## 1. Hedge Fund Strategies

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---

### I. Introduction — purpose and key insights
- Purpose: bring together theoretical strands on collateral use and confront models with data.
- Three theoretical strands:
  - Collateral and default focusing on margin and “haircuts” (Geanakoplos, 2003; Brunnermeier and Pedersen, 2009; Gorton and Metrick, 2009; Krishnamurthy, Nagel, Orlov, 2010; Shleifer and Vishny, 2011).
  - Rehypothecation and collateral velocity (Adrian and Shin, 2010; Singh, 2010).
  - Liquidity mismatches and intermediation chains, including liquidity mismatch index (Brunnermeier, Gorton and Krishnamurthy, 2011).
- Empirical contribution: using Shin (2009) framework to decompose deleveraging into:
  - Collateral squeeze (decline in debt capacity due to price declines/haircuts).
  - Margin spiral (de-leveraging triggered by shortening of re-pledging chains).
- Key empirical findings (post-Lehman):
  - Overall collateral availability has declined.
  - Intermediation chains have become much shorter; this second effect is quantitatively larger than the first.
- Macro implication:
  - Decline in leverage and re-use of collateral reduces financial lubrication; an estimated $4-5 trillion reduction in velocity-like effects of collateral.
- Open analytical questions highlighted:
  - How shortening chains impact the real economy.
  - How monetary aggregates (e.g., M2) can interact with or substitute for re-used financial collateral.

### II. Centralization of Collateral — mechanics and participants
- Collateral that can be repledged (re-used) is typically centralized at large banks/dealers as secured funding against:
  - Margin loans
  - Securities borrowing
  - Reverse repo transactions
  - OTC derivatives
- Typical financial-statement disclosure example (Goldman Sachs):
  - “As of December 2009 and November 2008, the fair value of financial instruments received as collateral by the firm that it was permitted to deliver or re-pledge was $561 billion and $578 billion, respectively, of which the firm delivered or re-pledged $392 billion and $445 billion, respectively.”
- Major dealers (U.S.): Goldman Sachs, Morgan Stanley, JP Morgan, BoA/Merrill, Citibank.
- Major dealers (Europe/elsewhere): Deutsche Bank, UBS, Barclays, Credit Suisse, Societe General, BNP Paribas, HSBC, Royal Bank of Scotland, Nomura.
- Primary suppliers of pledged collateral to dealers:
  - (i) Hedge funds
  - (ii) Securities lending via custodians representing pension, insurers, official sector accounts, etc.
  - (iii) Commercial banks liaising with dealers
- Typical use: central collateral desks at dealers re-use collateral to meet market demand; re-use enables dynamic intermediation chains.

### III. Hedge funds — funding channels, leverage, and collateral provision
- Two principal funding channels for HF positions:
  - Pledged collateral to prime brokers (rehypothecation / re-use) in exchange for cash borrowing.
    - U.S. constraints: Regulation T and SEC Rule 15c3 limits prime brokers’ use of rehypothecated collateral.
    - Regulation T limits debt to 50 percent (leverage factor of 2); portfolio margining can increase leverage beyond factor of 2.
  - Repos: HFs repo out collateral to PBs or other dealers.
- Representative leverage and strategy notes:
  - Fixed income arbitrage, convertible arbitrage, and global macro seek higher leverage, financed via repo.
  - Managed futures and Emerging Markets strategies less reliant on collateral/leverage.
- Figure/table note:
  - Repo-related financing was about 27% and 32% of HF mark-to-market positions (after including leverage) in 2007 and 2010, respectively.

### IV. Quantitative estimates of hedge fund collateral (end-2007 and end-2010)
- Hedge fund industry estimates of AUM:
  - $2.0 trillion for end-2007
  - $1.7 trillion for end-2010
- Consensus estimates for global HF gross leverage:
  - about 2.0 as of end-2007
  - about 1.75 as of end-2010
- Mark-to-market collateral (AUM times gross leverage):
  - about $4.0 trillion as of end-2007
  - about $3.0 trillion as of end-2010
- Repo-financing estimate (end-2007):
  - 27% of $4 trillion = repo-related financing estimated at about $750 billion
- Prime-broker (PB) borrowing estimate (end-2007):
  - Calculated estimate about $850 billion borrowed from PBs
- Total collateral from HFs to large dealers (end-2007):
  - about $1.6 trillion, composed of:
    - $750 billion via repo-financing
    - $850 billion from direct borrowing/leverage in lieu of collateral posted to PBs
- Notes on leverage heterogeneity:
  - Larger funds (greater than $1 billion AUM): 23 percent utilize leverage between 2 and 5 times investment capital.
  - Smaller funds utilize leverage between 1 and 2 times.

### V. Securities lending as a primary collateral source
- Securities lending functions similarly to repo: provides collateralized short-term funding and typically involves full transfer of title.
- Asset managers (pension funds, insurers, ETFs, etc.) are important primary sources of collateral via securities lending.
- Securities lending transactions are more flexible than repos: generally no set end date or set price; beneficial owner can recall shares on loan at any time.
- Legal/operational similarity: both repo and securities lending commonly use title transfer; ISDA CSA under English Law also uses title transfer in collateral support agreements.

