An Econometric Analysis of Inventory Turnover

Performance in Retail Services

Vishal GaurStern School of Business, New York University

Marshall FisherThe Wharton School, University of Pennsylvania

Ananth RamanHarvard 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 – 8.5Circuit City Stores, Inc. 4.0 – 5.6The Gap, Inc. 3.6 – 6.3Radio Shack Corp. 1.1 – 3.1Wal-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

0

1

2

3

4

5

6

7

8

9

10

1986 1988 1990 1992 1994 1996 1998 2000

Time (years)

Annual Inventory Turnover

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

2. Gross Margin

3. Capital Intensity

4. Sales Surprise

=Sales - Cost of Goods Sold

GMSales

=Cost of Goods Sold

ITAverage Inventory

=+

Avg Gross Fixed AssetsCI

Avg Inventory Avg Gross Fixed Assets

=Sales Realized

SSSales 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 firm-specific 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 andthe “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.

, 1 , 1

, 1 , 1

, 1 , 1

Sales Forecast

where (1 )( ),

( ) (1 )

sit si t si t

sit sit si t si t

sit sit si t si t

L T

L S L T

T L L T

Model Specification

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, b2

s, b3s: segment-wise coefficients.

b1s 0 for hypothesis 1, b2

s > 0 for hypothesis 2, b3s > 0 for hypothesis 3.

sit denotes the error term.

1 2 3sit i t s sit s sit s sit sitlogIT F c b logGM b logCI b logSS= + + + + +e

Alternative Model Specifications

• Coefficients pooled across segments

• Intercept pooled across firms

• Interaction effects– Separate year-wise fixed effects for each segment– Separate coefficients for each segment and each

year

• Inventory as dependent variable

= + + + + +e1 2 3sit i t sit sit sit sitlogIT F c b logGM b logCI b logSS

= + + + + +e1 2 3sit s t s sit s sit s sit sitlogIT F c b logGM b logCI b logSS

= + + + + + +e1 2 3 4sit i t sit sit sit sit sitlog(Inv ) F c b logGM b logCI b logSS b logCGS

Summary of Data

72 786 979.1 4.57 0.37 0.592.13 0.08 0.14

45 441 439.9 8.60 0.39 0.509.11 0.17 0.18

23 309 6058.6 3.87 0.34 0.631.45 0.08 0.10

23 256 2309.5 5.26 0.28 0.482.90 0.07 0.12

57 650 4573.6 10.78 0.26 0.754.58 0.06 0.08

10 98 1455.5 2.99 0.35 0.461.08 0.07 0.14

13 125 391.2 5.44 0.40 0.5510.43 0.07 0.16

15 156 475.2 1.68 0.42 0.360.58 0.13 0.11

17 200 1585.0 4.10 0.31 0.441.54 0.11 0.09

36 386 6548.7 4.45 0.29 0.512.92 0.09 0.15

311 3407 2791.4 6.08 0.33 0.575.41 0.11 0.17

Aggregate statistics

Average Sales ($ million)

Home Furniture & Equip StoresJewelry Stores

Radio,TV, Cons Electr StoresVariety Stores

Department Stores

Drug & Proprietary StoresFood Stores

Hobby, Toy, And Game Shops 

Gross Margin

Capital Intensity

Apparel And Accessory Stores Catalog, Mail-Order Houses

Retail Industry Segment # of firms

# annual observations

Inventory Turnover

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

2

, ,

2

, ,

2

, ,

log log

1 97.16%.

log log

log log

1

log

s i t

s i t

s i t

IT IT

IT IT

IT IT

IT

Predicted Value of

Overall prediction accuracyAggregate Mean of

Predicted Value of

Within-firm prediction accuracyWithin-firm Me 2

, ,

66.7%.

log

s i t

ITan of

The model explains 97.2% of the total variation and 66.7% of the within-firm variation in log(Inventory Turnover).

