Manufacturing Portfolio Theory

Abstract

Manufacturing is an extremely risk-averse business. Large-scale physical plant, equipment, and workforce requirements make rapid adjustments to changing business and economic conditions extremely difficult and expensive. Planning, designing, building, starting, and eventually stopping a factory can cost billions of dollars. Thus, manufacturing businesses employ several strategies to control risk, including economies of scale, outsourcing, and diversification.

The latter strategy, diversification, is employed extensively in financial risk management, and modern portfolio theory (MPT), is directly applicable to securities investing. MPT, originally developed by Harry Markowitz (Markovitz, 1952) and leading to a Nobel Prize in Economics, helps investors control the amount of risk and return they can expect in a portfolio of investments such as stocks. MPT shows that certain weighted combinations of investments offer both lower expected risk and higher expected return than other combinations. MPT also shows that certain combinations only offer increased reward with increased risk. This set of combinations is referred to as the efficient frontier. Thus, the first step is to eliminate the combinations that offer higher risk and lower return. Then, the second step is to identify how much risk the investor can tolerate to obtain a higher return, and then select a portfolio of weighted combinations along the efficient frontier.

This paper will use these historical datasets to model a hypothetical manufacturing business based on input pricing risk, and will illustrate two things:

1. How selecting a less volatile (i.e. less risky) input can yield higher profits in single input model, and
2. How applying MPT can increase profits while reducing risk in a multiple-input model.

Full text

Page%1!(2010,%Manufacturing%Portfolio%Theory,%Tony%Sabbadini)%
!
Manufacturing!Portfolio!Theory!
Tony!Sabbadini,!President!@!Economic!Risk!Management,!LLC!
Berkeley,!CA,!United!States!of!America!
sabbadini@economiciskmanagement.com!
for$the$RISK$ANALYSIS$AND$RISK$MANAGEMENT$Symposium$at$the$22nd$International$
Conference$on$Systems$Research,$Informatics$and$Cybernetics$–$InterSymp$2010$
!
Introduction!
!
! Manufacturing! is! an! extremely! risk‐averse! business.! Large‐scale! physical! plant,!
equipment,! and! workforce! requirements! make! rapid! adjustments! to! changing! business! and!
economic!conditions!extremely!difficult!and! expensive.! !Planning,!designing,!building,!starting,!
and!eventually!stopping! a! factory!can!cost! billions! of!dollars.!! Thus,!manufacturing!businesses!
employ! several! strategies! to! control! risk,! including! economies! of! scale,! outsourcing,! and!
diversification.!
!
The!latter!strategy,!diversification,!is!employed!extensively!in!financial!risk!management,!
and!modern!portfolio!theory!(MPT),!is!directly!applicable!to!securities!investing.!!MPT,!originally!
developed! by! Harry! Markowitz! (Markovitz,! 1952)! and! leading! to! a! Nobel! Prize! in! Economics,!
helps! investors! control! the! amount! of! risk! and! return! they! can! expect! in! a! portfolio! of!
investments! such! as! stocks.! ! MPT! shows! that! certain! weighted! combinations! of! investments!
offer!both!lower!expected!risk!and!higher!expected!return!than!other!combinations.!!MPT!also!
shows! that! certain! combinations! only! offer! increased! reward! with! increased! risk.! ! This! set! of!
combinations! is! referred! to! as! the! efficient! frontier.! ! Thus,! the! first! step! is! to! eliminate! the!
combinations!that!offer!higher!risk!and!lower!return.!!Then,!the!second!step!is!to!identify!how!
much! risk! the! investor! can! tolerate! to! obtain! a! higher! return,! and! then! select! a! portfolio! of!
weighted!combinations!along!the!efficient!frontier.!
!
! This! paper! will! use! these! historical! datasets! to! model! a! hypothetical! manufacturing!
business!based!on!input!pricing!risk,!and!will!illustrate!two!things:!
!
1.! How! selecting! a! less! volatile! (i.e.! less! risky)! input! can! yield! higher! profits! in! single!
input!model,!and!
2.!How!applying!MPT!can!increase!profits!while!reducing!risk!in!a!multiple‐input!model.!
!
Keywords!
!
! risk!management,!portfolio!theory,!volatility,!manufacturing!

Page%2!(2010,%Manufacturing%Portfolio%Theory,%Tony%Sabbadini)%
!
Optimization!in!a!Single‐Input!Model!
!
! Before!we!examine!the!real‐world!datasets,!let!us!first!consider!a!hypothetical!
manufacturing!model!based!on!a!single!input!price.!!To!illustrate!lower!volatility,!the!first!input!
price!pattern!(1)!follows!a!sinusoidal!curve!with!a!single!period,!while!the!second!input!price!
pattern!(2)!follows!a!sinusoidal!curve!with!two!periods.!
!
!
!
! To!keep!the!model!simple,!output!price!is!held!constant,!so!the!only!time!a!
manufacturer!can!make!money!in!this!scenario!is!to!produce!when!the!input!price!is!less!than!
output!price.!!In!order!to!reflect!fixed!factory!costs,!a!capital!charge!is!incurred!each!time!
period!the!factory!is!operational,!a!startup!cost,!and!a!shutdown!cost.!!The!factory!is!not!
operational!before!and!during!the!startup!period,!nor!during!and!after!the!shutdown!period.!
!
! The!first!input!pricing!pattern!(3)!has!significant!higher!profits,!545!to!486,!in!our!
example,!or!12%!higher!profits.!!This!is!directly!attributable!to!the!higher!startup!and!shutdown!
costs!in!the!second!input!pricing!pattern!(4),!as!the!factory!manager!starts!up!and!shuts!down!
the!factory!twice!as!often!in!defense!against!more!volatile!input!prices.!!This!illustrates!how!
lower!volatility!can!increase!profit.!
!