### VI. Legal distinctions — rehypothecation vs. pledged collateral that can be re-used
- Pledged collateral (pledge agreement):
  - Collateral recipient (pledgee) does not have explicit rights of re-use unless expressly agreed.
  - Pledgee cannot seize or use collateral unless pledgor defaults.
- Rehypothecation and title transfer:
  - Rehypothecation: collateral taker uses financial collateral as security for his own obligations to third parties (onward pledging).
  - Re-use broader: includes re-pledging, selling, or lending consistent with ownership.
  - Title transfer arrangements transfer ownership of collateral to collateral taker; common in repo, securities lending, and many CSAs under English law.
  - Under title transfer, collateral taker returns equivalent collateral (not the original security) once obligations are discharged.
- Jurisdictional note:
  - Rehypothecation more prevalent outside the U.S. (U.K. and continental Europe), supporting market-clearing pricing for re-usable collateral.
  - U.K. practices may nonetheless impose U.S.-like restrictions contractually in PB agreements.

### VII. Structure of the paper (sections and focus)
- Section II: centralization of re-usable collateral at large banks and methodology for calculating a velocity factor for pledged collateral as of end-2007.
- Section III: deleveraging since end-2007, decline in primary sources of collateral as of end-2010, calculation of pledged collateral velocity at end-2010 vs. end-2007.
- Section IV: possible links between collateral velocity and velocity of money (M2) from a monetary policy perspective.
- Section V: policy suggestions and open questions.

*Source: _wp11256 - 1. Hedge Fund Strategies (IMF PDF chapter contents provided).*

### Box 2: Accounting for pledged collateral in U.S. and non-U.S. jurisdictions

### Non-U.S. example — transaction chain and consolidated balance sheet
- Transaction chain:
  - Prime Broker (PB) makes a margin loan to HF of £100.
  - PB takes as pledge equities worth £140 from HF.
  - PB pledges those equities to a custodial securities lender against a borrowing of U.S. Treasuries worth £133 (5% haircut).
  - PB repos the £133 U.S. Treasuries to a money market fund to raise £129 (3% margin).
- Consolidated balance sheet (Non-U.S. Balance Sheet) — Assets:
  - Cash 29
  - Securities Sold under Repo Agreement 129
  - Receivables 100
- Footnote:
  - Fair value of collateral received that can be pledged and re-used is £273

### U.S. example — regulatory constraints and accounting consequences
- Key constraint: Reg T and 15c(3) lock-up rules in the U.S. prevent full replication of the non-U.S. example.
- Practical implication:
  - Even if there is a debit balance as per the non-U.S. example, the credit balance of the PB needs to be offset first before collateral can be re-used.
  - Therefore, the other legs of the non-U.S. example (pledging equities to securities lender and then repo-ing to a money market fund) cannot take place in the U.S.
  - Result: due to this ‘net’ lock up between debit and credit balances, rehypothecation and collateral re-use is dampened in the US.
  - Rehypothecation is mostly a non-US phenomenon where collateral re-use is not subject to regulatory constraints.
- U.S. Balance Sheet example — Assets:
  - Receivables
  - Cash 100
  - Liabilities:
    - Customer Payable 100
- Footnote:
  - Fair value of collateral received that can be pledged and reused will depend on the credit balance of the PB.
  - Debt balance of ($100) needs to be offset with the overall credit balance of the PB before any pledged collateral can be re-used.

### Securities lending practices and data sources
- Main data source: Risk Management Association (RMA).
  - RMA includes only primary sources of securities lending from clients such as pension funds, insurers, official sector accounts and some corporate/money funds.
  - RMA’s data includes the largest custodians such as BoNY, State Street, JPMorgan etc.
- Comparative note: A recent paper by Bank of England’s Quarterly (September, 2011) states that about $ 2 trillion of securities were on loan but includes secondary holdings also (i.e., also counts the bank to bank holdings of primary sources).
- Market practice differences:
  - U.S.: securities lenders generally reinvest cash collateral in very liquid money-market instruments, earning something close to Fed funds; driven by daily mark-to-market, rate changes, and daily lending/return of shares.
  - Europe: markets usually hold bonds or equities as securities for collateral (instead of cash).
- Footnote on Data Explorers:
  - Data Explorers shows larger numbers as they include a significant part of the secondary market activity also.

### Table 2 — Securities Lending, 2007-2010 (Collateral Received from Pension Funds, Insurers, Official Accounts etc.; US dollar, billions)
- Securities Lending vs. Cash Collateral:
  - 2007: 1,209
  - 2008: 935
  - 2009: 875
  - 2010: 818
- Securities Lending vs. Non-Cash Collateral:
  - 2007: 486
  - 2008: 251
  - 2009: 270
  - 2010: 301
- Total Securities Lending:
  - 2007: 1,695
  - 2008: 1,187
  - 2009: 1,146
  - 2010: 1,119
- Source: RMA

### Bank-dealer collateral and other collateral sources
- Bank-Dealer Collateral:
  - Dealers occasionally receive requests from commercial banks for collateral swaps where collateral posted may need an ‘upgrade’.
  - Discussions with dealers indicate such requests are generally minimal and insignificant relative to collateral flows from key clients (hedge funds, pension funds, insurers, official accounts etc.).
  - Such flows are acknowledged in Figures 1 and 4 with a de minimis but are not considered to impact the arithmetic results (i.e., the velocity of pledged collateral).
- Other collateral sources:
  - Other sources were considered; Box 3 explains why these are not material since only collateral with no legal constraints on re-use was included.