Coefficients’ EstimatesGross Margin Capital Intensity Sales Surprise

Apparel And Accessory Stores -0.153 0.977 0.053Catalog, Mail-Order Houses -0.226 -0.039* 0.225Department Stores -0.310 0.861 0.189Drug & Proprietary Stores -0.186 0.361 0.143Food Stores -0.351 1.085 0.179Hobby, Toy, And Game Shops -0.571 -0.015* 0.215Home Furniture & Equip Stores -0.017* 0.562** 0.174Jewelry Stores -0.438 0.038* 0.279Radio,TV,Cons Electr Stores -0.500 0.268 0.140Variety Stores -0.313 0.106 0.176Pooled coefficients -0.285 0.252 0.143

Segment-wise coefficients

• 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.

• Adjusted Inventory Turnover (AIT)– equals the residual from the model and shows the distance

of a firm from its tradeoff curve (benchmark).

log log 0.285log

0.252log 0.143logsit sit sit

sit sit

AIT IT GM

CI SS

Residual

0.283 0.252 0.143Firm-specific constant

Time-specific constant

GM CI SS IT

Example 1: Comparison of Four Consumer Electronics Retailers

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6

Gross Margin (%)

Inve

ntor

y T

urns

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

0

2

4

6

8

10

12

14

0 0.1 0.2 0.3 0.4 0.5 0.6Gross Margin

Inve

ntor

y T

urns

Best Buy Co. Inc.

Circuit City Stores

CompUSA

Radio Shack

Note: Figures are drawn using the average values of CI and setting SS = 1.

y = -0.0194x + 8.3937

R2 = 0.0592

y = 0.0704x + 6.2215

R2 = 0.5705

6

6.5

7

7.5

8

8.5

9

9.5

1987 1989 1991 1993 1995 1997 1999

Time (in years)

Example 2: Comparison across years within a firm - Ruddick Corp.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1986 1988 1990 1992 1994 1996 1998 2000

Gross Margin Capital Intensity

Gross Margin and Capital Intensity are increasing with time.

IT is decreasing with time, but AIT is increasing with time.

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 + bt + error term

Here, ai is the firm-specific intercept, and b is the slope w.r.t. time.

Variable Coefficient Std Error t-statistic p-valueCI 0.00568 0.00030 19.00 <0.0001log CI 0.01250 0.00077 16.23 <0.0001IT -0.05460 0.01354 -4.03 <0.0001log IT -0.00454 0.00110 -4.11 <0.0001GM -0.00018 0.00031 -0.59 0.5568log GM 0.00093 0.00130 0.72 0.4736

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1986 1988 1990 1992 1994 1996 1998 2000

Time (in years)

c(t)

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.

Error-bars around the estimates show intervals of ± 2 standard deviation.

0

20

40

60

80

100

120

140

-0.375 -0.275 -0.175 -0.075 0.025 0.125 0.225 0.325

Estimated Time Trend

Num

ber

of fi

rms

Histogram of Firm-wise Time Trends Estimated from Year-wise

Fixed Effects167 firms

with –ve trends144 firms

with +ve trend

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 Methodologies1. 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:

• 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)

3. 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 Total # of firms

Total # of obs.

Average # of obs. per year

Chapter 11 and Chapter 10 filings (Bankruptcy / Liquidation)

Total # of terminatio-ns

5311, 5331, 5399

Department stores, Discount stores

111 1071 53.55 15 49

5411 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

TOTAL 485 4148 8.55 26 134

Data Description - 2

Median Average Median Average Median Average Median Average Median Average53 950.8 6315.9 3.53 4.40 0.32 0.31 0.58 0.56 454.8 3996.25411 1393.8 5034.5 10.06 10.94 0.26 0.25 0.77 0.76 582.9 1865.256 345.7 1112.7 4.10 4.54 0.35 0.36 0.61 0.59 178.6 558.6573 306.0 1324.8 3.50 4.05 0.31 0.32 0.44 0.43 124.0 564.75961 116.6 396.2 5.29 13.72 0.38 0.37 0.50 0.51 65.3 215.6

CI Book Value ($m)SIC Code

Sales ($m) IT GM

• 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:• 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.

• 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:• 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.]

