Chapter 5 5.7

Liquidity Risk

Measuring liquidity: bid-ask spreads, price impact, market depth, and stress dynamics

Why Liquidity Matters

Market liquidity—the ease with which assets can be bought or sold without causing significant price changes—is fundamental to bond market functioning. For JGBs, liquidity affects:

Government Borrowing Costs: Liquid markets command lower yields (investors accept lower returns for ease of exit)
Monetary Policy Transmission: BOJ operations require deep, liquid markets to influence rates effectively
Financial Stability: Illiquid markets amplify shocks (witnessed during March 2020 COVID panic, YCC periods)
Investor Participation: Foreign investors demand liquidity premiums in shallow markets

Unlike stocks, where liquidity is relatively stable, bond liquidity is highly fragmented across maturities and vintages. A newly issued 10-year JGB trades vastly more than a 9.9-year bond issued just one month earlier—this phenomenon drives unique measurement challenges.

Theoretical Foundation: Price Impact

The Core Concept

Academic literature defines liquidity primarily through price impact: how much does an asset's price move in response to a given transaction?

$$\text{Price Impact (\lambda)} = \frac{\Delta P}{Q}$$

Where:

$\Delta P$ = Price change (in basis points)
$Q$ = Transaction size (e.g., ¥10bn)

Interpretation:

Liquid market: Large trades cause minimal price disruption → Low $\lambda$
Illiquid market: Small trades trigger significant price moves → High $\lambda$

Kyle’s Lambda (1985)

Albert Kyle's seminal model introduced $\lambda$ (lambda) as the market depth parameter, measuring how order flow translates into price changes. The intuition:

Markets with many uninformed traders ("noise traders") mask the signal from informed trades → Lower price impact
Markets with mostly informed traders see their trades immediately reflected in prices → Higher impact

Example Calculation:

A ¥50bn purchase of 10Y JGBs moves yields down 0.5bp
Kyle's $\lambda = 0.5bp / ¥50bn = 0.01bp$ per ¥1bn
Lower $\lambda$ = more liquid (same-sized trade causes less price movement)

💡 Practical Relevance: During YCC (2016–2024), BOJ purchases compressed price impact near the 0% target for 10Y yields. Post-YCC, $\lambda$ increased 3-5× as market-determined pricing returned, making large trades more expensive to execute.

Practical Liquidity Metrics

1. Bid-Ask Spread

The most widely used liquidity indicator in practice:

\[\text{Bid-Ask Spread} = P_{\text{ask}} - P_{\text{bid}}\]

Represents the cost of immediacy—what you pay to trade instantly rather than waiting for a better price.

JGB Maturity	Typical Spread (Normal Conditions)	Stress Period Spread (March 2020)
2-Year (On-the-run)	0.3–0.5 ticks (¥3,000–¥5,000/¥100M)	2–3 ticks (¥20,000–¥30,000/¥100M)
10-Year (On-the-run)	0.5–1 tick	3–5 ticks
30-Year (On-the-run)	1–2 ticks	5–8 ticks
Off-the-run issues	2–5× wider than on-the-run	10–20× wider (often no quotes)

Limitations:

Only captures cost for small trades at quoted size (typically ¥1–5bn)
Large institutional orders (¥50bn+) face much wider effective spreads
Requires quote data (not always available for off-the-run bonds or corporate bonds)

2. Market Depth

Definition: The volume of orders available at prices near the current market level (often visualized as "order book depth").

Mathematically, depth is the inverse of price impact:

\[\text{Depth} = \frac{1}{\lambda} = \frac{Q}{\Delta P}\]

Practical Interpretation:

Deep market: ¥100bn can be absorbed within 0.5bp price movement → High depth
Shallow market: ¥10bn moves prices 2bp → Low depth

JGB Futures Example (10Y):

Normal conditions: Order book shows ¥50–100bn within 2 ticks of midprice
YCC period (2020–2023): Depth collapsed to ¥5–20bn as BOJ absorbed supply
Post-YCC (2024+): Depth recovering but remains ~60% of pre-2016 levels

3. Turnover and Trading Volume

Turnover ratio:

\[\text{Turnover} = \frac{\text{Trading Volume (period)}}{\text{Outstanding Amount}}\]

JGB Turnover Trends:

Period	Annual Turnover Ratio	Context
2010–2012	3.5–4.2×	Pre-QQE baseline
2013–2015	2.8–3.2×	QQE launch, initial liquidity concerns
2016–2019	1.9–2.4×	YCC era, BOJ owns 40–50% of market
2020–2023	1.2–1.8×	COVID + YCC defense, liquidity drought
2024–Present	2.0–2.5×	YCC exit, gradual recovery

Interpretation Challenge: Low turnover doesn't always mean illiquidity—it can reflect buy-and-hold behavior (e.g., pension funds, insurance companies). However, declining turnover + widening spreads together signal deteriorating liquidity.

