Liquidity Risk of Corporate Bond Returns Viral Acharya (NYU Stern)

12 Pages·2012·0.35 MB·English

Liquidity Risk of Corporate Bond Returns
Viral Acharya(NYU Stern), Yakov Amihud
(NYU Stern) and SreedharBharath(ASU)
Forthcoming, JFE
Sponsored by
Centre for Advanced Financial Research and Learning (CAFRAL)
and
Fixed Income Money Market and Derivatives Association of India (FIMMDA)
A short introduction:
The effect of market liquidity on asset pricing Our formal model assumes that
Assets are characterized by dividendstream and trading costs.
The prevailing theory of asset pricing: Investors’need to trade occurs randomly.
Positive risk-return relation.
However, the empirical evidence for the stock market is that on In equilibrium, we prove that …
average, RM -Rf> 0. 1. Asset returnsare increasingfunction of trading costs.
Across stocks, empirical evidence is scarceor non-existent, or (The function is concave.)
higherrisk loweraverage return. Or
Problems in estimating risk. Asset pricesare decreasingand convexfunction of trading costs.
The theory of Amihud & Mendelosn(1986):
2. Netreturns too are an increasingfunction of trading costs.
Positive illiquidity-return relation.
The expected excess monthly return (or yield) on a stock as a function of
the stock’s bid-ask spread, reflecting clienteles (Amihud-Mendelson1986)
P/E ratio and liquidity(Loderer& Roth, JEF 2003)
R= 0.0065 + 0.01β+ 0.0021ln(S) + year dummies
i i i The effect of illiquidity (relative bid-ask spread) on the P/E ratio, controlling for
0.80% (1) beta, (2) dividend payout, (3) current EPS growth and (4) expected earnings
0.70%
growth (from analysts’reports).
0.60%
Excess Monthly Return000...345000%%% Result: discount of over 20%for a median-spread stock compared to zero-
0.20% spread stock (1995-2001).
0.10%
Discount as a function of spread is observed for both Nasdaqand Swiss stocks.
0.00%
0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0%
Bid-Ask Spread (%)
Restricted stock. Price discount of about 1/3. (Silber 1991).
There is ample empirical support for this relation by independent studies.
Why do small trading costs have a big price effect? Liquidity is hard to observe, but we observe trading frequency, which by Amihud-
Because they are incurred repeatedly, for ever. Mendelson(1986) is affected by trading costs.
Turnover= (volume /number of shares) proxies for trading frequency.
A quick calculation:
More liquid stocks are traded more frequently.
Valuation of transaction cost of c
PV= c / (r-g).
The effect of turnover on stock returns –cross-section analysis
It growswith the stock price, whose growth rate is r –D/P.
Explanatory Variables: All months Excl. January
PV= c * P/D
Turnover: -.04 (8.58) -.04 (7.91)
Book/Market: .14 (5.97) .08 (3.29)
Assume that trading is once a year.
log(Size): -.05 (4.65) .02 (1.60)
Stock dividend yield, D/P, is now about 2%-2.5%. β: -.37 (5.76) -.05 (6.84)
the price multipleof trading cost cis 40-50.
0.1% trading cost leads to at least 4% discount in stock price. Higherliquidity, or turnover lowerexpected returns.
The effect of ILLIQ= avg(|R|/$Volume) on stock expected return
(constant omitted), monthly, 1964-1997 [From Amihud (2002)] Liquidity changes over time:
Evidence from the recent crisis
Variable All months Excl. January 1964-1980 1981-1997 U.S. trading costs as % of stock prices. Based on data from ITG.
BETA 0.217 (0.64) 0.260 (0.79) 0.297 (0.59) 0.137 (0.30)
1.8%
Small Cap
ILLIQMA 0.112 (5.39) 0.103 (4.91) 0.135 (3.69) 0.088 (4.56) 1.6% All
1.4% Large Cap
LnSIZE -0.134 (3.50) -0.073 (2.00) -0.217 (3.51) -0.051 (1.14) 1.2%
1.0%
StdDevof Return -0.179 (1.90) -0.274 (2.89) -0.136 (0.96) -0.223 (1.77) 0.8%
0.6%
DIVYLD -0.048 (3.36) -0.063 (4.28) -0.075 (2.81) -0.021 (2.11) 0.4%
0.2%
R100 0.888 (3.70) 1.335 (6.19) 0.813 (2.33) 0.962 (2.92) 0.0%
Q3  Q1  Q3  Q1  Q3  Q1  Q3  Q1  Q3  Q1  Q3  Q1 
RYR 0.359 (3.40) 0.439 (4.27) 0.324 (2.04) 0.395 (2.82) 2005 2006 2006 2007 2007 2008 2008 2009 2009 2010 2010 2011
The effects of expectedand unexpectedilliquidity(illiquidity shocks)
on excess monthly stock returns, 1964-1996. Current paper, Liquidity Risk of Corporate Bond Returns
Note: The (absolute) effect of liquidity declines in size.
