Secondary Transaction
Costs in Bonds
Larry Harris
1
Formal Disclaimer
• The Securities and Exchange
Commission, as a matter of policy,
disclaims responsibility for any private
publication or statement by any of its
employees.
• The views expressed herein are those
of the author and do not necessarily
reflect the views of the Commission or
of the authors’ colleagues upon the
staff of the Commission.
2
Secondary Bond Markets
• Corporate bonds.
• Municipal bonds.
• Government bonds.
3
Bond Market Characteristics
• Many securities.
• Infrequently traded.
• Almost no contemporaneous price
transparency.
• Almost no quotes.
4
The Main Policy Issue
• How does market opacity affect
liquidity?
– New car dealer comparison.
– Comparison to equity markets.
5
Important Issues
• What are secondary transaction costs
in the bond markets?
• What determines these costs?
– How does bond complexity affect these
costs?
6
The Research Program
• Examine all municipal (MSRB) and
corporate (TRACE) bond trades.
• Measure average transaction costs for
each bond.
• Identify cross-sectional determinants of
these costs.
• Identify how costs change when bond
trades become more transparent.
7
The Samples
8
The MRSB Sample
• Broker-dealers report all municipal
bond trades to the MRSB.
– Price, time, size, dealer, customer side.
– Our one-year sample period:
November 1999 – October 2000.
• These data are now available on the
next day on the Internet.
9
The TRACE Sample
• Broker-dealers report all corporate
bond trades to the NASD.
– Price, time, size, dealer, customer side.
– Our one-year sample period:
January 2003 – December 2003.
10
MRSB Sample Selection
(from Section 3.1)
Bonds
Records
Trades
Volume
($ billion)
463,346 7,024,678
2,575
Final sample 167,851 5,399,283
832
Deleted:
Unknown securities
Variable rate bonds
Unidentified cost
regressions
Derivatives
Missing data
Pricing errors
11
TRACE Sample Selection
(from Table 1)
Bonds
Trades
Volume
($ billion)
Records
68,877 8,668,987
9,413
Final sample
16,746
5,079
6,649,758
Same deletion criteria as applied to the
MSRB sample.
12
MSRB Bond Characteristics
Mean
Trades per week
0.6
Dollar trade size ($000)
Minimum
16
Median
73
Maximum
977
1st
pctl
<0.1
99th
pctl
5.4
2
5
10
105
992
11,199
13
TRACE Bond Characteristics
(from Table 2)
Mean
Trades per day
1.9
Dollar trade size ($000)
Minimum
32
Median
584
Maximum
12,401
1st
pctl
<0.1
99th
pctl
22
0.4
545
5.4
6,806
26 105,243
14
MSRB Characteristics
(from Table 1, Panel B)
Credit Quality
Superior AA/AAA
Other inv. quality
Speculative <BBB
Missing
Value
Bonds Trades traded
74%
77
78
8
10
9
<1
<1
<1
18
13
13
15
TRACE Characteristics
(from Table 1, Panel B)
Credit Quality
Superior AA/AAA
Other inv. quality
Speculative <BBB
Defaulted
Not Rated
Value
Bonds Trades traded
9%
8
8
63
63
57
23
26
31
3
2
2
3
1
2
16
Municipal Bond
Complexity Features
•
•
•
•
Callable
Sinking fund
Extraordinary call
Nonstandard interest payment
frequency
• Nonstandard interest accrual method
• Credit enhanced
17
MSRB Characteristics
(from Table 1, Panel D)
Bond Complexity
Simple 0
Typical 1-2
Complex 3+
Value
Bonds Trades traded
14%
10
14
65
54
56
21
36
29
18
MRSB Transparency
• During most of the sample period, bond
trades were made public on the next
day if the bond traded four times.
• Transparency and trade activity
therefore are correlated.
19
Corporate Transparency
• NYSE ABS bond trades are completely
transparent.
• Trades for TRACE-transparent bonds
were reported with a 45 minute lag.
• Bonds have been made TRACEtransparent based on credit quality and
original issue size (IOS).