Segmentwise composition of portfolios Portfolio Rank # of obs 5300 5411 5600 5731 5961

Median Sales

Average Sales

Std Dev Sales

1 274 24.8 22.3 23.7 10.6 18.6 330.7 2277.3 4749.5 2 323 25.7 21.7 22.6 11.1 18.9 527.5 2724.5 5970.3 3 309 25.9 21.7 23.0 11.3 18.1 666.9 3085.2 7151.7 4 324 25.3 21.6 22.8 11.1 19.1 677.7 3137.0 7066.9 5 330 24.8 20.9 23.0 13.0 18.2 681.7 3546.3 8290.1 6 298 25.5 21.8 22.8 10.4 19.5 698.0 4163.3 12037.3 7 312 25.0 21.5 23.4 11.5 18.6 597.5 4515.6 14507.0 8 321 26.2 21.8 22.4 10.9 18.7 776.8 4379.7 10716.4 9 311 25.4 21.5 23.2 11.6 18.3 450.4 4401.7 19092.6 10 361 23.8 21.6 22.2 12.7 19.7 374.9 3404.9 13427.5

Examples of portfolio ranks of large firms

Segment Company Name # of Obs.

Average Sales Portfolio rank

($m) Average Std. Dev. 53 Target Corp 19 21785.1 7.47 0.96 53 Penney (J C) Co 19 22428.1 4.21 2.59 53 Costco Wholesale Corp 10 27616.0 9.20 0.79 53 K-Mart Holding Corp 18 31425.1 3.61 1.33 53 Wal-Mart Stores 19 86660.4 7.16 1.50

56 Nordstrom Inc 19 3695.0 4.11 1.29 56 Gap Inc 19 5221.9 6.37 1.64 56 Limited Brands Inc 19 6640.8 7.89 1.20 56 Foot Locker Inc 19 7116.2 3.53 1.43

573 CompUSA Inc 8 3387.1 8.75 2.38 573 RadioShack Corp 20 4423.0 3.70 2.05 573 Circuit City Stores Inc 19 5143.4 6.79 1.32 573 Best Buy Co Inc 18 6382.6 8.50 1.42

5961 Amazon.com Inc 7 2496.9 7.86 2.34 5961 Spiegel Inc -CL A 15 2535.6 3.13 1.81

Comparison of returns on highest and lowest ranked

portfolios

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Portfolios 1-3

Portfolios 8-10

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Portfolios 1-3

Portfolios 8-10

Annual returns on a $1 investment in portfolios formed using AIT

Annual returns on a $1 investment in portfolios formed using IT

• 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

Comparison of total returns on all decile portfolios

Portfolio rank

Annualized returns on AIT based

portfolios

Annualized returns on IT based portfolios

1 -3.55% -3.00%2 1.42% 5.38%3 8.81% 6.19%4 2.23% 8.39%5 4.38% 4.40%6 2.01% 8.91%7 14.10% 4.13%8 9.46% 8.71%9 16.13% 18.55%

10 13.50% 6.85%

Portfolios 1-3 3.48% 4.05%Portfolios 8-10 13.72% 12.16%

Highest ranked decile

portfolio

Lowest ranked decile

portfolio

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 + 1i*RMRFt + 2i*SMBt + 3i*HMLt + 4i*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 factor-

mimicking 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 below-

average 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

(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.

Using Adjusted Inventory Turns Using Inventory Turns Portfolio RMRF SMB HML Momentum RMRF SMB HML Momentum

1 -0.013** 0.969** 0.794** 0.631** -0.194* -0.009 0.983** 0.837** 0.354* -0.129 0.004 0.094 0.118 0.142 0.082 0.005 0.115 0.143 0.173 0.100 2 -0.007* 1.105** 0.746** 0.385** -0.366** -0.006 0.994** 0.684** 0.464** -0.257** 0.003 0.079 0.099 0.119 0.069 0.003 0.085 0.105 0.127 0.074

3 0.000 1.009** 0.660** 0.464** -0.257** -0.005 1.113** 0.815** 0.639** -0.238** 0.004 0.092 0.114 0.137 0.080 0.003 0.081 0.101 0.122 0.071 4 -0.007 1.127** 0.935** 0.521** -0.323** -0.003 1.243** 0.673** 0.507** -0.325** 0.004 0.093 0.115 0.139 0.080 0.004 0.087 0.108 0.130 0.075