The yield spread on corporate bonds is considered a riskand defaultpremium.
Excess returns on size-based portfolios
RM-Rf
RSZ -Rf RSZ -Rf RSZ -Rf RSZ -Rf RSZ –Rf
(EW) 2 4 6 8 10 Corporate bonds are usually less liquidthan Treasury bonds, especially the
Constant -3.876 -4.864 -4.335 -4.060 -3.660 -1.553
high-yield ones.
(1.97) (2.03) (2.12) (2.13) (2.05) (0.99)
LnMILLIQ 0.712 0.863 0.808 0.761 0.701 0.319
m-1
(2.12) (2.11) (2.33) (2.36) (2.30) (1.18) Therefore, bond returns should respond to liquidity shocks (in addition to other
LnMILLIQ U -5.520 -6.513 -5.705 -5.238 -4.426 -3.104 shocks that affect bond prices) because the required yield changes then.
m
(4.42) (4.53) (4.34) (4.12) (4.04) (3.38)
The yield spread reflects both risk\default premium and illiquidity premium.
JANDUM 5.280 8.067 5.446 4.232 3.000 1.425
m
(4.20) (5.03) (4.08) (3.45) (2.64) (1.47)
Chen, Lesmond& Wei (2007) –pricing of the levelof illiquidity.
R-squared 0.144 0.188 0.140 0.119 0.089 0.049
D-W 1.98 1.99 1.96 1.99 2.03 2.14 deJong& Driessen(2007), Lin, Wang & Wu (2011) –pricing liquidity risk.
Liquidity costs and corporate bond yields
Liquidity and Treasury securities yields Yield spreads are known to exceed the expected cost of default, given data on
default probability and recovery rate.
1) Amihud-Mendelson(JF 1991): The excess yield compensates for both riskand illiquidity.
Treasury billsand Treasury noteswith the same(short) maturity: Lower ratinglower liquidity(higher bid-ask spread and other measures of
Riskis the same. illiquidity) higher illiquidity premium.
Bills are more liquidthan bonds,
bills have lower yieldthan notes. Chen, Lesmond& Wei (JF 2007) estimate the effect of the levelof trading costs
on the cross-section of bond yields,
2) On-the-run bonds are more liquid than off-the-run bonds, and have lower controlling for bond and firm characteristics, such as rating, leverage, risk.
yield. Results:
Trading costs have a positiveand highly significant effect on yield spread.
Estimating the effect of Liquidity Risk on bond returns Research questions:
(current paper) Market liquidity changes over time.
We study liquidity risk, the exposureof bond prices to liquidity shocks (the
R = a+ β TERM + β DEF+ β Silliq+ β Billiq e , returns-liquidity shocks covariance).
j,t j T,j t D,j t SI,j t BI,j t+ j,t
-Does the liquidity risk changeover time? (risk in liquidity risk)
-Is this change different for different ratingclasses of bonds?
R, = excess return on bond portfolio (over 30-day T-Bill rate)
jt
-Is the liquidity risk conditional?
TERM: Long-term govt(30yr) minus 30-day T-Bill return
t
-If so –is there an economic identificationof changes in liquidity risk?
DEF:Eq-wtdreturns of all corporate bonds (maturity > 1 yr) –average return on
t
1-yr and 30-yr govtbonds
A two-step approach:
1) Statisticalanalysis: Test for a pattern in changes over time in liquidity risk
Silliq , Billiq:Innovations in stock and Treasury bond illiquidity (from AR(2)
t t 2) If there is a pattern of such a change –identify its economic determinants.
and AR(3) models).
