An Econometric Analysis of
Inventory Turnover Performance in
Retail Services
Vishal Gaur
Stern School of Business, New York University
Marshall Fisher
The Wharton School, University of Pennsylvania
Ananth Raman
Harvard Business School, Harvard University
School of Management, Boston University, March 24, 2005
Research Papers
• Gaur, Fisher and Raman (2005), “An Econometric
Analysis of Inventory Turnover Performance in Retail
Services”
– Benchmarking of inventory productivity
• Gaur, Fisher and Raman (2004), “Inventory Productivity
and Financial Performance in U.S. Retail Services”
– External validation of the benchmarking methodology by
correlating performance relative to the inventory productivity
benchmark with long-run stock returns
Importance of Inventory Management
in Retailing
• $307 billion of investment in inventory in the U.S. retailing industry in
2004 ($469 billion including motor vehicles and spare parts).
• Inventory represents 36% of total assets and 53% of current assets
of retailing firms.
• Inventory turnover
– Routinely used for productivity comparisons by retailers, manufacturers,
consultants and analysts.
• Benefits of high inventory turnover
– Lower working capital requirement
– Lower inventory holding and obsolescence costs
– Greater ability to respond to market dynamics
Variation in Inventory Turnover
• Within-firms variation

Range of inventory turnover of commonly known firms
in 1985-2000:
Best Buy Co. Inc.
2.8 – 8.5
Circuit City Stores, Inc.
4.0 – 5.6
The Gap, Inc.
3.6 – 6.3
Radio Shack Corp.
1.1 – 3.1
Wal-Mart Stores, Inc.
4.9 – 7.2
• Across-firms variation

Range of inventory turnover of supermarket chains
during the year 2000: 4.7 to 19.5.
Time-Series Plot of Annual Inventory Turnover of Four
Consumer Electronics Retailers for 1987-2000
Annual Inventory
Turnover
10
9
8
7
6
5
4
3
2
1
0
1986
1988
1990
1992
1994
1996
1998
2000
Time (years)
Best Buy Co.
Circuit City Stores, Inc.
Radio Shack Corp
CompUSA, Inc.
Research Questions
•
Explain variation in inventory turnover using
covariates: gross margin, capital intensity and
deviation of sales from forecast.

•
•
•
Characterize the “earns versus turns” tradeoff.
Determine time-trends in inventory productivity.
Provide methodology for benchmarking inventory
productivity.
Understand how firms make aggregate-level
inventory decisions.
Literature Review
• Impact of operational improvements on operational and
financial performance
– Balakrishnan, Linsmeier, Venkatachalam (1996), Billesbach and
Hayen (1994), Chang and Lee (1995), Huson and Nanda (1995),
Hopp and Spearman (1996).
– Hendricks and Singhal (1996, 1997, 2001).
• Time-series analysis of inventory turnover
– Aggregate-level data for US manufacturing industry:
Rajagopalan and Malhotra (2001)
– Firm-level data for US manufacturing industry: Chen, Frank and
Wu (2004)
Literature Review (contd.)
• Impact of variety on performance
– Kekre and Srinivasan (1990)
– Pashigian (1988)
– Fisher and Ittner (1999), Randall and Ulrich (2001)
• Impact of EDI, CRP and VMI on performance
– Cachon and Fisher (1997), Clark and Hammond (1997)
– Case studies: Barilla SpA (Hammond 1994), H. E. Butt Grocery
Co. (McFarlan 1997), Wal-Mart Stores, Inc. (Bradley, et al.
1996), etc.
Description of Data
• Data:
– Obtained from S&P’s Compustat database
– 311 firms across 10 retailing segments for years 1985-2000.
– 3407 observations across firms and years; 11 annual
observations per firm.
• Preparation:
– At least five consecutive years of observation for each firm
• Causes of missing data: new entry, mergers, acquisitions,
liquidations.
– Missing data other than at the beginning or the end of the
period
• Bankruptcy and reorganization
– Inventory valuation method
• FIFO, LIFO, Average cost method, Retail method.
Variables
1. Inventory Turnover IT = Cost of Goods Sold
Average Inventory
Sales - Cost of Goods Sold
Sales
2. Gross Margin
GM =
3. Capital Intensity
Avg Gross Fixed Assets
CI =
Avg Inventory + Avg Gross Fixed Assets
4. Sales Surprise
SS =
Sales Realized
Sales Forecast
Modeling Assumptions
• Focus on year-to-year variation within firms.