*Source: Box 2, _wp11256 - Accounting for pledged collateral in U.S. and non-U.S. jurisdictions.*

### Box 3. Are There Any Other Buckets That Are Sources Of Pledged Collateral?

### Dealer to Dealer Collateral
- Dealers generally prefer not to use their balance sheet when moving collateral for clients; collateral coming in via reverse repos typically exceeds collateral leaving dealers via repos.
- Dealers may occasionally use own balance sheet to diversify funding when cost of repo is less than alternative funding. 1/
- Balance sheet “dips” are scrutinized by dealer Treasuries and generally do not exceed $5-10 billion per large dealer.
- If there are 10 dealers active, they may have $50-$100 billion of balance sheet funding that effectively does not leave the dealer-to-dealer rectangle.
- Context: $50-$100 billion is only ½-1% of the total collateral that churns between dealers (about $10 trillion).

### Tri-party Repo Collateral Market and Rehypothecation
- Tri-party repo market size: $1.6 trillion (July, 2011) (New York Fed statistics).
- Collateral posted through clearing banks (BNY Mellon and JP Morgan) is segregated and identifiable and is not rehypothecable to the street; this reduces cash investor risk.
- Haircuts during the 2008 crisis were minimal within the tri-party system versus the ‘street’ where rehypothecation and renegotiation occurred.
- European tri-party repo market size: € 1.1 trillion across Euroclear, Clearstream, BNY Mellon and JP Morgan.
- Note: tri-party collateral can be substituted during the repo; churning due to re-pledging is restricted to the rectangle in Figure 1. 2/

### Securitization Vehicles
- ABCP-funded vehicles (SIVs, conduits) did not rely on dealers for funding; they raised funds directly from institutional cash pools (corporate treasurers, securities lenders, money funds).
- Collateral from such securitization-based vehicles was difficult to pledge for funding; therefore, collateral related to these flows is not considered “source” collateral churned by dealers.

### Methodology for Calculating the Velocity of Pledged Collateral (end-2007)
- Number of large banks active in collateral management globally: 10-14.
- Total collateral received as of end-2007: almost $10 trillion.
- Primary source collateral (HFs and Security lenders etc.): $3.3 trillion.
- Velocity of collateral (end-2007): $ 10 trillion / $ 3.3 trillion or about 3.

### How Have the Sources of Collateral Changed Recently (end-2010 data)
- Hedge Fund AUM as of end-2010: $1.7 trillion (lower than in 2007 but higher than early 2009 $1.4 trillion).
- Consensus estimate of global HF leverage: 1.75.
- Mark-to-market collateral with HFs: about $3 trillion ($1.7 trillion x 1.75).
- Repo funding by HFs: 32% of $3 trillion or about $750 billion (after adjusting for initial AUM in that 32%).
- Prime broker (PB) related funding has dropped; PB-related funding estimate: $600 billion (composed of $400 billion (FSA HF survey estimate) + $200 billion from the U.S., as calculated in Annex 2).
- Total HF-related collateral to dealers (end-2010): $750 billion (repo) + $600 billion (PB borrowing) = $1.35 trillion.
- Securities lending (end-2010): $1.1 trillion (RMA data).
- Total collateral from primary sources that could be re-pledged (end-2010): $1.35 trillion + $1.1 trillion = $2.45 trillion.
- Total collateral received by the 14 large dealers (end-2010): $5.8 trillion (down from $10 trillion peak end-2007, up from $5.0 trillion end-2009).
- Velocity of collateral (end-2010): $5.8 trillion / $2.45 trillion or approx 2.4.

### Collateral Squeeze, Margin Spiral and Chain Lengths
- Decline in debt capacity due to an adverse shock stems from two factors:
  - (1) haircuts on collateral assets due to a fall in asset/collateral prices, and
  - (2) deleveraging due to lower leverage multiplier of the financial system that stems from the length of ‘pledged collateral chains’.
- Empirical evidence:
  - Chain length pre-Lehman (end-2007): around 3.
  - Chain length end-2010: decreased to about 2.4.
  - Interpretation: collateral from a primary source takes fewer steps to reach ultimate client; results from reduced supply of collateral from primary source clients (counterparty risk) and demand for higher quality collateral.

### Collateral Velocity and Monetary Policy
- “Velocity of collateral” analogous to “velocity of money”; shortage of acceptable collateral can have cascading impact on lending akin to reduction in monetary base.
- First-round impact: reduction in “primary source” collateral pools (hedge funds, pensions, insurers) due to counterparty risk.
- Second-round impact: shorter chains and higher cost of capital from decreased financial lubrication.
- Monetary aggregates:
  - Fed and ECB consider many variables; M2 and M3 have been used historically (ECB still uses M3; U.K. and ECB publish M3).
  - The Fed discontinued publishing M3 since 2006.
- Post-Lehman: counterparty risk led to significant drop in pledged collateral among major U.S. and European banks; global liquidity remains below pre-Lehman levels when considering collateral use/reuse along with M2.
- Recommendation: Data on pledged collateral that may be repledged and associated velocity factor should be considered by major central banks; pledged collateral market state matters for monetary policy (cross-border funding and U.S. dollar demand by European banks).