20
TRACE-Transparent Bonds
• Throughout 2003: All bonds rated A
and above with original issue size>$1B.
• March 1, 2003: All bonds rated A and
above with $100M>OIS>$B.
• April 14, 2003: 120 bonds rated BBB
with stratified original issue sizes.
21
2003 Corporate Transparency
(from Table 1, Panel D)
Value
Bonds Trades traded
TRACE (any time)
22%
49
53
ABS-listed
3
5
3
ABS and TRACE
1
2
2
Never transparent
76
48
45
22
Transaction Cost
Measurement Methods
23
Benchmark Methods
• Most transaction cost measures require
price benchmarks.
– Quotes
– Average price: Warga and others
– Closing or opening prices
• Without benchmarks, we must use
econometric methods.
24
Econometric Approaches
• Bid/ask bounce is due to transaction
costs.
– Measure the bounce.
• The Roll Serial covariance spread
estimator.
• Regression methods useful when we
know the side trade initiators
(customers) are on.
25
A Constructive Introduction
to Our Econometric Method
26
Price and Value
• Log Price = Log Value +/- trade cost
• Let Qt indicate with values 1, or -1
whether trade t was initiated by a
customer buyer or seller.
log Pt  log Vt  ct Qt
27
Add Interdealer Trades
• Let It indicate with values 1 or 0 whether
trade t was an interdealer trade.
• Set Qt to 0 for interdealer trades.
• Let dt be the unknown interdealer price
impact.
log Pt  log Vt  ct Qt  d t It
28
Let Cost Vary with Size
• An average response function plus a
random error.
ct  c  St   t
29
Bond Transaction Returns
• Log price change between trades t
and s produces a regression equation.
(The trades need not be in order.)
r r
P
ts
V
ts
 c  St  Qt  c  S s  Qs
 t Qt   s Qs  d I  d I
D
t t
D
s s
30
Model Value Returns
• Bond value returns have drift, common,
and idiosyncratic components.
• Random in bond-specific value.
r  Daysts  5%  CouponRate 
V
ts
  Avg SLAvgts   Dif SLDif ts
 st
31
The Cost Function
• Municipal bonds:
1
c  St   c0  c1  c2 log St
St
• Corporate bonds:
1
2
c  St   c0  c1  c2 log St  c3 St  c4 St
St
32
The Regression Model
Combining terms gives
r  Daysts  5%  CouponRate  
P
ts
 SLAvg SLAvgts   SLDif SLDif ts
 Qt Qs 
 c0  Qt  Qs   c1   
 St S s 
 c2  Qt log St  Qs log S s 
 ts
33
The Error Term
ts   ts  Qt t  Qs s  I d  I d
D
t
t
D
s
s
has variance
 N
2
ts

Sessions
ts
2
Sessions
 Dts d   2  Dts  
2
2
where Dts =0, 1, or 2 counts the
interdealer trades among trades t and s.
34
Estimation Strategy
• Estimate the model without the indices
for each bond.
• Adjust prices to remove trade costs.
• Use repeat sales methods to compute
the indices.
– Involves weighted regressions.
• Re-estimate the model with the indices.
35
Weighted Least Squares
• Estimate the model with OLS for each
bond.
• Use pooled constrained WLS to regress
the squared residuals on independent
variables to estimate the variance
components.
• Re-estimate the model with WLS.
• Iterate until convergence.
36
Cost Estimates
• Estimated cost for a given size is
1
c  S   c0  c1  c2 log S
S
• The estimate error variance is  1 
 1
Var  c  S    1
 S
 1 
 ˆ 

log S   c
 S 

log S 


37
Mean Cost Estimates
• Compute weighted means across
bonds. For weights, use estimates of
the precision of the cost estimate
(inverse estimator error variance).
• The data thus tell us where the
information is.