– Control for firm characteristics exogenous to the
model, such as differences in accounting policies,
location strategy, management, etc. using firmspecific fixed effects.
• Effects of aggregate industry characteristics, such as
competition, and economic conditions are controlled for
using time-specific fixed effects.
Hypothesis 1: Inventory turnover is negatively
correlated with gross margin.
• Gross margin directly affects inventory turnover
through service level
 Increase in GM
 Higher optimal inventory level
 Higher average inventory level
 Lower inventory turnover.
Hypothesis 1 (contd.)
• Gross margin is indirectly related to inventory turnover
through product variety and length of product lifecycle.
– Gross margin increases with increase in variety.
Increase in variety  Increase in consumer utility  Higher price 
Higher gross margin.
• Lancaster (1990), Dixit and Stiglitz (1977), Kotler (1986), Nagle
(1987), Lazear (1986), Pashigian (1988).
– Inventory turnover decreases with increase in variety.
Increase in variety  Increase in demand uncertainty  Higher safety
stock requirement  Decrease in inventory turnover
• Benetton SpA (Heskett and Signorelli 1989), Hewlett-Packard
(Feitzinger and Lee 1997), Swaminathan and Tayur (1998), Zipkin
(2000), van Ryzin and Mahajan (1999).
Hypothesis 1 and
the “earns versus turns” tradeoff
• Multiplicative models used in managerial practice
– Du Pont Model, Strategic profit model (Levy and
Weitz, 2001)
– Gross Margin Return on Inventory (GMROI)
GMROI = GM  IT
– These models do not explain why GM and IT should
be correlated with each other!
Hypothesis 2: Inventory turnover is positively
correlated with capital intensity.
• Factors that increase capital intensity increase
inventory turnover
– Adding a new warehouse
• Reduction in safety stock, flexibility to re-balance store inventory in
season: Eppen and Schrage (1981), Jackson (1988).
– Introducing information technology systems
• Continuous replenishment process: Clark and Hammond (1997),
Cachon and Fisher (1997).
• Benefits of sharing information: Gavirneni et al. (1999), Lee et al.
(2000), Cachon and Fisher (2000).
• Case studies: Campbell Soup, Barilla Spa, H.E.B., Wal-Mart Stores.
Hypothesis 3: Inventory turnover is positively
correlated with sales surprise.
• Sales higher than forecast
 Less inventory at the end of the period
 Less average inventory during the period
 Higher inventory turnover.
• Computation of sales forecast
– Holt’s Linear Exponential Smoothing model
• Smoothing parameters chosen from a range of values.
• Lower prediction error and less biased forecasts than Simple Exponential
Smoothing or Double Exponential Smoothing.
Sales Forecast sit  Lsi ,t 1  Tsi ,t 1
where
Lsit  S sit  (1  )( Lsi ,t 1  Tsi ,t 1 ),
Tsit   ( Lsit  Lsi ,t 1 )  (1   )Tsi ,t 1
Model Specification
logITsit = Fi + c t + b1s logGMsit + b2s logCIsit + b3s logSSsit + esit
where
• s denotes segment index, i the firm index, and t the year index.
• Fi : firm-specific fixed effects.
Control for differences in the intercept between firms, such as between their
managerial efficiency, location, accounting policies, marketing, etc.
• ct : year-specific fixed effects.
Control for differences in economic conditions over time.
• b1s, b2s, b3s: segment-wise coefficients.
b1s  0 for hypothesis 1, b2s > 0 for hypothesis 2, b3s > 0 for hypothesis 3.
• sit denotes the error term.
