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Show how liquidity black holes come about, and name the forces behind trading that reinforces price moves (positive feedback trading).

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Liquidity Risk · FRM2.LTR.1.d

The idea

A liquidity black hole is a market state in which almost every participant wants to trade the same way. Sellers find no buyers, prices gap, and liquidity disappears just when it is needed. It forms when participants share similar models, limits, regulation or information, so their reactions are correlated. Positive feedback traders sell as prices fall and buy as they rise, which reinforces the move. Examples are stop-loss rules, portfolio insurance, and the delta hedging of short option positions (negative gamma). Others are margin calls and haircut increases on leveraged investors, and VaR-based limits that force position cuts when volatility rises. Negative feedback traders, such as value investors and market makers who lean against moves, supply liquidity. A black hole appears when they are scarce or constrained. Remember that short gamma hedging is destabilising and long gamma hedging is not.

A practice question

From the question bank, with the reason each wrong option is wrong.

What is a liquidity black hole?

  1. A market with permanently wide bid-ask spreads caused by low trading volume even in calm conditions of trade.Why not: Describes chronic illiquidity, not a sudden collapse caused by one-sided trading.
  2. A situation in which central bank reserves in the banking system are drained by market intervention.Why not: Confuses market liquidity with the supply of central bank reserves.
  3. A price fall caused only by a deterioration in fundamentals, with normal liquidity and two-way trading.Why not: A black hole is driven by one-sided trading, not just by news about fundamentals.
  4. A market state where nearly everyone wants to trade the same way, so few take the other side and prices gap. - correct

Liquidity black holes arise when participants have similar reactions, so buyers disappear. Price moves are amplified by the one-sidedness of trading, not only by new information.

A harder one

Which dealer's delta hedging of an option position adds to downward pressure on the underlying when its price falls?

  1. A dealer long put options, who must buy more of the underlying as the price falls to stay delta neutral.Why not: A long put hedger buys on falls, a stabilising action; it does not add to downward pressure.
  2. A dealer long call options, who buys back part of the short hedge as the price falls to stay delta neutral.Why not: A long call position has positive gamma, so the hedge is bought on falls and sold on rises.
  3. A dealer short put options, who must sell more of the underlying as the price falls to stay delta neutral. - correct
  4. A pension fund that rebalances to a fixed equity weight, buying equities after a fall.Why not: Rebalancing to a fixed weight is contrarian and stabilising; it is not option delta hedging.

A short put has positive delta that grows as the price falls, so the hedge (short underlying) must be increased: selling into a falling market. This is negative gamma hedging. Long option positions (positive gamma) hedge in a stabilising way.

The hardest tier

A dealer has sold put options on 2 million units of an index and delta hedges. As the index falls, the delta of the put position changes from -0.35 to -0.48 per option. To rebalance its hedge the dealer must trade closest to:

  1. buy 260,000 units of the indexWhy not: Direction error: a short put is hedged by shorting the index, so a larger delta means selling more.
  2. sell 260,000 units of the index - correct
  3. sell 960,000 units of the indexWhy not: Sells the entire new hedge (0.48 x 2 million) instead of only the change in delta.
  4. sell 700,000 units of the indexWhy not: Uses the old delta (0.35 x 2 million) rather than the change in delta.

The dealer is short puts, so its position has positive delta of 0.35 rising to 0.48; the hedge is short index units. Extra selling = (0.48 - 0.35) x 2,000,000 = 260,000 units. This forced selling reinforces the fall.

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