### Policy Issues and Recommendations
- Recent regulations focus on building equity and reducing leverage at large banks; policymakers should also consider elasticity of “nonbank/bank funding”.
- Decline in overall availability of collateral is sizable and roughly $4-5 trillion since pre-Lehman (reduced ‘source’ collateral times velocity of collateral).
- Increase in M2 due to quantitative easing (QE) may not substitute for loss in financial collateral.
- The size and length of nonbank funding chains relative to securities lending, repo, and related markets gauge potential dislocation from unwinding such funding.
- Regulatory changes (Basel liquidity ratios, EU Solvency II and CRD IV, moving OTC derivatives to CCPs) will require significant collateral; without rebound in pledgeable collateral, asymmetry in demand and supply may force difficult choices for markets and regulators.
- Potential areas of collateral demand growth:
  - Clients upgrading collateral for posting to CCPs (if OTC derivatives move to CCPs).
  - Rising demand for collateral swaps from insurers, pension funds and the ETF industry.
- Quantitative notes:
  - Increased monetary stimulus Jan-Aug, 2011 (not captured in Figure 5) has been above $1.6 trillion (change in Fed and ECB M2 figures).
  - Estimates suggest collateral needs in the OTC derivatives market may require $2 trillion in collateral to be posted to CCPs if regulatory efforts succeed in moving a significant share of OTC derivatives to CCPs.

*Source: Box 3, “Are There Any Other Buckets That Are Sources Of Pledged Collateral?”, IMF Working Paper (_wp11256).*

### Annex 1. Deleveraging Components—Collateral Squeeze and Margin Spiral

### Mathematical framework and notation
- Variables (as defined):
  - xi = market value of bank i’s total liabilities
  - yi = market value of bank i’s assets that can be pledged as collateral
  - ei = market value of bank i’s equity
  - ai = market value of bank i’s assets
  - πji = proportion of j’s liabilities held by i
  - di = (ai − ei)/ai is the ratio of debt to total assets
- Accounting identities:
  - Total assets of bank i: ai = Σj πji yj + yi
  - Total debt via leverage: xi = di ai = di (Σj πji yj + yi)
- Vector/matrix notation:
  - x = [x1 ... xn]′, y = [y1 ... yn]′, Δ = diag(d1 ... dn)
  - Π is the matrix of πji entries and the vector form of the aggregate identity is: ΠΔ + Δ = x − y
- Taylor series expansion solution used:
  - x = (I − ΠΔ)−1 Δ y = Δ y + ΠΔ Δ y + (ΠΔ)2 Δ y + (ΠΔ)3 Δ y + ···
  - Note: The sum of the elements of the rows of ΠΔ is always strictly less than 1, so the infinite Taylor series converges and I − ΠΔ has a well-defined inverse.

### Interpretation of ΠΔ and re-pledging chains
- Structure of ΠΔ:
  - ΠΔ = matrix with entries πji dj in off-diagonal and zeroes on diagonal.
- Economic interpretation:
  - Sum of elements of the i-th row of ΠΔ: net impact of bank i’s leverage on the remaining system.
  - Sum of elements of the i-th column of ΠΔ: net impact of systemic leverage on bank i.
  - Powered matrices (ΠΔ)^t capture the collateral value of the asset in the t-th link of the re-pledging chain (i.e., the chain length/churning of collateral).

### Decomposition of change in debt capacity: collateral squeeze vs margin spiral
- Setup:
  - Let σ be a parameter capturing measured risks that affect both market prices y(σ) and haircuts/debt ratios Δ(σ).
  - Define M(σ) ≡ (I − ΠΔ(σ))−1.
- For a decline from σ to σ′ (σ′ < σ), the decline in debt is:
  - x(σ) − x(σ′) = M(σ) y(σ) − M(σ′) y(σ′)
- Rewritten decomposition (exact form):
  - x(σ) − x(σ′) = [M(σ) (y(σ) − y(σ′))]  +  [(M(σ) − M(σ′)) y(σ′)]
  - First bracket labeled “collateral squeeze” (due to price decline).
  - Second bracket labeled “margin spiral” (due to deleveraging, i.e., decline in the churning factor, independent of price declines driven by haircuts).
- Economic implications:
  - Collateral squeeze: decline in debt capacity attributable to market price declines of pledgeable assets.
  - Margin spiral: decline in debt capacity attributable to shortening of re-pledging chains and reductions in the churning/velocity of collateral (captured by change in M(σ)).
  - The margin spiral term can be significantly larger than the collateral squeeze term.

### Empirical note and policy-relevant insight
- Empirical finding reported in the paper:
  - Post-Lehman, re-pledging chains are shorter, implying a larger role for the margin spiral (shorter churning reduces system debt capacity beyond pure price declines).
- Policy relevance:
  - Distinguishing between collateral squeeze and margin spiral clarifies how changes in market prices versus changes in rehypothecation/churning practices each contribute to systemic deleveraging.
  - Measures that affect re-pledging chains (custody arrangements, rehypothecation rights, legal structuring) can materially alter systemic leverage via the margin spiral channel.

*Source: Annex 1. Deleveraging Components—Collateral Squeeze and Margin Spiral (IMF working paper annex content).*

### 1.   Hedge Fund Strategies .............................................................................................