Alternative Model Specifications
• Coefficients pooled across segments
logITsit = Fi + c t + b1 logGMsit + b2 logCIsit + b3 logSSsit + esit
• Intercept pooled across firms
logITsit = Fs + c t + b1s logGMsit + b2s logCIsit + b3s logSSsit + esit
• Interaction effects
– Separate year-wise fixed effects for each segment
– Separate coefficients for each segment and each
year
• Inventory as dependent variable
log(Inv sit ) = Fi + c t + b1 logGMsit + b2 logCIsit + b3 logSSsit + b4 logCGSsit + esit
Summary of Data
Retail Industry
Segment
Apparel And
Accessory Stores
Catalog, Mail-Order
Houses
Department Stores
Drug & Proprietary
Stores
Food Stores
Hobby, Toy, And
Game Shops
Home Furniture &
Equip Stores
Jewelry Stores
Radio,TV, Cons
Electr Stores
Variety Stores
Aggregate statistics
# annual
Average Sales Inventory
# of firms observations
($ million)
Turnover
72
786
979.1
4.57
2.13
45
441
439.9
8.60
9.11
23
309
6058.6
3.87
1.45
23
256
2309.5
5.26
2.90
57
650
4573.6
10.78
4.58
10
98
1455.5
2.99
1.08
13
125
391.2
5.44
10.43
15
156
475.2
1.68
0.58
17
200
1585.0
4.10
1.54
36
386
6548.7
4.45
2.92
311
3407
2791.4
6.08
5.41
Gross
Margin
0.37
0.08
0.39
0.17
0.34
0.08
0.28
0.07
0.26
0.06
0.35
0.07
0.40
0.07
0.42
0.13
0.31
0.11
0.29
0.09
0.33
0.11
Capital
Intensity
0.59
0.14
0.50
0.18
0.63
0.10
0.48
0.12
0.75
0.08
0.46
0.14
0.55
0.16
0.36
0.11
0.44
0.09
0.51
0.15
0.57
0.17
Overall Fit Statistics
• Model explains 66.7% of the within-firm variation and
97.2% of the total variation (within and across firms) in
log(IT).
• Intercept of the regression line varies across firms and
across years.
• The coefficients of gross margin, capital intensity and
sales surprise are statistically significant. They differ by
segment.
Estimated Prediction Error
  log IT  Predicted Value of log IT 
Overall prediction accuracy  1 
2
 97.16%.
s ,i ,t
  log IT  Aggregate Mean of
log IT 
2
s ,i ,t
2
log
IT

Predicted
Value
of
log
IT



Within-firm prediction accuracy  1 
 66.7%.
s ,i ,t
  log IT  Within-firm Mean of log IT 
2
s ,i ,t
The model explains 97.2% of the total variation and 66.7% of
the within-firm variation in log(Inventory Turnover).
Coefficients’ Estimates
Segment-wise coefficients
Apparel And Accessory Stores
Catalog, Mail-Order Houses
Department Stores
Drug & Proprietary Stores
Food Stores
Hobby, Toy, And Game Shops
Home Furniture & Equip Stores
Jewelry Stores
Radio,TV,Cons Electr Stores
Variety Stores
Pooled coefficients
Gross Margin
Capital Intensity
Sales Surprise
-0.153
-0.226
-0.310
-0.186
-0.351
-0.571
-0.017*
-0.438
-0.500
-0.313
-0.285
0.977
-0.039*
0.861
0.361
1.085
-0.015*
0.562**
0.038*
0.268
0.106
0.252
0.053
0.225
0.189
0.143
0.179
0.215
0.174
0.279
0.140
0.176
0.143
• Coefficients marked * are not significant, coefficients marked ** have p<0.02, all
other coefficients have p<0.001.
Application to Benchmarking
• Tradeoff curve
– model specifies the tradeoff between IT, GM and CI, and
corrects for the effect of sales surprise.
 GM 
0.283
 CI 
0.252
 SS 
0.143
IT  Firm-specific constant
 Time-specific constant
• Adjusted Inventory Turnover (AIT)
– equals the residual from the model and shows the distance
of a firm from its tradeoff curve (benchmark).
Residual  log AITsit  log ITsit  0.285log GM sit
 0.252log CI sit  0.143log SSsit
Example 1: Comparison of Four Consumer
Electronics Retailers
10
9
Inventory Turns
8
7
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Gross Margin (%)
Best Buy Co. Inc.
Circuit City Stores
Radio Shack
CompUSA
Example 1: Values of Adjusted Inventory Turns for different gross
margins for the four consumer electronics retailers
14
Best Buy Co. Inc.
Circuit City Stores
CompUSA
Radio Shack
12
Inventory Turns
10
8
6
4
2
0
0
0.1
0.2
0.3
Gross Margin
0.4
Note: Figures are drawn using the average values of CI and setting SS = 1.
0.5
0.6
Example 2: Comparison across years within a
firm - Ruddick Corp.
IT is decreasing with time, but AIT
is increasing with time.
Gross Margin and Capital Intensity
are increasing with time.