5 -0.007* 1.157** 0.785** 0.610** -0.274** -0.006 1.144** 0.758** 0.528** -0.314** 0.004 0.088 0.110 0.132 0.077 0.004 0.094 0.117 0.140 0.081 6 -0.007* 1.204** 0.773** 0.389** -0.314** 0.003 1.134** 0.870** 0.484** -0.490** 0.004 0.087 0.108 0.130 0.076 0.004 0.106 0.132 0.158 0.092 7 0.006 1.131** 0.666** 0.169 -0.665** -0.005 1.160** 0.753** 0.285* -0.375** 0.004 0.096 0.120 0.144 0.084 0.003 0.082 0.103 0.124 0.072 8 0.001 1.172** 0.556** 0.215 -0.312** 0.001 1.180** 0.674** 0.125 -0.390** 0.004 0.109 0.135 0.163 0.094 0.004 0.104 0.129 0.156 0.090 9 0.004 1.083** 0.635** 0.083 -0.279** 0.003 1.151** 0.657** 0.123 -0.269** 0.004 0.100 0.124 0.149 0.087 0.004 0.108 0.134 0.162 0.094

10 0.004 1.155** 0.605** 0.042 -0.364** 0.003 1.052** 0.481** 0.031 -0.513** 0.004 0.105 0.131 0.157 0.091 0.004 0.104 0.130 0.156 0.090

0.009** 0.104 -0.137* -0.372* -0.042 0.007 0.127 -0.187* -0.362** -0.073 High - Low 0.003 0.065 0.081 0.097 0.056 0.007 0.070 0.090 0.107 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:

Qit = at + bt*Xit + ct*Wit + eitwherei = firm indext = year indexQit = 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 Qit (Shin and Stulz 2000).

Inventory productivity and the value of the firm – Regression

results Using AIT Using IT Portfolio rank High – Low Portfolio rank High – Low

1994 50.17* 397.72 21.70 148.92 24.50 207.57 24.53 206.00

1995 52.63 285.28 23.31 68.44 27.25 216.61 27.49 204.00

1996 79.19* 464.26 -8.71 -139.90 31.20 250.07 32.35 247.35

1997 109.73** 835.54** 47.42 354.65 40.34 296.15 41.41 337.60

1998 320.03** 2228.59** 233.53** 1576.27* 74.31 675.15 75.82 695.97

1999 146.61* 1095.07** 148.26* 1256.20** 60.51 418.73 60.16 350.59

2000 135.18** 1017.75** 59.44 356.55 43.42 339.89 44.51 254.89

2001 136.60** 886.09** 119.23* 841.16* 46.62 334.44 46.84 340.73

2002 72.65* 597.18* 73.90* 621.27 35.73 283.30 36.21 312.85

2003 147.57** 1032.21** 100.09* 555.87* 45.48 366.04 47.25 270.12 Mean 110.57** 810.82** 72.84** 517.13** 14.40 102.54 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

– 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.

• Interpretation from financial perspective– 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

• Within each segment, firms with lower gross margin have higher intercepts than firms with higher gross margin.

SegmentAverage of firm-wise

fixed effects

Catalog, Mail-Order Houses 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

Regression Across Firms

log Gross Margin

log Inventory Turns

Estimated regression lines for different firms in the apparel industry Slope = -0.15

Estimated line for a cross-sectional model with a single observation per firm.

Slope = -0.40

Fixed Firm Effect = Segment – 0.25 log (Average Gross Margin)

Thank you!

Alternative Estimation ofTime 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)

0

2

4

6

8

10

12

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Month-Year

Inve

ntor

y T

urns

Food and beverage stores General merchandise stores

Estimates of Time Trends from US Retail Trade Survey

DataAverage

ITTime trend coefficient

Standard Error

R2

(%)F-

statistic

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

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6

Gross Margin (%)

Inve

ntor

y T

urns

Best Buy Co. Inc. Circuit City Stores Radio Shack CompUSA