### 1. Hedge Fund Strategies

### I. Introduction — purpose and key insights
- Purpose: bring together theoretical strands on collateral use and confront models with data.
- Three theoretical strands:
  - Collateral and default focusing on margin and “haircuts” (Geanakoplos, 2003; Brunnermeier and Pedersen, 2009; Gorton and Metrick, 2009; Krishnamurthy, Nagel, Orlov, 2010; Shleifer and Vishny, 2011).
  - Rehypothecation and collateral velocity (Adrian and Shin, 2010; Singh, 2010).
  - Liquidity mismatches and intermediation chains, including liquidity mismatch index (Brunnermeier, Gorton and Krishnamurthy, 2011).
- Empirical contribution: using Shin (2009) framework to decompose deleveraging into:
  - Collateral squeeze (decline in debt capacity due to price declines/haircuts).
  - Margin spiral (de-leveraging triggered by shortening of re-pledging chains).
- Key empirical findings (post-Lehman):
  - Overall collateral availability has declined.
  - Intermediation chains have become much shorter; this second effect is quantitatively larger than the first.
- Macro implication: decline in leverage and re-use of collateral reduces financial lubrication; an estimated $4-5 trillion reduction in velocity-like effects of collateral.
- Open analytical questions highlighted:
  - How shortening chains impact the real economy.
  - How monetary aggregates (e.g., M2) can interact with or substitute for re-used financial collateral.

### II. Centralization of Collateral — mechanics and participants
- Collateral that can be repledged (re-used) is typically centralized at large banks/dealers as secured funding against:
  - Margin loans
  - Securities borrowing
  - Reverse repo transactions
  - OTC derivatives
- Typical financial-statement disclosure example (Goldman Sachs):
  - “As of December 2009 and November 2008, the fair value of financial instruments received as collateral by the firm that it was permitted to deliver or re-pledge was $561 billion and $578 billion, respectively, of which the firm delivered or re-pledged $392 billion and $445 billion, respectively.”
- Major dealers (U.S.): Goldman Sachs, Morgan Stanley, JP Morgan, BoA/Merrill, Citibank.
- Major dealers (Europe/elsewhere): Deutsche Bank, UBS, Barclays, Credit Suisse, Societe General, BNP Paribas, HSBC, Royal Bank of Scotland, Nomura.
- Primary suppliers of pledged collateral to dealers:
  - (i) Hedge funds
  - (ii) Securities lending via custodians representing pension, insurers, official sector accounts, etc.
  - (iii) Commercial banks liaising with dealers
- Typical use: central collateral desks at dealers re-use collateral to meet market demand; re-use enables dynamic intermediation chains.

### III. Hedge funds — funding channels, leverage, and collateral provision
- Two principal funding channels for HF positions:
  - Pledged collateral to prime brokers (rehypothecation / re-use) in exchange for cash borrowing.
    - U.S. constraints: Regulation T and SEC Rule 15c3 limits prime brokers’ use of rehypothecated collateral.
    - Regulation T limits debt to 50 percent (leverage factor of 2); portfolio margining can increase leverage beyond factor of 2.
  - Repos: HFs repo out collateral to PBs or other dealers.
- Representative leverage and strategy notes:
  - Fixed income arbitrage, convertible arbitrage, and global macro seek higher leverage, financed via repo.
  - Managed futures and Emerging Markets strategies less reliant on collateral/leverage.
- Table/figure notes:
  - Repo-related financing was about 27% and 32% of HF mark-to-market positions (after including leverage) in 2007 and 2010, respectively.

### IV. Quantitative estimates of hedge fund collateral (end-2007 and end-2010)
- Hedge fund industry estimates of AUM:
  - $2.0 trillion for end-2007
  - $1.7 trillion for end-2010
- Consensus estimates for global HF gross leverage:
  - about 2.0 as of end-2007
  - about 1.75 as of end-2010
- Mark-to-market collateral (AUM times gross leverage):
  - about $4.0 trillion as of end-2007
  - about $3.0 trillion as of end-2010
- Repo-financing estimate (end-2007):
  - 27% of $4 trillion = repo-related financing estimated at about $750 billion
- Prime-broker (PB) borrowing estimate (end-2007):
  - Calculated estimate about $850 billion borrowed from PBs (see Annex 2 referenced in source for details)
- Total collateral from HFs to large dealers (end-2007):
  - about $1.6 trillion, composed of:
    - $750 billion via repo-financing
    - $850 billion from direct borrowing/leverage in lieu of collateral posted to PBs
- Notes on leverage heterogeneity:
  - Larger funds (greater than $1 billion AUM): 23 percent utilize leverage between 2 and 5 times investment capital.
  - Smaller funds utilize leverage between 1 and 2 times.

### V. Securities lending as a primary collateral source
- Securities lending functions similarly to repo: provides collateralized short-term funding and typically involves full transfer of title.
- Asset managers (pension funds, insurers, ETFs, etc.) are important primary sources of collateral via securities lending.
- Securities lending transactions are more flexible than repos: generally no set end date or set price; beneficial owner can recall shares on loan at any time.
- Legal/operational similarity: both repo and securities lending commonly use title transfer; ISDA CSA under English Law also uses title transfer in collateral support agreements.

### VI. Legal distinctions — Box on rehypothecation vs. pledged collateral that can be re-used
- Pledged collateral (pledge agreement):
  - Collateral recipient (pledgee) does not have explicit rights of re-use unless expressly agreed.
  - Pledgee cannot seize or use collateral unless pledgor defaults.
- Rehypothecation and title transfer:
  - Rehypothecation: collateral taker uses financial collateral as security for his own obligations to third parties (onward pledging).
  - Re-use broader: includes re-pledging, selling, or lending consistent with ownership.
  - Title transfer arrangements transfer ownership of collateral to collateral taker; common in repo, securities lending, and many CSAs under English law.
  - Under title transfer, collateral taker returns equivalent collateral (not the original security) once obligations are discharged.
- Jurisdictional note:
  - Rehypothecation more prevalent outside the U.S. (U.K. and continental Europe), supporting market-clearing pricing for re-usable collateral.
  - U.K. practices may nonetheless impose U.S.-like restrictions contractually in PB agreements.