9.5
0.9
9
y = -0.0194x + 8.3937
R2 = 0.0592
0.8
0.7
8.5
0.6
8
0.5
0.4
7.5
0.3
7
0.2
0
1986
y = 0.0704x + 6.2215
R2 = 0.5705
6.5
0.1
6
1988
1990
1992
Gross Margin
1994
1996
1998
Capital Intensity
2000
1987
1989
1991
1993
1995
1997
1999
Time (in years)
Inventory Turnover
Adjusted Inventory Turnover
Time Trends in CI, IT, GM
• Capital intensity has increased with time, Inventory turnover has
decreased with time, and Gross Margin shows no trend with time.
• Computation of unadjusted time trends:
yit = ai + bt + error term
Here, ai is the firm-specific intercept, and b is the slope w.r.t. time.
Variable
CI
log CI
IT
log IT
GM
log GM
Coefficient
0.00568
0.01250
-0.05460
-0.00454
-0.00018
0.00093
Std Error
0.00030
0.00077
0.01354
0.00110
0.00031
0.00130
t-statistic
19.00
16.23
-4.03
-4.11
-0.59
0.72
p-value
<0.0001
<0.0001
<0.0001
<0.0001
0.5568
0.4736
Time Trend in Inventory Productivity
Estimated from Year-wise Fixed Effects
The values of year-wise fixed effects, ct, show the time trend in
inventory productivity by adjusting for changes in GM, CI and SS, and
for differences across firms. This trend is downward sloping.
0.14
0.12
0.1
0.08
c(t)
•
0.06
0.04
0.02
0
1986
-0.02
1988
1990
1992
1994
1996
1998
-0.04
Time (in years)
Error-bars around the estimates show intervals of ± 2 standard deviation.
2000
Histogram of Firm-wise Time Trends
Estimated from Year-wise Fixed Effects
167 firms
with –ve trends
144 firms
with +ve trend
140
Number of firms
120
100
80
60
40
20
0
-0.375
-0.275
-0.175
-0.075
0.025
Estimated Time Trend
0.125
0.225
0.325
Summary
• Model to evaluate inventory productivity in retailing
– Results differ from the Du Pont model
– Adjusted Inventory Turnover
• Estimate the effect of sales surprise on inventory
turnover
• Separate the effects of covariates, investment in
capital intensity and time-trends in inventory
productivity
– Time-trend differs significantly across firms.
Inventory Productivity and Financial
Performance in the U.S. Retail Sector
Research Questions
•
Is superior IT performance or AIT performance correlated with financial
performance (stock returns; incidence of bankruptcy)?
•
Does the financial market provide external validation for AIT as a
performance metric?
Research Methodologies
1. Event-study
–
–
Analyze a firm’s stock returns following a change in inventory turns
Issues:
•
•
Separating material changes from random variation in inventory turns
Defining the time window in which the event can be said to have taken place
2. Contemporaneous correlation with long-run stock returns
–
Issues:
•
•
•
 3.
Survival bias – only firms that survived over the long time period can be used
Hard to make a causal argument: did better inventory turns precede higher stock returns?
Results could be confounded by missing intermediate variables that are correlated with both inventory
turns and stock returns (e.g., risk measures and factor-mimicking variables)
Long-run event-study
–
–
–
–
Construct portfolios of firms based on AIT at the end of each year using historical data
Analyze the results of investments in these portfolios over the subsequent year
Conduct analysis over a long time-horizon by rebalancing the portfolio every so often
References: Carhart (1997), Cochrane (2001), Gompers et al. (2003), Jegadeesh and Titman
(1993).
Data Description
•
•
Time period: 1984-2003
Source:
– Annual financial statements: S&P’s Compustat database
– Monthly stock returns: CRSP
SIC Codes
Description
5311, 5331,
5399
Department stores, Discount
stores
5411
Total # of
obs.
