11 price dispersion in otc markets: a new measure of liquidity rainer jankowitsch amrut nashikkar...
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11
Price Dispersion in OTC Markets: A New Measure of Liquidity
Rainer JankowitschAmrut Nashikkar
Marti Subrahmanyam
Stern School of Business New York University
For presentation at the conference onLiquidity: Pricing and Risk Management
Bank of England, 23-24 June 2008
3
Liquidity and Asset Prices
• Why are liquidity effects important in asset pricing?• Theory on liquidity effects and asset prices: The current
literature.• Empirical evidence on liquidity effects in asset prices:
The current literature.• Liquidity effects in highly illiquid markets: Problems of
measurement.• Liquidity effects in highly illiquid markets: An example of
the US corporate bond market.• Liquidity effects in OTC markets
4
Why are liquidity effects important? • Assets with similar risk characteristics have different
expected returns.• One candidate for missing factor – liquidity.• Liquidity differentials may explain differences in return
performance for the same level of risk.• Liquidity raises trading volume and reduces the cost of
capital – even small improvements reduce the cost of capital substantially.
• Example: Hedge funds buy illiquid assets and sell liquid ones–“off-the-run” versus “on-the-run.”
5
Liquidity effects in highly illiquid markets
• Problem with most liquidity metrics is that they are transaction-based measures.
• Applicable in the more liquid markets, e.g. equities, foreign exchange, some treasury bonds.
• Many asset markets are too illiquid to permit measures such as bid-offer spread, depth, trading volume or even the Amihud measure of market impact (Kyle’s λ).
• Classic case of “looking for lost keys under the lamp-post rather than where they were lost.”
77
Microstructure of OTC markets
• Importance of over-the-counter (OTC) markets: Real estate, bond (Treasury and corporate), most new derivative markets etc.
• Microstructure of OTC markets is different from exchange-traded (ET) markets.
• Lack of a centralized trading platform: Trades are result of bilateral negotiations → Trades can take place at different prices at the same time.
• Search costs for investors and inventory costs for broker-dealers (and information asymmetry).
• Challenges of assembling market-wide data.
• Important issues of illiquidity, in crises such as the present credit crisis.
88
Research Questions
• In the presence of search costs for traders and inventory costs for dealers: how are prices determined in an OTC market?
• What determines price dispersion effects, i.e., deviations between the transaction prices and their relevant market-wide valuation?
• How does price dispersion capture illiquidity in such markets?
• How is the “hit rate” – the proportion of transactions within the average quoted bid-ask spread – related to illiquidity?
99
Literature Review
• Price quote determination in a inventory cost setting:– Garbade and Silber (1976, 1979), Garman (1976), Amihud and
Mendelson (1980), Ho and Stoll (1980, 1983)
• Price determination in an asymmetric information setting:– Bagehot (1971), Glosten and Milgrom (1985), Kyle (1985)
• OTC markets:– Garbade and Silber (1976, 1979), Ho and Stoll (1980, 1983),
Duffie et al. (2005, 2007)
• Liquidity effects in Corporate Bond Markets– Edwards et al. (2007), Chen et al. (2007), Mahanti et al. (2008)
1111
Market Microstructure Model
• There are i assets, i = 1,2…I, and a continuum of dealers of measure J. j indexes the type of the agent
• Competitive dealers face inventory costs and quote bid and ask prices depending on their desired inventory levels.
• Several investors, who have exogenously given buying and selling needs, trade with the dealers.
• Investors have to directly contact dealers to observe their price quotes (“telephone market”).
• Investors face search costs every time they contact a dealer, before they can trade.
1212
The Dealer’s Decision
• Denote by si,j the inventory of asset i with dealer of type j.
• Each dealer faces inventory holding costs H that are convex in the absolute quantity held, given by H = H(s). Independent across assets.
• The marginal holding cost of adding a unit is approximated by h = H’(s).
• Each trade incurs a marginal transaction cost function fa and fb
• The ask price of asset i quoted by dealer j is denoted as pai,j , the bid
price pbi,j, for one additional unit.
• Since the dealership market is competitive: pai,j = mi,j + fa(h(si,j))
and pbi,j = mi,j – fb(h(si,j)) .
• The market’s expectation of the price of asset i is defined by mi = E(mi,j).
1313
The Investor’s Decision
• An investor wishes to execute a buy-trade of one (infinitesimal) unit.
• The investor has contact with one dealer and is offered an ask price pa,0.
• The investor faces search cost c for contacting an additional dealer; thus, she evaluates the marginal cost and benefit of doing so.
• Garbade and Silber (1976) show that the investor will buy the asset at pa,0 if this price is lower than his reservation price pa*.