### VII. Structure of the paper (sections and focus)
- Section II: centralization of re-usable collateral at large banks and methodology for calculating a velocity factor for pledged collateral as of end-2007.
- Section III: deleveraging since end-2007, decline in primary sources of collateral as of end-2010, calculation of pledged collateral velocity at end-2010 vs. end-2007.
- Section IV: possible links between collateral velocity and velocity of money (M2) from a monetary policy perspective.
- Section V: policy suggestions and open questions.

*Source: _wp11256 - 1. Hedge Fund Strategies (IMF PDF chapter contents provided).*

### Box 2: Accounting for pledged collateral in U.S. and non-U.S. jurisdictions

### Box 2: Accounting for pledged collateral in U.S. and non-U.S. jurisdictions

### Non-U.S. example — transaction chain and consolidated balance sheet
- Transaction chain:
  - Prime Broker (PB) makes a margin loan to HF of £100.
  - PB takes as pledge equities worth £140 from HF.
  - PB pledges those equities to a custodial securities lender against a borrowing of U.S. Treasuries worth £133 (5% haircut).
  - PB repos the £133 U.S. Treasuries to a money market fund to raise £129 (3% margin).
- Consolidated balance sheet (Non-U.S. Balance Sheet):
  - Assets:
    - Cash 29
    - Securities Sold under Repo Agreement 129
    - Receivables 100
  - Liabilities: (no explicit line items given beyond the above)
- Footnote:
  - Fair value of collateral received that can be pledged and re-used is £273

### U.S. example — regulatory constraints and accounting consequences
- Key constraint: Reg T and 15c(3) lock-up rules in the U.S. prevent full replication of the non-U.S. example.
- Practical implication:
  - Even if there is a debit balance as per the non-U.S. example, the credit balance of the PB needs to be offset first before collateral can be re-used.
  - Therefore, the other legs of the non-U.S. example (pledging equities to securities lender and then repo-ing to a money market fund) cannot take place in the U.S.
  - Result: due to this ‘net’ lock up between debit and credit balances, rehypothecation and collateral re-use is dampened in the US.
  - Rehypothecation is mostly a non-US phenomenon where collateral re-use is not subject to regulatory constraints.
- U.S. Balance Sheet example (as presented):
  - Assets:
    - Receivables
    - Cash 100
  - Liabilities:
    - Customer Payable 100
- Footnote:
  - Fair value of collateral received that can be pledged and reused will depend on the credit balance of the PB.
  - Debt balance of ($100) needs to be offset with the overall credit balance of the PB before any pledged collateral can be re-used.

### Securities lending practices and data sources
- Main data source: Risk Management Association (RMA) (see Table 2).
  - RMA includes only primary sources of securities lending from clients such as pension funds, insurers, official sector accounts and some corporate/money funds.
  - RMA’s data includes the largest custodians such as BoNY, State Street, JPMorgan etc.
- Comparative note: A recent paper by Bank of England’s Quarterly (September, 2011) states that about $ 2 trillion of securities were on loan but includes secondary holdings also (i.e., also counts the bank to bank holdings of primary sources).10
- Market practice differences:
  - U.S.: securities lenders generally reinvest cash collateral in very liquid money-market instruments, earning something close to Fed funds; driven by daily mark-to-market, rate changes, and daily lending/return of shares.
  - Europe: markets usually hold bonds or equities as securities for collateral (instead of cash).
- Footnote on Data Explorers:
  - Data Explorers shows larger numbers as they include a significant part of the secondary market activity also.

### Table 2 — Securities Lending, 2007-2010 (Collateral Received from Pension Funds, Insurers, Official Accounts etc.; US dollar, billions)
- Securities Lending vs. Cash Collateral:
  - 2007: 1,209
  - 2008: 935
  - 2009: 875
  - 2010: 818
- Securities Lending vs. Non-Cash Collateral:
  - 2007: 486
  - 2008: 251
  - 2009: 270
  - 2010: 301
- Total Securities Lending:
  - 2007: 1,695
  - 2008: 1,187
  - 2009: 1,146
  - 2010: 1,119
- Source: RMA

### Bank-dealer collateral and other collateral sources
- Bank-Dealer Collateral:
  - Dealers occasionally receive requests from commercial banks for collateral swaps where collateral posted may need an ‘upgrade’.
  - Discussions with dealers indicate such requests are generally minimal and insignificant relative to collateral flows from key clients (hedge funds, pension funds, insurers, official accounts etc.).
  - Such flows are acknowledged in Figures 1 and 4 with a de minimis but are not considered to impact the arithmetic results (i.e., the velocity of pledged collateral).
- Other collateral sources:
  - Other sources were considered; Box 3 explains why these are not material since only collateral with no legal constraints on re-use was included.