Related models and theories: Firm’s policy-related model: Focus on incentives and endogenizedconstraint:
Brunnermeierand Pedersen(2009): marketliquidity can be adversely affected Acharyaand Viswanathan(2011):
by fundingliquidity. Because of margin constraints, a negative value shock Adverse value shock affect financial firms\intermediaries
causes a liquidity shock because of correlated liquidations. This lowers asset greater firm’s leverage
values and exacerbates the effect of the shock. incentive of firm’s managers to risk-shift
greater constraint on outside funding (rolling over debt)
He and Krishnamurthy(2010): Households invest through intermediaries. A worsening funding liquidity
negative wealth shock makes them allocate money away from risky to riskless need of firm to de-lever
assets, lowering intermediaries’wealth and causing capital constraints and sale of assets
forced liquidation. worsening liquidity. This in turns affects asset prices.
Sample period: 1973-2007, 420 months. Bond data are from Lehman Fixed
Income Database (Warga, 1998) for 1981-1996, and Merrill Lynch corporate
bond index database (Schafer & Strebulaev, 2008) thereafter, incl. 2008-9.
Returnsare calculated from monthly prices and accrued interest.
Corporate bonds are largely held in institutionalportfolios rather than in retail
ones. Studying their return-liquidity relations is an appropriate setting to identify -We use actual prices, no matrix pricing. Bonds with no options(call, sinking
these liquidity effects. funds). Excluded: bonds not in Lehman or Merrill indexes; with maturity < 1
year; not rated; non-identical S&P\Moody’s rating; special features (call, sinking
funds, floating rate).
-Average # bonds in each month: 2,234(between 245 and 9,286).
-We construct indices of bond returns, VW, by rating class.
Illiquidity innovations Stock illiqinnovations
Equity-market illiquidity: Amihud’s(2002) ILLIQ, the equally-weighted monthly
average of daily |return|/dollar volume, as modified by Acharyaand Pedersen
(2005). ILLIQmeasures price impact, related to Kyle’s (1985) λ.
Treasury bond market illiquidity: the monthly quoted % bid-ask spread of
short maturity on-the-run treasuries (source: Goyenko(2006)). Was used by
Longstaff, Mithal, Neis(2004), deJongand Driessen(2009).
The innovations are residualsfrom an autoregressivemodel, AR(3) for stocks
and AR(2) for bonds. The coefficients are adjusted for finite sample by Shaman
and Stine’s (1989) method.
Unconditional liquidity risk (red=significant)
Bond illiqinnovations Coefficients
Rating α ßT(allsignif.) ßD(allsignif.) ßSI ßBI Adj-Rsq
AAA 2.68 0.42 0.76 73.70 13.58 0.76
AA 5.68 0.47 0.81 61.69 1.81 0.79
A 3.55 0.50 0.90 40.39 -1.66 0.82
BBB 3.72 0.47 0.97 17.06 -11.42 0.75
BB (Junk) 14.91 0.38 0.98 -90.15 -57.28 0.51
B 23.61 0.35 0.99 -193.55 -70.07 0.30
CCC & 84.52 0.21 0.89 -328.70 -63.19 0.11
below
TERM DEFAULT SILLIQ
DEF -0.529 1
Silliq 0.041 -0.153 1
Billiq -0.057 -0.057 0.086
Time-varying betas Time-varying betas
Estimate a Markov regime-switching model in a two-equation model, for
Investment Grade (IG) and Junk (Jnk) • Estimate a Markov regime-switchingmodel
Regime-switching analysis, Hamilton (1994) Regime-Dependent Variance-Covariance Matrix (s= 1,2):
t
R , = a + β TERM+ β , DEF+ β Silliq+ β Billiq+e ,
IGt IG IG,T t IGD t IG,SI t IG,BI t IGt
R ,=a + β TERM +β , DEF + β Silliq + β Billiq+
JNkt IG JNK,T t JNKD t JNK,SI t JNK,BI t
e , Markov switching probability for state transition:
JNKt
P(s= 1| s = 1) = p
t t–1
P(s= 2| s = 2) = q
t t–1
Liquidity betas changesubstantially between regimes Wald tests for differences in coefficients–Chi-sq tests