• The reservation price solves:
where ga(.) is the density function for the ask price when contacting an arbitrary dealer.
*
0
* )()(ap aa dxxgxpc
1414
Price Dispersion and “Hit Rate”
• Assumption for inventory holding distribution:– Uniformly distributed with mean zero (zero net supply)
– Support from –S to +S
– Independent across assets
• Assumption for the holding costs:
H = αs2/4 → h = αs/2• Assumption for the transaction cost:
h = αS/2
• Solving for the reservation prices for a trader gives:
pa* = m + (2cαs)0.5
pb* = m - (2cαs)0.5
• Ask and bid prices, when contacting a dealer are uniformly distributed with supports [m; m+αs] and [m; m-αs]
15
Graphical depiction of solution – zero net inventory
mPbl= m – αS/2 Pa
h= m + αS/2
Pb*= m – √2αcS Pa*= m – √2αcS
Range of quotes
Range of transactedprices
E(Pb) E(Pa)
Average Bid-ask spread
16
Price Dispersion and “Hit Rate”
• Based on this setup, the dispersion of transacted prices pk from the market’s valuation, m, have a mean zero and variance equal to:
• Percentage of trades that fall within the median quote (hit-rate) can be derived:
16
2 if )31(
2 if )32()( 22
2
ScS
ScScmpE k
S/8 c if %100
S/2c S/8 if 2c2
S/2c if %50
SHR
1717
Liquidity Measure
• Based on the model we propose the following new liquidity measure for bond i on day t:
where Ni,t … number of transactions, for bond i on day t
pi,j,t … transaction price for j = 1 to Ni,t, for bond i on day t
Vi,j,t … trade volume j = 1 to Ni,t,for bond i, trade j, on day t
mi,t … market-wide valuation, for bond i on day t
• Intuition behind the measure: Sample estimate of the price dispersion using all trades within a day.
t,j,i
N
1j
2t,it,j,iN
1j t,j,i
t,i V )mp(V
1d t ,i
t ,i
1818
Liquidity Measure
• Represents the root mean squared difference between the traded prices and the respective market-wide valuation.
• Is an estimate for the absolute deviation and, more importantly, has the interpretation as the volatility of the price dispersion distribution.
• Volume-weighting assumes that price dispersion is revealed more reliably in larger trades and eliminates potential erratic prices of particularly small trades.
2020
Data for the Present Study
• Time period: October 2004 to October 2006
• US bond market data from three sources:– TRACE: all transaction prices and volumes– Markit: average market-wide valuation each trading day– Bloomberg: closing bid/ask quotes at the end of each trading
day– Bloomberg: bond characteristics
→ 1,800 bonds with 3,889,017 transactions:• Dollar denominated• Fixed coupon or floating rate• Bullet or callable repayment structure• Issue rating from Standard & Poor’s, Moody’s or Fitch• Traded on at least 20 days in the selected time period
2121
Data for the Present Study
• Selected bonds represent:– 7.98% of all US corporate bonds– 25.31% (i.e., $1.308 trillion) of the total amount outstanding– 37.12% of the total trading volume
• Available bond characteristics:– Coupon, maturity, age, amount issued, issue rating, and industry
• Available trading activity variables:– trade volume, number of trades, bid-ask spread and depth (i.e.,
number of major dealers providing information to Markit)
2222
Data for the Present Study
• Distribution of bonds across Bloomberg industry categories:
BANK FINANCIAL INDUSTRIAL TRANS - NON RAIL UTILITY - ELEC
Industry
Nu
mb
er
of B
on
ds
02
00
40
06
00
80
0
Bank Gas Transm Telephone Trans Rail Utility-Gas Financial Industrial Trans-Non Rail Utility-Elec Industry
Nu
mb
er o
f B
on
ds
2323
Data for the Present Study
• Distribution of bonds across ratings:
AAA AA A BBB BB B C/CCC
01
00
20
03
00
40
05
00
Rating Grade
Nu
mb
er o
f B
on
ds
2424
Data for the Present Study
• Distribution of other variables:
Min Median Max _
Coupon 1.95% 6.125% 11.25%
Maturity 0.07 4.80 31.61
Age 0.04 3.34 16.23
Amount Issued $100m $500m $6.5b
Bid-Ask 1.55bp 32.17bp 90bp
Trade Volume $127,925 $2.8m $61.3m
Trades 1.21 4.14 121.6
Depth 3 4.62 12.86
2525
Data for the Present Study
• Trading frequencies:
Days per year 10/2004 to 10/2005 10/2005 to 10/2006
> 200 411 392
151 – 200 309 369
101 – 150 236 322
51 – 100 221 222
≤ 50 444 459 _
Total # bonds 1621 1704
2727
Empirical Results – Market Level Analysis
• Volume-weighted average difference between TRACE prices and respective Markit quotations is 4.88 bp with a standard deviation of 71.85 bp → no economically significant bias.
