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Getting More Out of

Two-Asse

t

Portfolio

s To m

Arnold

Lanc e A Nail an d Terr y D Nixo n

Two-asset

portfolio mathematics is a fixture in many introductory finance and investment courses.

However,

(he actual development ofthe efficient frontier and capital market line are generally left tn a heuristic discussion with diagrams. In this article, the mathematics for calculating these attributes of two-asset portfolios are introduced in a framework intended for the undergraduate classroom. G 10 Gil •Th e us e o f two-asse t portfolio s i n th e classroo m i svery convenient,, as the instructor is able to demonstrate th e benefit s o f ris k diversificatio n withou t introducin g muc h i n th e wa y o f mathematics B y varyin g portfoli o weights i t i s simpl e t o demonstrat e tha t som e portfoli o weigh t combination s resul t i n bette r risk-retur n tradeoff s tha n other s (i.e. th e efficien t frontier)

Althoug

h th e portfoli o i n questio n i s small th e basi clessons it demonstrates are applicable to much larger portfolios

However

mor e ca n b e demonstrate d wit h th e two-asse t portfoli o tha n portfoli o mea n an d portfoli o varianc e calculations I n thi s article a framewor k i s develope d tha t allow s th e studen t t o calculat e th e minimu m varianc e portfoli o weight s an d th e weight s o f a tangenc y portfoli o whe n a thir d"riskless" security is added to the portfolio. This metho d allow s th e studen t t o demonstrat e ho w a capita l allocatio n lin e dominate s th e efficien t frontier naturall y leadin g t o a discussio n o f th e

Capita

l Asse t

Pricin

g Mode l (Sharpe 1964)
Th e remainde r o f thi s articl e i s organize d a s follows Tom

Arnold

is a

Professor

of

Finance

at the

University

of

Richmond

in

Richmond,

VA

23173.

Lance A. Nail is a Professorof Finance at the University of Alabama-Birmingham in

Birmingham,

AL

35294.

Terry D. Nixon is a

Professor

of

Finance

at Miami

University

in

Oxford.

OH

45056-1879.

The author.^ gratefully acknowledge the helpful comments provided by Mark D.

Griffiths.

David G.

Shrider.

and an anonymous referee.in Section I, the efficient frontier is developed for a portfoli o consistin g oftw o risk y securities

Pursuan

t t o tha t goal formula e fo r determinin g th e minimu m varianc e portfoli o weight s ar e give n an d a n exampl eis developed for a two-stock portfolio consisting of

McDonald'

s an d

Pepsico

I n

Sectio

n II, th e framewor k i s expande d t o includ e a risk-fre e securityquotesdbs_dbs19.pdfusesText_25