Numbers are p-values
Regime 1
Investment G t-stat Junk Grade t-stat Parameters
Constant 2.34 1.36 27.21 4.72 P 0.96
TERM 0.35 44.38 0.28 12.56 q 0.93
DEF 0.37 12.06 1.08 10.07 Between regime 1 and 2 Between IG and Junk
Silliq 13.95 1.21 -68.89 -2.08 ρSt =1 0.10 Investment G Junk Regime 1 Regime 2
Billiq -2.40 -0.49 -14.11 -0.91 ρSt =2 -0.40 TERM & DEF 0.00 0.00 0.00 0.15
σi 24.31 82.96
Regime 2 Liquidity 0.01 0.01 0.04 0.00
Investment G t-stat Junk Grade t-stat TERM 0.00 0.01 0.00 0.36
Constant 7.21 1.59 22.07 1.44 DEF 0.00 0.92 0.00 0.47
TERM 0.52 29.92 0.46 7.56 Silliq 0.03 0.01 0.01 0.00
DEF 0.97 26.76 1.06 8.78
Billiq 0.02 0.10 0.44 0.00
Silliq 64.77 3.13 -195.19 -4.31
Billiq 20.69 2.37 -65.76 -2.37
σi 53.18 188.23
Probability of “stress”regime. Pairs of estimates:
Stress regime linked to recessions
(1)OLS, with logittransformation of prob(Regime2)
(2)Logitestimation, with dummy = 1 if prob(Regime2)> 0.70
Variables lagged (1) (2) (3) (4) (5) (6) (7) (8)
Const. -1.92*** -1.03*** -1.11*** -.70*** -2.69*** -1.40*** -1.92*** -1.06***
NBER Recession 5.88*** 2.62***
Stock-Watson Index -1.69*** -.76***
Prob(Recession) 4.71*** 2.01***
-Hamiliton
Negative Market 3.12*** 1.78***
Return dummy
Business -1.81*** -.93***
Conditions Index
Paper-Bill Spread .01** .004**
TED Spread .03*** .01***
Obs. 419 419 419 419 419 419 419 419
AdjR2 / PsedoR2(%) 18 13 11 8 14 10 23 16
Out of sample predictions of the “stress”regime
Probability of Regime 2
Dep. Var= 1 if the actual prob(Regime2)> 70%, from statistical model
Variables lagged (9) (10) (11) (12) (13) (14)
Predicted prob(Regime2)is rolling monthly estimate from the economic
Const. -4.57*** -2.50*** -4.69*** -2.54*** -4.75*** -2.62***
NBER Recession 1.43* 1.20* prediction model (14), we start with estimates from 1973-1989 (1/2 the sample),
Stock-Watson Index 0.12 .06 0.006 -0.03 and predict for 1990-2007
Prof(Recession)-Hamilton 1.08 1.01** 1.32** 1.21** Regime 2 (as per Regime Switching Model 1990-2007)
Negative Market Return 0.85 0.85 1.11 1.04*
Business Conditions -0.99*** -0.47** -1.13*** -0.60** Constant -1.78***
Index (.24)
Paper-Bill Spread .002 -0.005 0.004 -0.002
Predicted prob(Regime2) 5.77***
TED Spread .03*** 0.01*** 0.03*** 0.01***
(.94)
EE measure year growth -229.49*** -245.46*** -200.11*** -239.90*** -206.00*** -239.09*** __________________________________________________________________
_
Equity Volatility 93.82*** 53.44*** 80.39*** 49.93*** 80.53*** 50.01***
Obs. 216
Equity Volatility* EE 5099.01*** 5009.99*** 4248.32*** 4011.05*** 4364.55*** 4029.97*** Pseudo R2(%) 27
measure year growth _____________________________________________________________________
Obs. 419 419 419 419 419 419 _
Adj/ Pseudo R2(%) 28 23 44 36 43 35
Flight to Liquidity
Out-of-sample prediction of conditional bond returns
Junk-IG Junk-IG DEF -(T-Bill -(T-Bill Short Medium Long
Return Return Return Yld Yld Junk-IG Junk-IG (Junk-IG) for the financial crisis years, 2008-2009
-Fed -Fed
Funds) Funds)
(1) (2) (3) (4) (5) (6) (7) (8)
Const. 26.46*** 26.02*** 6.89 68.09** 48.57*** 24.24*** 28.43*** 24.13** In each month, we calculate Prob(Regime2)using our logitprediction model
Prob(Regime2) -2.80 -13.27 -.10 50.71*** -3.50 -27.00 13.40
TERM -.07*** -.08*** .002 -.18*** -.47*** (column (14)).
DEF .84*** .77*** -.07** -.11** .55*** .61*** .62*** We calculate portfolio returns using the coefficients of each ofthe two regimes,
Silliq -64.66* -75.38** 25.02 -10.08 -57.79* -64.59 -126.09*
Billiq -2.00 -29.67** 21.37** -7.63 -7.38 -5.81 -13.50 conditional on the realized factors TERM, DEF, BILLIQ, SILLIQfor that month.