• Price dispersion measure (i.e. root mean squared difference) is 49.94 bp with a standard deviation of 63.36 bp.
• Market-wide average bid-ask spread is only 35.90 bp with a standard deviation of 23.73 bp.
• Overall, we find significant differences between TRACE prices and Markit composite that cannot be simply explained by bid-ask spreads or trade time effects.
2828
Empirical Results – Bond Level Analysis
• At the individual bond level, we relate our liquidity measure to bond characteristics and trading activity variables to show its relation to liquidity.
• We employ cross-sectional linear regressions using time-weighted averages of all variables.
• We present results based on the whole time period, as well as based on each available quarter (2004 Q4 to 2006 Q3).
• To further validate the results, we analyze the explanatory power of our liquidity measure in predicting established estimators of liquidity → Amihud ILLIQ measure.
2929
Empirical Results – Bond Level Analysis
• Cross-sectional regressions with the new price dispersion measure as dependent variable:
2004 Q4 2006 Q3 Overall __ Constant 231.732*** 167.760*** 187.648***Maturity 2.576*** 1.453*** 1.840***Amount Issued -5.597*** -3.710*** -3.060***Age 3.849*** 1.242*** 2.064***Rating 2.090*** 1.096*** 1.254***Bid-Ask 0.237*** 0.544*** 0.568***Trade Volume -7.963*** -6.023*** -8.458*** _R2 44.9% 49.3% 61.5% _Observations 1270 1513 1800
3636
Empirical Results – Bond Level Analysis
• To validate these results, we compare the new measure to established estimators of liquidity in the literature.
• One important approach to measure liquidity is through the price impact of trading.
• A popular (and intuitive) measure was introduced by Amihud:
where ri,t … return on the bond i on day t
Vi,t ... trade volume of the bond i on day t
T
tti
ti
V
r
Ti
1,
,1 bondfor measure ILLIQ Amihud
3737
Empirical Results – Bond Level Analysis
• Cross-sectional univariate regressions with the Amihud measure as dependent variable:
2004 Q4 2006 Q3 Overall __
Constant -18.192*** -18.377*** -17.932***
Price Dispersion 0.021*** 0.027*** 0.025*** _
R2 22.0% 27.3% 31.3% __
Observations 1169 1426 1800
3838
Empirical Results – Bond Level Analysis
• Cross-sectional multivariate regressions with the Amihud measure as dependent variable:
2004 Q4 2006 Q3 Overall Overall 2__
Constant -10.033*** -8.464*** -7.624*** 0.177
Price Dispersion 0.015*** 0.021*** 0.018*** -
Coupon 0.190*** 0.198*** 0.186*** 0.296***
Amount Issued -0.156* -0.226*** -0.275*** -0.583***
Trades -0.049*** -0.059*** -0.067*** -0.050***
Trade Volume -0.366*** -0.375*** -0.336*** -0.436*** _
R2 42.5% 59.2% 63.7% 52.8% _
Observations 1169 1426 1800 1800
3939
Empirical Results – Hit Rate Analysis
• Many studies use bid-ask quotations (or mid quotes) as proxies for traded prices. Our data set allows us to validate this assumption.
• The hit-rate for the TRACE price is 51.37% (i.e., in these cases, the traded price lies within the bid and ask quotation)
• Deviations are symmetric → 50.12% are lower than the bid and 49.88% are higher than the ask.
• Even the hit rate of the Markit quotation (58.59%) is quite low.
• Overall, we find that deviations of traded prices from bid-ask quotations are far more frequent than assumed by most studies.
4040
Future Research
• The proposed liquidity measure can potentially be used to explain the liquidity premia in the corporate bond market.
• The time-series properties of the measure can be explored and potentially used to forecast “true” bond returns.
• We can explore whether observed changes in search costs or inventory costs (e.g. when a shock reduces dealers capital) affect the price dispersion.
• With additional data, we can study the behavior of our liquidity measure in crisis periods such as post-July 2007.
4141
Conclusions
• A new liquidity measure based on price dispersion effects is derived from a market microstructure model.
• The proposed measure is quantified in the context of the US corporate bond market.
• It is larger and more volatile than bid-ask spreads and shows a strong relation to bond characteristics and trading activity variables, as well as established liquidity proxies.
• A “hit-rate” analysis shows that bid-ask spreads can only be seen as a rough approximation of liquidity costs.
• The proposed measure can potentially explain and quantify the liquidity premia.
• These findings foster a better understanding of OTC markets and are relevant for many practical applications, e.g. bond pricing, risk management, and financial market regulation.
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