Page%3!(2010,%Manufacturing%Portfolio%Theory,%Tony%Sabbadini)%
!
Real‐World*Scenario!
!
! Applying!the!same!factory!model!to!real‐world!input!pricing!data!for!oil,!steel,!and!
rubber,!the!following!charts!illustrate!similar!findings!to!the!hypothetical!scenario:!more!
volatility!given!the!same!average!price!=!less!profit.!!Specifically,!oil,!steel,!and!rubber!return!
profits!of!1055,!1288,!and!1259,!respectively!(5).!
!
!
!
Optimization!in!a!Multiple‐Input!Model!
!
! In!the!real!world,!very!few!products!are!composed!of!one!final!input,!such!as!salt,!and!
no!products!are!produced!using!only!one!input!–!material,!labor!(manual!or!automated),!and!
processing!are!the!absolute!minimum!required!for!manufacturing!a!product.!!In!the!following!
model,!we!extend!the!single‐input!model!to!consider!a!three‐input!product!composed!of!
varying!proportions!of!oil,!steel,!and!rubber.!!An!example!might!be!a!toy!truck,!where!parts!are!
made!of!oil!(plastic),!steel,!and!rubber.!
!
! In!the!single‐input!model,!we!already!know!that!steel!offers!the!greatest!expected!profit.!!
In!our!multiple‐input!model,!if!we!decided!to!manufacture!our!product!out!of!0%!oil,!100%!steel,!
and!0%!rubber,!we!would!have!the!highest!expected!profit!compared!to!any!other!combination!
of!oil,!steel,!and!rubber.!!However,!we!would!also!have!the!highest!expected!variance,!or!risk.!!
The!future!is!not!certain,!and!this!means!that!in!the!future,!there!is!a!higher!chance!of!a!

Page%4!(2010,%Manufacturing%Portfolio%Theory,%Tony%Sabbadini)%
!
dramatic!fluctuation!in!profits!if!we!rely!solely!on!steel!than!we!would!if!we!had!chosen!a!
basket!of!inputs!composed!of!oil,!steel,!and!rubber.!!As!a!manager!of!a!company,!having!
dramatic!swings!in!profit!severely!complicates!your!job,!subjecting!you!to!closer!scrutiny!from!
not!only!the!board!of!directors,!but!also!your!customers,!your!employees,!and!your!investors.!!
Volatility!casts!doubt!on!your!effectiveness!to!manage,!and!increases!the!amount!of!work!you!
have!to!do!to!calm!worried!observers.!!This!is!where!MPT!can!help!by!decreasing!the!chance!of!
dramatic!swings!in!profitability.!
!
! Formally,!MPT!uses!the!following!definitions:!
!
! The!expected!return!of!a!portfolio!Rp!is!the!weighted!average!of!the!expected!returns!Ri!
of!the!individual!inputs!i:!
!
!
!
!
! The!portfolio!variance!σP
2!is!the!dot‐product!of!the!row‐vector!of!weights,!the!
covariance!matrix!of!returns!of!individual!inputs,!and!the!transpose!of!the!row‐vector!of!
weights.!
!
!
!
!
! To!compute!the!expected!returns!of!each!input,!we!simply!take!the!average!of!the!
annual!profits!of!each!input.!
!
!
!
! To!compute!the!covariance!matrix,!we!compute!the!covariance!of!the!annual!profits!of!
each!combination!of!input!types!(e.g.!oil!and!steel):!
!
!
!
! To!then!see!the!expected!returns!and!variances!of!different!weights!of!combinations!of!
inputs,!we!consider!all!baskets!of!inputs!in!25%!increments:!
!

Page%5!(2010,%Manufacturing%Portfolio%Theory,%Tony%Sabbadini)%
!
!
!
! Then,!to!visualize!the!expected!returns!against!their!standard!deviation!and!illustrate!
the!efficient!frontier,!we!create!a!scatter!plot!(6):!
!
! The!portfolio!baskets!circled!offer!inferior!risk/return!tradeoffs!than!those!along!the!
dashed!line!form!the!efficient!frontier.!!Those!circled!offer!lower!return!for!the!same!amount!of!
risk.!Using!this!analysis,!a!manager!can!thus!reduce!the!potential!risk!exposure!his!business!has!
while!simultaneously!increasing!the!return.!
!
The!Dataset!
!
1.!Basic!materials:!steel,!copper,!lead!from!the!United!States!Geological!Survey!(USGS).!
2.!Oil!from!the!United!States!Department!of!Energy!(DOE).!
3.!Rubber!from!the!United!Nations!Conference!on!Trade!and!Development!(UNCTAD).!
!
Inflation!data!is!taken!from!the!USGS!dataset!and!applied!throughout!the!other!datasets!
to! normalize! pricing! values! to! 1998! US! dollars! ($).! ! To! smooth! seasonal! and! minor! cyclical!
effects,!a!3‐year! moving! average!(MA)!is! applied! to!all! the! datasets.!!And! in! order!to! increase!
comparability! of! the! datasets! on! a! chart,! a! natural! logarithm! (ln)! has! been! applied.! ! The! five!
datasets,!covering! oil,! steel,! copper,! rubber,!and! lead! prices,! extend! from!1962! to! 2007! for! a!
total!of!46!data!points!in!each!set.!
!
References!
!
Markowitz,!Harry!M.!(1952);!Portfolio!Selection;!Journal!of!Finance,!Vol.!7!No.!1!(pp.!77–91)!