Average #
of obs. per
year
Chapter 11 and
Chapter 10 filings
(Bankruptcy /
Liquidation)
Total # of
terminations
111
1071
53.55
15
49
Food stores
105
944
47.2
2
33
5600-5699
Apparel and accessory stores,
Shoe stores
86
881
44.05
4
15
5731, 5734
Radio, TV, consumer electronics,
computer and s/w stores
67
504
25.2
4
24
5961
Catalog, Mail-order and E-tailing
116
748
37.4
1
13
485
4148
8.55
26
134
TOTAL
Total # of
firms
Data Description - 2
SIC
Code
53
5411
56
573
5961
•
•
•
•
Sales ($m)
IT
GM
CI
Book Value ($m)
Median Average Median Average Median Average Median Average Median Average
950.8
6315.9
3.53
4.40
0.32
0.31
0.58
0.56
454.8
3996.2
1393.8
5034.5
10.06
10.94
0.26
0.25
0.77
0.76
582.9
1865.2
345.7
1112.7
4.10
4.54
0.35
0.36
0.61
0.59
178.6
558.6
306.0
1324.8
3.50
4.05
0.31
0.32
0.44
0.43
124.0
564.7
116.6
396.2
5.29
13.72
0.38
0.37
0.50
0.51
65.3
215.6
IT = [cost of goods sold]/[inventory]
GM = [sales – cost of goods sold]/[sales]
CI = [gross fixed assets]/[inventory + gross fixed assets]
Annual closing values are used for all balance-sheet items
No observations are omitted from the dataset to avoid survival bias
Large differences between median and average values of performance variables
Assignment of firms to portfolios
•
Let i = firm index, s = segment index, t = calendar year index.
–
–
•
If fiscal year-end date for fiscal year 1995 for a firm is June 30, 1996, then data for fiscal year 1995 are
assigned to calendar year 1996.
For portfolios formed in year t, stock returns are assessed for year t+1.
Using AIT
–
–
–
–
Regression done in each year:
log(ITsit) = as + b1*log(GMsit) + b2*log(CIsit) + esit
Firms are ranked into 10 decile portfolios based on the values of studentized residuals [= e sit / std. err.(esit)]
Remarks:
•
•
Using IT
–
–
–
–
Regression done in each year:
log(ITsit) = as + esit
Firms are ranked into 10 decile portfolios based on the values of studentized residuals [= e sit / std. err.(esit)]
Remarks:
•
•
Cross-sectional regression because (i) we require comparisons across firms in each year to rank firms; (ii) we cannot use
entire time period to estimate the coefficients of the model.
A linear model may be used instead of a log-model. We use a log-model for consistency.
In both models, comparisons across firms can be confounded by missing variables, for example,
differences in accounting practices, location of stores, management differences, etc.
Characteristics of Decile Portfolios
• Portfolio 1: lowest decile; Portfolio 10: highest decile.
• Portfolios are uniform in composition with respect to retail segments and sizes of
firms.
• 3163 annual observations are used in the final analysis; remaining 985 observations
had missing stock returns data. [Stock returns are computed over the calendar year
following the formation of portfolio.]
Portfolio
Rank
1
2
3
4
5
6
7
8
9
10
# of obs
274
323
309
324
330
298
312
321
311
361
Segmentwise composition of portfolios
5300
5411
5600
5731
5961
24.8
22.3
23.7
10.6
18.6
25.7
21.7
22.6
11.1
18.9
25.9
21.7
23.0
11.3
18.1
25.3
21.6
22.8
11.1
19.1
24.8
20.9
23.0
13.0
18.2
25.5
21.8
22.8
10.4
19.5
25.0
21.5
23.4
11.5
18.6
26.2
21.8
22.4
10.9
18.7
25.4
21.5
23.2
11.6
18.3
23.8
21.6
22.2
12.7
19.7
Median
Sales
330.7
527.5
666.9
677.7
681.7
698.0
597.5
776.8
450.4
374.9
Average
Sales
2277.3
2724.5
3085.2
3137.0
3546.3
4163.3
4515.6
4379.7
4401.7
3404.9
Std Dev
Sales
4749.5
5970.3
7151.7
7066.9
8290.1
12037.3
14507.0
10716.4
19092.6
13427.5
Examples of portfolio ranks of large
firms
53
53
53
53
53
Target Corp
Penney (J C) Co
Costco Wholesale Corp
K-Mart Holding Corp
Wal-Mart Stores
19
19
10
18
19
Average
Sales
($m)
21785.1
22428.1
27616.0
31425.1
86660.4
56
56
56
56
Nordstrom Inc
Gap Inc
Limited Brands Inc
Foot Locker Inc
19
19
19
19
3695.0
5221.9
6640.8
7116.2
4.11
6.37
7.89
3.53
1.29
1.64
1.20
1.43
573
573
573
573
CompUSA Inc
RadioShack Corp
Circuit City Stores Inc
Best Buy Co Inc
8
20
19
18
3387.1
4423.0
5143.4
6382.6
8.75
3.70
6.79
8.50
2.38
2.05
1.32
1.42
5961
5961
Amazon.com Inc
Spiegel Inc -CL A
7
15
2496.9
2535.6
7.86
3.13
2.34
1.81
Segment
Company Name
# of
Obs.