*Source: Box 2, _wp11256 - Accounting for pledged collateral in U.S. and non-U.S. jurisdictions.*

### Box 3. Are There Any Other Buckets That Are Sources Of Pledged Collateral?

### Box 3. Are There Any Other Buckets That Are Sources Of Pledged Collateral?

### Dealer to Dealer Collateral
- Dealers generally prefer not to use their balance sheet when moving collateral for clients; collateral coming in via reverse repos typically exceeds collateral leaving dealers via repos.
- Dealers may occasionally use own balance sheet to diversify funding when cost of repo is less than alternative funding. 1/
- Balance sheet “dips” are scrutinized by dealer Treasuries and generally do not exceed $5-10 billion per large dealer.
- If there are 10 dealers active, they may have $50-$100 billion of balance sheet funding that effectively does not leave the dealer-to-dealer rectangle.
- Context: $50-$100 billion is only ½-1% of the total collateral that churns between dealers (about $10 trillion).

### Tri-party Repo Collateral Market and Rehypothecation
- Tri-party repo market size: $1.6 trillion (July, 2011) (New York Fed statistics).
- Collateral posted through clearing banks (BNY Mellon and JP Morgan) is segregated and identifiable and is not rehypothecable to the street; this reduces cash investor risk.
- Haircuts during the 2008 crisis were minimal within the tri-party system versus the ‘street’ where rehypothecation and renegotiation occurred.
- European tri-party repo market size: € 1.1 trillion across Euroclear, Clearstream, BNY Mellon and JP Morgan.
- Note: tri-party collateral can be substituted during the repo; churning due to re-pledging is restricted to the rectangle in Figure 1. 2/

### Securitization Vehicles
- ABCP-funded vehicles (SIVs, conduits) did not rely on dealers for funding; they raised funds directly from institutional cash pools (corporate treasurers, securities lenders, money funds).
- Collateral from such securitization-based vehicles was difficult to pledge for funding; therefore, collateral related to these flows is not considered “source” collateral churned by dealers.

### Methodology for Calculating the Velocity of Pledged Collateral (end-2007)
- Number of large banks active in collateral management globally: 10-14.
- Total collateral received as of end-2007: almost $10 trillion.
- Primary source collateral (HFs and Security lenders etc.): $3.3 trillion.
- Velocity of collateral (end-2007): $ 10 trillion / $ 3.3 trillion or about 3.

### How Have the Sources of Collateral Changed Recently (end-2010 data)
- Hedge Fund AUM as of end-2010: $1.7 trillion (lower than in 2007 but higher than early 2009 $1.4 trillion).
- Consensus estimate of global HF leverage: 1.75.
- Mark-to-market collateral with HFs: about $3 trillion ($1.7 trillion x 1.75).
- Repo funding by HFs: 32% of $3 trillion or about $750 billion (after adjusting for initial AUM in that 32%).
- Prime broker (PB) related funding has dropped; PB-related funding estimate: $600 billion (composed of $400 billion (FSA HF survey estimate) + $200 billion from the U.S., as calculated in Annex 2).
- Total HF-related collateral to dealers (end-2010): $750 billion (repo) + $600 billion (PB borrowing) = $1.35 trillion.
- Securities lending (end-2010): $1.1 trillion (RMA data).
- Total collateral from primary sources that could be re-pledged (end-2010): $1.35 trillion + $1.1 trillion = $2.45 trillion.
- Total collateral received by the 14 large dealers (end-2010): $5.8 trillion (down from $10 trillion peak end-2007, up from $5.0 trillion end-2009).
- Velocity of collateral (end-2010): $5.8 trillion / $2.45 trillion or approx 2.4.

### Collateral Squeeze, Margin Spiral and Chain Lengths
- Decline in debt capacity due to an adverse shock stems from two factors:
  - (1) haircuts on collateral assets due to a fall in asset/collateral prices, and
  - (2) deleveraging due to lower leverage multiplier of the financial system that stems from the length of ‘pledged collateral chains’.
- Margin spiral and collateral squeeze relationship (as presented):
  - (   (   )(    '))(   )(    ')  ((   )(   '))
    collateral squeezemargin spiral
    yyM yMM
    
     
- Empirical evidence:
  - Chain length pre-Lehman (end-2007): around 3.
  - Chain length end-2010: decreased to about 2.4.
  - Interpretation: collateral from a primary source takes fewer steps to reach ultimate client; results from reduced supply of collateral from primary source clients (counterparty risk) and demand for higher quality collateral.

### Collateral Velocity and Monetary Policy
- “Velocity of collateral” analogous to “velocity of money”; shortage of acceptable collateral can have cascading impact on lending akin to reduction in monetary base.
- First-round impact: reduction in “primary source” collateral pools (hedge funds, pensions, insurers) due to counterparty risk.
- Second-round impact: shorter chains and higher cost of capital from decreased financial lubrication.
- Monetary aggregates:
  - Fed and ECB consider many variables; M2 and M3 have been used historically (ECB still uses M3; U.K. and ECB publish M3).
  - The Fed discontinued publishing M3 since 2006.
- Post-Lehman: counterparty risk led to significant drop in pledged collateral among major U.S. and European banks; global liquidity remains below pre-Lehman levels when considering collateral use/reuse along with M2 (see Figure 5).
- Recommendation: Data on pledged collateral that may be repledged and associated velocity factor should be considered by major central banks; pledged collateral market state matters for monetary policy (cross-border funding and U.S. dollar demand by European banks).