Prob(Regime2)* .04 .03 .01 -.06 .15
TERM
Prob(Regime2)*DEF -.66*** -.67*** 0.5 -.37** -.71*** -.82*** Then, denoting p2= Prob(Regime2),
Prob(Regime2)* -210.23* -66.43 58.05 -132.14 -274.55** -233.20*
Silliq
PBrilolibq(Regime2)* -90.79** 35.84 57.14*** -28.04 -76.95* -104.61** Predicted return= (1-p2)*(predicted return using regime 1 coefficients)
Obs. 420 420 420 420 420 420 420 420
AdjR2(%) 11 18 3 3 12 20 30 42 + p2*(predicted return using regime 2 coefficients)
Predicting investmentgrade bond returns in 2008-2009 Predicting junkbond returns in 2008-2009
Actual Bond Returns vs. Predicted Bond Returns Actual Bond Returns vs. Predicted Bond Returns
1500 Investment Grade, Year 2008-9 11 1500 Junk Grade, Year 2008-9 15 11
Actual Bond returns (bps)-1000-50005001000 RMR8MSES E(4 (51r3 edgerge9rseseio lnin)e =) 2=11 0240251141.22132211371.426960A231R2tc42-1s-t07uStaaqtlu =a(18 r08e.15.d858 4=) P 7 r7 e % d i c t e d ( 0+. 141.6)5 Actual Bond returns (bps)-1000-500050010008 RMRSME5S9 E(4 (5r edg1e2r1ge139rsesei2o 1lnin)e1 2=1)67 3=12 032633.9703.754314AcRt-tsu-Sta2a2qlt = u 1( a608r..e842d0642 4 )=1P 8 r7 e 6 d % i c t e d (+0 .5717.)15
-1500 -1000 -500 0 500 1000 -1500 -1000 -500 0 500 1000
Regime Switching Model Prediction (bps) Regime Switching Model Prediction (bps)
Data source: Regime Switching Model, Table 3 Data source: Regime Switching Model, Table 3
Out-of-sample predictions during the financial crisis 2008-2009 The effects on stocks, classified by Book/Market
Predicted value use estimated prob(Regime2) from the logitmodel,
using the economic time series, the estimated coefficients of each
regime and the current values of TERM, DEF, BILLIQ, SILLIQ Famaand French (1995): “Firms with high BE/ME…tend to be persistently
(SE in parentheses) distressed. They have low ratios of earnings to book equityfor at least 11
Dependent variable:  Actual IG Returns Actual Junk years around portfolio formation. Conversely, low BE/ME…is associated with
Returns sustained strong profitability.”
Constant 4.65 (42.93) 51.15 (66.82)
Recent studies (e.g., Chen, Noe& Tice, 2009) confirm that.
Predicted cond. IG return 0.839 (0.098)
Predicted cond. Junk return 0.862 (0.102)
We replicate the analysis for the high and low BE/ME quintiles.
R-sqr(%) 77 76
p-value of F-test if slope = 1.0 0.12 0.19
High and low BE/ME are taking the role of “junk”bonds and IG bonds,
Obs 24 24
respectively.
Liquidity betas change substantially between regimes
Wald tests for differences in coefficients–Chi-sq tests
Regime 1
Numbers are p-values
Low BM t-stat High BM t-stat Parameters
Constant -71.88 -7.95 -5.17 -0.43 P 0.96
Rm-Rf 113.44 50.65 86.20 26.69 q 0.90
TERM -0.07 -2.11 0.05 1.28
DEF -0.35 -2.89 0.36 2.04 ρSt =1 -0.650 Between regime 1 and 2 Between High & Low BM
Silliq 83.38 1.01 -54.92 -0.72 ρSt =2 -0.495 Low BM High BM Regime 1 Regime 2
Billiq 55.15 3.11 -65.46 -2.63 Rm-Rf 0.17 0.66 0.00 0.00
σi 117.50 156.09 TERM 0.62 0.48 0.06 0.28
Regime 2
DEF 0.30 0.71 0.01 0.07
Low BM t-stat High BM t-stat
Constant -49.15 -1.42 -12.76 -0.31 Silliq 0.92 0.02 0.36 0.00
Rm-Rf 107.66 33.70 82.79 12.83 Billiq 0.23 0.67 0.00 0.27
TERM -0.03 -0.38 0.16 1.17
DEF -0.16 -1.18 0.50 1.77
Silliq 73.62 1.70 -242.21 -4.20
Billiq 6.30 0.18 -88.32 -1.48
σi 179.18 366.86