Portfolio rank
Average Std. Dev.
7.47
0.96
4.21
2.59
9.20
0.79
3.61
1.33
7.16
1.50
Comparison of returns on highest and
lowest ranked portfolios
Annual returns on a $1 investment in portfolios formed using AIT
2
1.8
1.6
1.4
1.2
1
0.8
Portfolios 1-3
0.6
Portfolios 8-10
0.4
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
Annual returns on a $1 investment in portfolios formed using IT
2
Portfolios 1-3
1.8
Portfolios 8-10
1.6
• Portfolios 1-3: formed
using the lowest
ranked 30% of the
firms
• Portfolios 8-10: formed
using the highest
ranked 30% of the
firms
• Portfolios are
rebalanced every year
• Firms that undergo
bankruptcy or
liquidation in a year are
assigned zero returns
that year
1.4
1.2
1
0.8
0.6
0.4
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
Comparison of total returns on all decile
portfolios
Portfolio rank
Lowest ranked
1
decile portfolio
2
3
4
5
6
7
8
9
Highest ranked
10
decile portfolio
Portfolios 1-3
Portfolios 8-10
Annualized returns
on AIT based
portfolios
-3.55%
1.42%
8.81%
2.23%
4.38%
2.01%
14.10%
9.46%
16.13%
13.50%
Annualized returns
on IT based
portfolios
-3.00%
5.38%
6.19%
8.39%
4.40%
8.91%
4.13%
8.71%
18.55%
6.85%
3.48%
13.72%
4.05%
12.16%
AIT: Total returns over 20 years for portfolio 8-10 are 1208%, while for portfolio 1-3 are 98%.
IT: Total returns over 20 years for portfolio 8-10 are 893%, while for portfolio 1-3 are 121%.
Performance-attribution regressions for
decile portfolios
•
Four-factor model (Carhart 1997) to explain differences in returns:
Rit = i + b1i*RMRFt + b2i*SMBt + b3i*HMLt + b4i*Momentumt + it
where
Rit
= excess return on portfolio i in month t,
RMRFt = value-weighted market return minus the riskfree rate
SMBt, HMLt, Momentumt = month t returns on zero-investment factormimicking portfolios to capture size, book-to-market and momentum
effects (Fama and French 1993; Jegadeesh and Titman 1993)
•
i = estimated intercept, interpreted as the abnormal return in excess of that
achieved by passive investments in the factors.
Results of performance-attribution
regressions - Summary
•
Using AIT
– Estimate of the intercept, , increases as portfolio rank increases.
– Low ranked portfolios have significantly negative intercept, showing belowaverage returns.
– Five out of ten portfolios have statistically significant intercept (p=0.10)
– Abnormal return on a zero investment portfolio (buy top 30% and short-sell
bottom 30% firms at the beginning of each year) = 0.9 bp/month = 11.25% per
year. (p<0.01)
•
Using IT
– Estimate of the intercept, , has a less evident trend as portfolio rank increases.
– Two out of ten portfolios have statistically significant intercept (p=0.10)
– Abnormal return on a zero investment portfolio is not statistically significant.
•
All regressions yield significant F-statistics (p<0.01) with R2 ranging
between 36.5% and 61.2%.
