* The daily MIC = 1.25% * $36 million = $0.45 million.
* The total MIC over the 5-day liquidation period = $0.45 million/day * 5 days = $2.25 million.
4. **Bid-Ask Spread Cost**: This is applied to the entire amount liquidated.
* Bid-ask spread cost = 0.75% * $480 million = $3.60 million.
5. **Market Risk (VaR) of the Liquidated Portion**: The 1-day 99% VaR for the *entire portfolio* is $20 million. When estimating the cost of *unwinding 60%*, the relevant VaR is for the portion being liquidated.
* 1-day VaR for the liquidated portion = $20 million * 0.60 = $12 million.
* Scaling this to a 5-day horizon using the square root of time rule: 5-day VaR = $12 million * sqrt(5) = $12 million * 2.236067977 = $26.8328 million.
6. **Total Estimated Liquidity Cost**: Summing these components:
* Total Cost = 5-day VaR (liquidated portion) + Total MIC + Bid-Ask Spread Cost
* Total Cost = $26.8328 million + $2.25 million + $3.60 million = $32.6828 million.
* Rounded to two decimal places, the total cost is $32.68 million.
The funding cost of holding the portfolio and the haircut on secured lending are irrelevant for calculating the direct liquidity cost of unwinding the portfolio in this context.
The option calculating $50.57 million incorrectly scales the VaR for the entire portfolio ($20 million) rather than for just the liquidated portion ($12 million), leading to an overestimation of the market risk component. The option calculating $36.43 million incorrectly applies the market impact cost rule by calculating 1.25% of the *full daily liquidation amount* ($96 million) instead of only the *excess daily liquidation amount* ($36 million). The option calculating $30.43 million incorrectly ignores the market impact cost component entirely.
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