38
Results
39
Mean Estimated Municipal
Transaction Costs (Figure 1)
40
Mean Estimated Corporate
Transaction Costs (Figure 1)
41
Alternative Cost Functions
(Municipal Figure 2)
42
By Trading Activity (Muni’s)
43
By Trading Activity (Corp’s)
44
By Credit Quality (Muni’s)
45
By Credit Quality (Corp’s)
46
By Issue Size (Muni’s)
47
By Issue Size (Corp’s)
48
By Bond Complexity (Muni’s)
49
By Time Since Issuance (Muni’s)
50
By Time To Maturity (Muni’s)
51
By Transparency (Corp’s)
52
Cross-sectional
Regressions
53
Cross-sectional Regressions
• Cross-sectional regression analyses
help isolate effects by disentangling
conflicting effects.
• Dependent variable: Average bond
transaction cost estimate for a
representative trade size.
• Estimate the models with WLS.
54
Information Considerations
• The dependent variable observations
are noisy estimates for which we have
estimates of the estimator error
variances.
• The model should have an
independent, equal variance error term.
55
Regression Weights
• Obtain OLS residuals.
• Regress OLS squared residuals on a
constant and on the error variances to
obtain predicted variances.
• Use the inverse of the predicted
variances as weights for the WLS
analysis.
56
Regressors
• Inverse Price
– Fixed costs (clearing?)
• Credit Rating Index
• Complexity Features
• Age/Maturity Features
• Size/Scale Features
57
Municipal Results
From Table 3, $100,000 Trade Size
58
Inverse Price and
Credit Rating Coefficients
Regressor
Intercept (bps)
Inverse price
Credit quality index
Missing credit rating
Estimate
14
4524
-2.1
-47
t-stat
4
77
-33
-30
59
A Quick Digression
• Credit is missing for 18 percent of the
bonds. We set the credit quality index
to 0 and the missing credit dummy to 1.
• The missing credit coefficient should
equal the average (missing) credit
quality index times the credit quality
index coefficient.
• The implied average credit quality
index is 47÷ 2.1 = 22+.
60
Complexity Coefficients
(in bps)
Regressor
Callable
Sinking fund
Extraordinary call
Nonstandard int pmt freq
Nonstandard int accrual
Credit enhanced
Estimate t-stat
23
95
15
54
9
40
2
4
9
7
11
44
61
Age/Maturity Coefficients
Regressor
Time since issuance
Time to maturity
Pre-refunded
Super sinker
Estimate
3
16
-31
-33
t-stat
57
130
-95
-13
62
Size/Scale Coefficients
Regressor
Value of the bond
Value of all bonds by the
same issuer
Value of all bonds in the
same state
State bond demand index
Adjusted R2
Estimate t-stat
0.9
10
-0.2
-2.6
-2.3
-9.0
3.6
50%
14.5
63
Other Municipal Results
(From Table 3)
• Generally similar results for other trade
sizes.
• However, some evidence that
institutional investors are less adversely
affected by instrument complexity than
retail investors.
64
Corporate Results
From Table 5, $100,000 Trade Size
65
Credit Rating Coefficients
(in bps)
Regressor
Rating is BBB
Rating is B or BB
Rating is C and below
Bond is in default
Estimate
4
6
10
8
t-stat
7.0
6.8
6.6
2.3
66
Additional Risk Coefficients
Regressor
Coupon rate (in percent)
Average price (in % of par)
Convertible to stock
Estimate t-stat
3.1
17
-1.9
30 bps
-51
20
67
Maturity and Age Coefficients
Regressor
Years since issuance
Estimate
5
t-stat
17
16
76
(square root)
Years to maturity
(square root)
Bond soon to be called
Sinking fund
-40 bps
-13 bps
-10
-3
68
Size Coefficients
Regressor
Issue size
Estimate
-0.16
t-stat
-6
0.07
22
(sq. root of millions)
Total other issues by
same issuer
(sq. root of millions)
69
Some Complexity Coefficients
(in bps)
Regressor
Attached call
Estimate
-11
t-stat
-12
Attached put
-44
-26
Floating rate
-12
-6
Variable rate
6
3
Nonstandard accrual
7
6
Maturity date extended
or extendable
5
5
70
Transparency Coefficients
(in bps)
Regressor
TRACE-transparent
Estimate
-3.8
t-stat
-4.2
-3.5
-2.0
(fraction of trades reported
to public during 2003)
Listed on NYSE ABS
71
Corporate Cost Determinants
(From Table 5)
• Generally similar results for other trade
sizes.
