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Risk and Return Introduction
For 9.220, Term 1, 2002/03
02_Lecture12.ppt
Student ersion
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!ut"ine
Introduction
#$at is risk%
&n o'er'ie( o) market per)ormance *easurin+ per)ormance
Return and risk measures
Summar and -onc"usions
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Introduction
It is important to understand t$e re"ationet(een risk and return so (e candetermine appropriate riskadusted
discount rates )or our ana"sis. &t "east as important, t$e re"ation et(een
risk and return is use)u" )or in'estors ($ou securities4, corporations t$at se""securities to )inance t$emse"'es4, and )or)inancia" intermediaries t$at in'est,orro(, "end, and price securities on e$a")o) t$eir c"ients4.
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#$at is risk%
5e)inition6 risk is t$e potentia" )ordi'er+ence et(een t$e actua"outcome and ($at is e7pected.
In )inance, risk is usua"" re"ated to($et$er e7pected cas$ )"o(s (i""materia"i8e, ($et$er securit prices
(i"" )"uctuate une7pected", or($et$er returns (i"" e as e7pected.
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&n o'er'ie( o) market per)ormance is t$ere risk%
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&n o'er'ie( o) market per)ormance is t$ere risk%
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&n o'er'ie( o) market per)ormance is t$ere risk%
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&n o'er'ie( o) market per)ormance is t$ere risk%
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&n o'er'ie( o) market per)ormance is t$ere risk%
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&n o'er'ie( o) market per)ormance is t$ere risk%
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*easurin+ er)ormance6 Returns
5o""ar return o'er one period46 5i'idends : ;nd o) eriod rice
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Do"din+ eriod Returns
Let Rte t$e oser'edreturn earned in ear t,t$en t$e $o"din+ periodreturn o'er a Tperiodtime )rame is as )o""o(s6
T$e a'era+e compoundrate o) return or+eometric a'era+e rate o)return A&R4 ust con'erts
t$e DR to an eEui'a"ente))ecti'e annua" rate6
( )=
+=+T
1t
tTto1R1HPR1
( ) ( )T
1
T
1t
tT
1
Tto1Tto1 )R(1HPR1GAR1
+=+=+
=
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*ean returns
T$e mean return is t$earit$metic a'era+erate o) return and isca"cu"ated as )o""o(s6 T
R
RreturnMean
T
1t
t===
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T$e risk premium
5e)inition6 t$e risk premiumis t$e returnon a risk securit minus t$e return on arisk)ree securit o)ten Ti""s are used ast$e risk)ree securit4 ¬$er name )or a securits risk premium is
t$e excess return o) t$e risk securit. T$e market risk premium is t$e return on
t$e market as a ($o"e4 minus t$e risk)reerate o) return.
#e ma ta"k aout t$e past oser'ed riskpremium, t$e a'era+e risk premium, or t$ee7pected risk premium.
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Risk *easures
Studies o) stock returns indicate t$e areappro7imate" norma"" distriuted. T(o statisticsdescrie a norma" distriution, t$e mean and t$estandard de'iation ($ic$ is t$e sEuare root o) t$e'ariance4. T$e standard de'iation s$o(s $o( spread
out is t$e distriution. For stock returns, a more spread out distriution
means t$ere is a $i+$er proai"it o) returns ein+)art$er a(a )rom t$e mean or e7pected return4.
For our estimate o) t$e e7pected return, (e can uset$e mean o) returns )rom a samp"e o) stock returns.
For our estimate o) t$e risk, (e can use t$e standardde'iation or 'ariance ca"cu"ated )rom a samp"e o)stock returns.
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Samp"e standard de'iation and 'ariance
Samp"e 'ariance isa measure o) t$esEuared de'iations
)rom t$e mean andis ca"cu"ated as)o""o(s6
Samp"e standardde'iation is ustt$e sEuare root o)t$e samp"e'ariance6
( )
VarSDs
R-R1T
1Vars
T
1t
2
t2
==
==
=
and
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Do( to interpret t$e standard de'iationas a measure o) risk
Ai'en a norma" distriution o) stock returns G t$ere is aout a HC.2H> proai"it t$at t$e
actua" return (i"" e (it$in 1 standard de'iation
o) t$e mean. t$ere is aout a 9?.BB> proai"it t$at t$e
actua" return (i"" e (it$in 2 standard de'iationso) t$e mean.
T$ere is aout a 99.@B> proai"it t$at t$e
actua" return (i"" e (it$in 3 standard de'iationso) t$e mean.
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Summar and conc"usions
#e can easi" ca"cu"ate =, >, $o"din+period, +eometric a'era+e, and meanreturns )rom a samp"e o) returns data.
#e can a"so do t$e same )or a securitsrisk premium.
T$e mean and standard de'iationca"cu"ated )rom samp"e returns data are
o)ten used as estimates o) e7pected returnsand t$e risk measure )or a securit or )ort$e market as a ($o"e.