### Policy Issues and Recommendations
- Recent regulations focus on building equity and reducing leverage at large banks; policymakers should also consider elasticity of “nonbank/bank funding”.
- Decline in overall availability of collateral is sizable and roughly $4-5 trillion since pre-Lehman (reduced ‘source’ collateral times velocity of collateral).
- Increase in M2 due to quantitative easing (QE) may not substitute for loss in financial collateral.
- The size and length of nonbank funding chains relative to securities lending, repo, and related markets gauge potential dislocation from unwinding such funding.
- Regulatory changes (Basel liquidity ratios, EU Solvency II and CRD IV, moving OTC derivatives to CCPs) will require significant collateral; without rebound in pledgeable collateral, asymmetry in demand and supply may force difficult choices for markets and regulators.
- Potential areas of collateral demand growth:
  - Clients upgrading collateral for posting to CCPs (if OTC derivatives move to CCPs).
  - Rising demand for collateral swaps from insurers, pension funds and the ETF industry.
- Quantitative notes:
  - Increased monetary stimulus Jan-Aug, 2011 (not captured in Figure 5) has been above $1.6 trillion (change in Fed and ECB M2 figures).
  - Estimates suggest collateral needs in the OTC derivatives market may require $2 trillion in collateral to be posted to CCPs if regulatory efforts succeed in moving a significant share of OTC derivatives to CCPs.

*Source: Box 3, “Are There Any Other Buckets That Are Sources Of Pledged Collateral?”, IMF Working Paper (_wp11256) (contents as supplied).*

### Annex 1. Deleveraging Components—Collateral Squeeze and Margin Spiral

### Annex 1. Deleveraging Components—Collateral Squeeze and Margin Spiral

### Mathematical framework and notation
- Variables (as defined):
  - xi = market value of bank i’s total liabilities
  - yi = market value of bank i’s assets that can be pledged as collateral
  - ei = market value of bank i’s equity
  - ai = market value of bank i’s assets
  - πji = proportion of j’s liabilities held by i
  - di = (ai − ei)/ai is the ratio of debt to total assets
- Accounting identities:
  - Total assets of bank i: ai = Σj πji yj + yi
  - Total debt via leverage: xi = di ai = di (Σj πji yj + yi)
- Vector/matrix notation:
  - x = [x1 ... xn]′, y = [y1 ... yn]′, Δ = diag(d1 ... dn)
  - Π is the matrix of πji entries and the vector form of the aggregate identity is: ΠΔ + Δ = x − y (rewritten in the source as ΠΔ + Δ = xyx; solved for x)
- Taylor series expansion solution used:
  - x = (I − ΠΔ)−1 Δ y = Δ y + ΠΔ Δ y + (ΠΔ)2 Δ y + (ΠΔ)3 Δ y + ···
  - Note: The sum of the elements of the rows of ΠΔ is always strictly less than 1, so the infinite Taylor series converges and I − ΠΔ has a well-defined inverse.

### Interpretation of ΠΔ and re-pledging chains
- Structure of ΠΔ (as in source):
  - ΠΔ = matrix with entries πji dj in off-diagonal and zeroes on diagonal (explicit block shown in source).
- Economic interpretation:
  - Sum of elements of the i-th row of ΠΔ: net impact of bank i’s leverage on the remaining system.
  - Sum of elements of the i-th column of ΠΔ: net impact of systemic leverage on bank i.
  - Powered matrices (ΠΔ)^t capture the collateral value of the asset in the t-th link of the re-pledging chain (i.e., the chain length/churning of collateral).

### Decomposition of change in debt capacity: collateral squeeze vs margin spiral
- Setup:
  - Let σ be a parameter capturing measured risks that affect both market prices y(σ) and haircuts/debt ratios Δ(σ).
  - Define M(σ) ≡ (I − ΠΔ(σ))−1.
- For a decline from σ to σ′ (σ′ < σ), the decline in debt is:
  - x(σ) − x(σ′) = M(σ) y(σ) − M(σ′) y(σ′)
- Rewritten decomposition (exact form from source):
  - x(σ) − x(σ′) = [M(σ) (y(σ) − y(σ′))]  +  [(M(σ) − M(σ′)) y(σ′)]
  - First bracket labeled “collateral squeeze” (due to price decline).
  - Second bracket labeled “margin spiral” (due to deleveraging, i.e., decline in the churning factor, independent of price declines driven by haircuts).
- Economic implications:
  - Collateral squeeze: decline in debt capacity attributable to market price declines of pledgeable assets.
  - Margin spiral: decline in debt capacity attributable to shortening of re-pledging chains and reductions in the churning/velocity of collateral (captured by change in M(σ)).
  - The margin spiral term can be significantly larger than the collateral squeeze term.

### Empirical note and policy-relevant insight
- Empirical finding reported in the paper:
  - Post-Lehman, re-pledging chains are shorter, implying a larger role for the margin spiral (shorter churning reduces system debt capacity beyond pure price declines).
- Policy relevance:
  - Distinguishing between collateral squeeze and margin spiral clarifies how changes in market prices versus changes in rehypothecation/churning practices each contribute to systemic deleveraging.
  - Measures that affect re-pledging chains (custody arrangements, rehypothecation rights, legal structuring) can materially alter systemic leverage via the margin spiral channel.

*Source: Annex 1. Deleveraging Components—Collateral Squeeze and Margin Spiral (IMF working paper annex content).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11256.pdf_