Results of performance-attribution
regressions - Details
Portfolio
1
2
3
4
5
6
7
8
9
10
High Low

-0.013**
0.004
-0.007*
0.003
0.000
0.004
-0.007
0.004
-0.007*
0.004
-0.007*
0.004
0.006
0.004
0.001
0.004
0.004
0.004
0.004
0.004
0.009**
0.003
Using Adjusted Inventory Turns
RMRF
SMB
HML
**
**
0.969
0.794
0.631**
0.094
0.118
0.142
**
**
1.105
0.746
0.385**
0.079
0.099
0.119
1.009**
0.660**
0.464**
0.092
0.114
0.137
**
**
1.127
0.935
0.521**
0.093
0.115
0.139
**
**
1.157
0.785
0.610**
0.088
0.110
0.132
**
**
1.204
0.773
0.389**
0.087
0.108
0.130
**
**
1.131
0.666
0.169
0.096
0.120
0.144
1.172**
0.556**
0.215
0.109
0.135
0.163
**
**
1.083
0.635
0.083
0.100
0.124
0.149
1.155**
0.605**
0.042
0.105
0.131
0.157
-0.137*
-0.372*
0.104
0.065
0.081
0.097
Momentum
-0.194*
0.082
-0.366**
0.069
-0.257**
0.080
-0.323**
0.080
-0.274**
0.077
-0.314**
0.076
-0.665**
0.084
-0.312**
0.094
-0.279**
0.087
-0.364**
0.091
-0.042
0.056

-0.009
0.005
-0.006
0.003
-0.005
0.003
-0.003
0.004
-0.006
0.004
0.003
0.004
-0.005
0.003
0.001
0.004
0.003
0.004
0.003
0.004
0.007
0.007
Using Inventory Turns
RMRF
SMB
HML
**
**
0.983
0.837
0.354*
0.115
0.143
0.173
0.994**
0.684**
0.464**
0.085
0.105
0.127
1.113**
0.815**
0.639**
0.081
0.101
0.122
**
**
1.243
0.673
0.507**
0.087
0.108
0.130
**
**
1.144
0.758
0.528**
0.094
0.117
0.140
**
**
1.134
0.870
0.484**
0.106
0.132
0.158
**
**
1.160
0.753
0.285*
0.082
0.103
0.124
1.180**
0.674**
0.125
0.104
0.129
0.156
**
**
1.151
0.657
0.123
0.108
0.134
0.162
1.052**
0.481**
0.031
0.104
0.130
0.156
0.127
-0.187*
-0.362**
0.070
0.090
0.107
(High – Low): Zero investment portfolio formed by investing $1 in the top 30% firms, and short selling $1 in
the bottom 30% firms in each year.
Momentum
-0.129
0.100
-0.257**
0.074
-0.238**
0.071
-0.325**
0.075
-0.314**
0.081
-0.490**
0.092
-0.375**
0.072
-0.390**
0.090
-0.269**
0.094
-0.513**
0.090
-0.073
1.586
Inventory productivity and the value of
the firm
•
Valuation measure: Tobin’s Q
–
–
•
Ratio of market value to book value of a firm.
Market value = (Book value of assets + Market value of common stock – Book value of common stock –
Deferred taxes).
Regression to estimate whether variation in inventory productivity is associated with differences in
firm value:
Qit = at + bt*Xit + ct*Wit + eit
where
i
= firm index
t
= year index
Qit
= industry-adjusted Tobin’s Q (firm Q minus median Q for the
retail segment)
Xit
= inventory productivity measure for firm i in year t (studentized residuals from
AIT or from IT)
Wit
= log(Book Value of assets); known to be correlated with Qit (Shin and Stulz 2000).
Inventory productivity and the value of
the firm – Regression results
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Mean
Using AIT
Portfolio rank High – Low
50.17*
397.72
24.50
207.57
52.63
285.28
27.25
216.61
*
79.19
464.26
31.20
250.07
**
109.73
835.54**
40.34
296.15
**
320.03
2228.59**
74.31
675.15
*
146.61
1095.07**
60.51
418.73
**
135.18
1017.75**
43.42
339.89
136.60**
886.09**
46.62
334.44
*
72.65
597.18*
35.73
283.30
**
147.57
1032.21**
45.48
366.04
**
110.57
810.82**
14.40
102.54
Using IT
Portfolio rank High – Low
21.70
148.92
24.53
206.00
23.31
68.44
27.49
204.00
-8.71
-139.90
32.35
247.35
47.42
354.65
41.41
337.60
**
233.53
1576.27*
75.82
695.97
*
148.26
1256.20**
60.16
350.59
59.44
356.55
44.51
254.89
119.23*
841.16*
46.84
340.73
*
73.90
621.27
36.21
312.85
*
100.09
555.87*
47.25
270.12
**
72.84
517.13**
14.45
103.07
• Regressions done
for portfolio rankings
obtained from AIT as well
as from IT
first using all portfolios,
then using the portfolios of
top 30% and the bottom
30% firms, with a dummy
variable for the top 30%
firms.