4. Amihud Illiquidity Measure

Developed by Yakov Amihud (2002), this metric estimates price impact per unit of trading volume:

$$\text{ILLIQ} = \frac{1}{D} \sum_{d=1}^{D} \frac{|R_d|}{V_d}$$

Where:

$R_d$ = Return on day $d$ (absolute value)
$V_d$ = Trading volume (yen)
$D$ = Number of days in measurement period

Intuition: Higher ratio = same trading volume causes larger price changes = less liquid.

JGB Application Example (10Y Benchmark):

Period	Avg Daily Return	Avg Daily Volume	Amihud ILLIQ
Pre-YCC (2015)	0.05%	¥800bn	0.625 × 10⁻⁶
YCC Peak (2020)	0.02%	¥350bn	0.571 × 10⁻⁶
Post-YCC (2024)	0.08%	¥600bn	1.33 × 10⁻⁶

Paradox Noted: YCC suppressed both volatility AND volume, making the Amihud measure ambiguous. Post-YCC, higher illiquidity reflects genuine price discovery returning rather than pure liquidity deterioration.

Advantages:

Simple to calculate with price and volume data only
Captures transaction cost dimension
Widely used in academic research for cross-sectional comparisons

Limitations:

Assumes linear price impact (real markets show nonlinear effects for large trades)
Sensitive to outlier days (single volatile day skews monthly average)
Requires accurate volume reporting (problematic for OTC corporate bonds)

JGB-Specific Liquidity Indicators

On-the-Run Premium

The on-the-run (OTR) premium exploits bond market fragmentation: newly issued bonds trade at tighter yields than nearly identical older bonds.

Setup:

On-the-run: Most recently auctioned 10Y JGB (e.g., Issue #380, auctioned December 2024)
Off-the-run: Previous issue (e.g., Issue #379, auctioned September 2024, now 9.75Y remaining)

Despite only 3-month maturity difference, the OTR bond commands a liquidity premium (yields 2–8bp lower).

\[\text{OTR Premium} = Y_{\text{off-the-run}} - Y_{\text{on-the-run}}\]

Historical OTR Premium (10Y JGBs):

Period	Avg OTR Premium	Market Context
2008–2012	4–6bp	Normal conditions, pre-Abenomics
2013–2015	2–4bp	QQE launch, BOJ buying compresses premium
2016–2019	1–2bp	YCC flattens OTR/OTTR distinction
March 2020	15–25bp (spike)	COVID panic, flight to most liquid issues
2024–Present	3–5bp	YCC exit, premium normalizing

Why Does OTR Premium Exist?

Concentration of Trading: Market makers focus liquidity provision on current issues → tighter spreads
Futures Deliverability: OTR bonds more likely to be cheapest-to-deliver (CTD) for JGB futures contracts
Repo Specialness: OTR bonds easier to borrow in repo markets (lower repo rates = "special")
Benchmark Status: Institutional mandates often reference OTR yields (e.g., "10Y JGB + 50bp")

💡 Trader Strategy: During the LTCM crisis (1998), arbitrageurs famously exploited OTR/OTTR spreads—buying cheap off-the-run bonds while shorting expensive on-the-run equivalents. When spreads normalized, profits were realized. However, this trade requires significant leverage and patience during spread widening phases.

Liquidity Supply Auctions (流動性供給入札)

Unique to Japan, the MOF conducts liquidity supply auctions (introduced 2006) to re-issue off-the-run bonds experiencing structural illiquidity:

Mechanism:

MOF identifies illiquid issues (typically 20Y–40Y, but now includes 2Y–10Y)
Additional amounts of these existing bonds are auctioned to primary dealers
Increases outstanding size → improves market depth

Impact on 20Y Sector:

Before (2005): 20Y bonds had ¥400–600bn per issue, bid-ask spreads 3–5 ticks
After (2010+): Accumulated size ¥1–1.5tn per issue, spreads compressed to 1.5–2.5 ticks
Evidence: Kakuma (2012) documented 30–40% reduction in execution costs post-introduction

Liquidity During Stress Periods

2008 Global Financial Crisis

The Lehman collapse (September 2008) triggered a flight to quality into JGBs, but with fragmented liquidity effects:

Metric	Pre-Crisis (Aug 2008)	Crisis Peak (Oct 2008)	Change
10Y Bid-Ask Spread	0.5 ticks	2–3 ticks	+400%
OTR Premium	4bp	18bp	+350%
Futures Depth (10Y)	¥80bn	¥25bn	-69%
Daily Turnover	¥12tn	¥8tn (initial drop), then ¥18tn (panic trading)	Volatile

Key Observation: Unlike US Treasuries (which saw indiscriminate selling), JGBs experienced bifurcated liquidity:

On-the-run 10Y bonds remained tradable (domestic institutional demand)
Off-the-run and 20Y+ issues became "untouchable" (spreads 10–15 ticks)
Futures market functioned but at reduced depth

March 2020 COVID-19 Panic

The most severe JGB liquidity shock in modern history occurred March 9–19, 2020:

Timeline:

March 9: Oil price collapse triggers global risk-off → JGB yields fall 15bp intraday
March 12–13: Foreign investors liquidate JGBs to raise USD (cross-currency basis widens to -100bp)
March 16: BOJ emergency bond purchases (¥2tn+), YCC defense operations
March 19: Liquidity partially restored as Fed announces USD swap lines

Liquidity Metrics During Peak Stress (March 13, 2020):

Indicator	Normal (Feb 2020)	Crisis (Mar 13)	Ratio
10Y Bid-Ask	0.5 ticks	5–8 ticks	10–16×
30Y Bid-Ask	1.5 ticks	10–15 ticks	7–10×
Amihud ILLIQ (10Y)	0.6 × 10⁻⁶	4.2 × 10⁻⁶	7×
Futures Order Book Depth	¥60bn	¥8bn	-87%
OTR Premium	2bp	25bp	12.5×

Unique Features:

USD Funding Stress: Unlike 2008, liquidity crisis driven by dollar shortage (Japanese banks/insurers selling JGBs to obtain USD)
Yield Curve Inversion: 5Y yields briefly traded above 10Y (March 13) as YCC anchor at 10Y created distortions
Futures Basis Blowout: 10Y JGB futures traded 150 ticks cheap to fair value (basis traders couldn't finance positions)

💡 Policy Response: BOJ's March 16 emergency measures included: (1) unlimited bond purchases at 0%, (2) CP/corporate bond buying expansion, (3) coordination with Fed on USD swap lines. Liquidity normalized within 2 weeks, but the episode revealed structural vulnerabilities in YCC framework.

YCC Era Liquidity Deterioration (2016–2024)

Yield Curve Control created a chronic liquidity problem distinct from acute crises:

Mechanism:

BOJ owns 50%+ of JGB market (¥580tn / ¥1,100tn total) → Reduced free float
10Y yields anchored at 0% (later ±0.25%, then ±0.5%) → Price discovery suppressed
Dealers reduce inventory (no profit in market-making when BOJ sets prices)
Turnover collapses, bid-ask spreads widen for off-the-run issues

Evidence of YCC-Induced Illiquidity:

Metric	Pre-YCC (2015)	YCC Peak (2022)	Post-YCC (2024)
Annual Turnover Ratio	3.2×	1.4×	2.3×
Avg Daily Volume	¥15tn	¥7tn	¥11tn
10Y Futures Depth	¥90bn	¥20bn	¥55bn
Off-the-Run Spread (20Y)	2 ticks	5–8 ticks	3–4 ticks
Price Volatility (10Y, annual)	0.8%	0.3%	1.2%

Research Findings:

Iwatsubo & Taishi (2017): BOJ buying frequency (not just volume) critical—more frequent small purchases better than infrequent large ones for liquidity
Pelizzon et al. (2017): "Scarcity effect" (BOJ ownership) reduced liquidity, but "spotlight effect" (bonds BOJ actively buys) improved it for those specific issues
Kurosaki et al. (2015): Order book depth declined sharply, but traditional bid-ask spreads remained stable (misleading signal)

Advanced Indicator: Noise Measure

Developed by Hu, Pan, and Wang (2013), the Noise measure captures arbitrage constraints by detecting yield curve deviations:

Concept:

Fit a smooth yield curve model (e.g., Nelson-Siegel) to observed bond yields
Calculate residuals (actual yield - model yield) for each bond
Noise = standard deviation of residuals across all bonds

$$\text{Noise}_t = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (y_{i,t} - \hat{y}_{i,t})^2}$$

Where $y_{i,t}$ is observed yield and $\hat{y}_{i,t}$ is model-implied yield.