• Transparency has the least effect in the
smallest and largest trade sizes.
72
Time-series Analysis of
Corporate Transparency
73
Transparency Changes
• All 3,004 bonds rated A and up with
$100M<original issue size<1B became
TRACE-transparent on March 1, 2003.
• A size-stratified sample of 120
intermediate sized BBB rated bonds
became transparent on April 14.
• What happened to costs?
74
Samples
Comparison Samples
Target
C1
C2
C3
Original
>$100M
>$1B <$100M >$100M
issue size
&<1B
&<1B
Rating
A & up A & up A & up
BBB
Transparent March 1 Always
Never
Never
Bonds
3,004
814
8,952
4,065
Trades
952
1,516
1,014
1,219
(thousands)
75
Time-series Method
• For each sample, use a regression
model to estimate a different pooled
average cost response function for
each day.
• Simultaneously estimate a common
factor return using repeat sales index
estimation method.
76
Sketch of Time-series Model
r  Daysts  5%  CouponRate  
P
ts
ct  St  Qt  cs  S s  Qs

t
r
J  s 1
J
 ts
77
Difference of Differences
Comparison Method
• On each day, compute difference in
costs between the March 1 sample and
the three control samples.
• Compare the average cost differences
before and after March 1.
• Use time-series sample variances to
construct t-statistics.
78
Results for $100K Trade Size
(from Table 6)
Difference of
Comparison differences
T minus C1
-10
T minus C2
-11
T minus C3
-14
C1 minus C2
-1
C2 minus C3
-3
t-statistic
-9
-9
-12
-1.5
-3.9
79
More Results
• Similar results for other trade sizes.
• Similar, but smaller, results for the 120
BBB bonds.
– -5 and -7 bps versus two comparison
samples, both statistically significant.
80
Learning about
Transparency
81
Diffusion of Impact
• The results underestimate the long run
benefits of transparency because many
were unaware that prices were
available.
• Obtaining last trade prices was—and is
still—difficult.
• These observations probably explain
why the BBB effect is smaller.
82
A Back of the
Envelope Calculation
• Cross-sectional effect at $100K trade
size: -3.8 bps for TRACE-transparent
and -3.5 for ABS-listed.
• Time-series effect: -10, -11, -15 bps for
versus various comparisons for the
March 1 bonds, and -5 and -7 for the
BBB bonds.
• Safe to say minimum -5 bps.
83
A Back of the
Envelope Calculation
• About $2 trillion 2003 volume in nontransparent corporate bonds.
• 5 bps of $2 trillion is one billion dollars.
• The estimate is not unrealistic in
comparison to total dealing profits.
84
Conclusion
85
Summary
• Municipal and corporate bonds are
expensive to trade.
• Retail investors, and perhaps even
issuers, could benefit if issuers issued
simpler bonds.
• Studies such as this one are essential
inputs into the regulatory process.
86
A Final Perspective
• A corporate bond can be hedged by a
portfolio of Treasury bonds and the
issuer’s stock.
• Both trade in fully price-transparent
markets!
87
An Important
Additional Argument
• Fair valuation of bond funds will be
improved by greater transparency.
88
Progress
• As of October 1, trades in 17,000
corporate bonds are available for
dissemination within 30 minutes.
• 99 percent of all corporate issues will
be TRACE-transparent with a 15-minute
lag by July 2005.
• Starting in January 2005, all trades in
municipal issues will available in real
time with a 15-minute lag.
89
Some Predictions
• Retail interest in bonds will surge.
• New trading systems will emerge.
• Volumes will increase.
• Dealers will continue to make money—
perhaps more—but it will be more
difficult.
90
Time for more sunshine!
91