• Coefficients are significantly
negative in 9/10 years using
AIT, and 5/10 years using IT
• Firms with stronger AIT (or IT)
outperform those with weaker
AIT (or IT).
Summary
•
Validation that AIT provides a better performance metric than IT for the retail sector
–
–
•
Interpretation from financial perspective
–
–
–
•
Consistent positive correlation with stock returns, risk-adjusted stock returns and value of the firm
Portfolio based on stronger AIT yielded 1208% total returns, while that based on weaker AIT yielded 98%
total returns over 20 years.
Results need not constitute new evidence of market inefficiency
Inventory productivity may be correlated with other variables known to predict stock returns, e.g., business
cycles
Is there sufficient reason to think that the stock market does not fully factor in the impact of superior
inventory productivity?
Limitations
–
–
–
–
Robustness of results with respect to changes in dataset
Sensitivity of results to outliers due to large variations in the values of performance variables
Changes in portfolios over time
Causal variables
Further Research
• Omitted variables: variety, lifecycle length, components of
capital investment.
– Within-firm analysis using product or store level data.
– Firm level analysis using disaggregated data
• Augmented data from I/B/E/S.
• Other variables, e.g. firm size, accounts payable.
• Case studies: how do firms make aggregate inventory and
margin decisions?
• Explain differences in the coefficients of benchmarking model
across segments.
• Manufacturing and distribution sectors
Systematic differences in fixed firm effects
• Across segments
Segment
Catalog, Mail-Order Houses
Average of firm-wise
fixed effects
0.8251
Food Stores
0.6584
Drug & Proprietary Stores
0.5180
Radio,TV,Cons Electr Stores
0.4256
Apparel And Accessory Stores
0.3797
Miscellaneous Retail
0.3345
Variety Stores
0.2708
Home Furniture & Equip Store
0.2219
Department Stores
0.1343
Hobby, Toy, And Game Shops
0.1290
Jewelry Stores
-0.1815
• Within each segment, firms with lower gross margin have higher
intercepts than firms with higher gross margin.
Regression Across Firms
log Inventory
Turns
Estimated
regression lines
for different firms
in the apparel
industry
Estimated line for a cross-sectional model with
a single observation per firm.
Slope = -0.40
Slope = -0.15
log Gross Margin
Fixed Firm Effect = Segment – 0.25 log (Average Gross Margin)
Thank you!
Alternative Estimation of
Time Trends in Inventory Turnover
• Monthly Retail Trade Surveys by the US Census
Bureau. Jan 1992 – Dec 2003.
• Data
– Monthly sales and end-of-month inventory estimates
– Annual gross margin estimates
• We compute COGS using annual estimates of gross margin
and monthly estimates of sales.
– By NAICS codes
– These data are aggregated across firms unlike the
Compustat dataset.
Example of Time Trends in Inventory
Turnover (US Retail Trade Survey Data)
12
8
6
4
2
Ja
n03
Ja
n02
Ja
n01
Ja
n00
Ja
n99
Ja
n98
Ja
n97
Ja
n96
Ja
n95
Ja
n94
Ja
n93
0
Ja
n92
Inventory Turns
10
Month-Year
Food and beverage stores
General merchandise stores
Estimates of Time Trends
from US Retail Trade Survey Data
Average
IT
Time trend
coefficient
Standard
Error
R2
(%)
Fstatistic
Apparel and Accessory Stores
2.74
0.027
0.019
1.4
2.07
Department Stores
3.65
0.082
0.025
7.1
10.84
Home Furniture and Consumer
Electronics Stores
4.35
0.083
0.013
22.7
41.69
General Merchandise Stores
(Variety Stores)
4.56
0.204
0.026
29.8
60.36
Building Materials, Garden Equip.
and Supplies Stores
4.91
0.041
0.013
6.7
10.12
Food Stores
10.25
0.010
0.013
0.4
0.55
Total excluding motor vehicle and
parts dealers
5.40
0.080
0.015
17.3
29.78
Motor vehicle and parts dealers
5.21
-0.001
0.014
0.0
0.01
Retail Trade
5.35
0.057
0.011
16.3
27.74
Annual Inventory Turnover versus Gross Margin for the
Four Consumer Electronics Retailers for 1987-2000
10
9
Inventory Turns
8
7
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Gross Margin (%)
Best Buy Co. Inc.
Circuit City Stores
Radio Shack
CompUSA