Download - 5-Utility and Capital Allocation
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8/19/2019 5-Utility and Capital Allocation
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Slide 1 W. Suo
Charactering Investors
And Capital Allocation
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Slide 2 W. Suo
Objective
How to describe an investor?Risk aversion and utility function
Capital AllocationRisk free asset and risky portfolio
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Slide 3 W. Suo
Investor’s Life Cycle
Accumulation !ase"arly to middle yearsLow net wort!Lon# time !ori$on
%earin# risk for !i#!er returns is reasonableConsolidation !ase
&id'point and later "arnin#s e(ceed needs&oderate risk to protect investments
)pendin# !ase"arnin#s !ave mostly ceased*ime !ori$on is s!orter
rotection of assets importantInflation an immediate concern
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Slide 4 W. Suo
How to C!aracteri$e an Investor?
"conomic t!eory assumes every person seeks toma(imi$e t!eir !appiness or utility
*!e more wealt! a person !as+ t!e more utility t!ey !ave*!e !i#!er an investment’s return+ t!e #reater a person’swealt!+ t!erefore+ t!e #reater t!eir utility
However+ uncertainty about e(pected returns makest!e decision more comple(
,e must ma(imi$e our e(pected utility
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Slide 5 W. Suo
*ypes of Investors
Risk'averse investors*!ey re-uire !i#!er returns to encoura#e t!em to accept #reater risks
At !i#!er levels of risk+ investors are less willin# to accept risk unless t!eyreceive increasin#ly lar#er risk premiums
Risk'lovin# investorsrefer to enter risky #ambles even #iven t!e !i#! likeli!ood of diminis!in#
wealt!A t!eoretical possibility but not a reality wit! rational investors
Risk'indifferent investorsrefer !i#!er returns+ but #reater risk doesn’t affect t!eir !appiness In investments, we always assume people are risk averse
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Slide 6 W. Suo
How to describe an investor?
.arious factors determine an investor’s risk'return preferences
A#e/t!e elderly are usually more risk averse"conomy/people are usually more risk averse durin# a recession
essimists are usually more risk averse t!an optimists*raumatic evens tend to make people more risk averseetc
Risk *olerance 0 ,illin#ness 1 Ability
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8/19/2019 5-Utility and Capital Allocation
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2ominance rinciple 3or Risk averse Investors
1
2 34
"(pected Return
.ariance or )tandard 2eviation4 dominates 56 !as a !i#!er return4 dominates 76 !as a lower risk 8 dominates 76 !as a !i#!er return,!at about 5 and 7+ or 4 and 8+ or 5 and 8?
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8/19/2019 5-Utility and Capital Allocation
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9tility 3unction
represents an investment opportunity*!e constant measures t!e de#ree of risk aversion
Risk Aversion : 9tility
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8/19/2019 5-Utility and Capital Allocation
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rofit 0 ;<
rofit 0 '4< 5
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Risk Aversion and .alue
*!e )ample Investment
0 44= ' >; B78= 4Risk Aversion 9tility
Hi#! ; 'D> <
7 8>DD Low 5 5D>44
*'bill 0 ;=
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9tility and Indifference Curves
Represent an investor’s willin#ness to trade'off return and risk "(ample Bfor an investor wit! A08
"(p Return B= )t 2eviation B=
5< 4<5; 4;>;4< 7<
4; 77>
44
4
4
44
4
4
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8/19/2019 5-Utility and Capital Allocation
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Indifference Curves
"(pected Return
)tandard 2eviation
Increasin# 9tility
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8/19/2019 5-Utility and Capital Allocation
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Indifference Curves in σ '"Br )pace
Indifference curves represent points at w!ic! a person is e-ually!appy Bindifferent
In all cases+ Investoris !i#!ly
riskaverse>
Investor ismoderatelyrisk averse>
Investoris a risklover> Investor is
indifferentto risk>
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8/19/2019 5-Utility and Capital Allocation
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Allocatin# capital between risky assets and risk free assetsossible to split investment funds between safe and risky
assetsRisk free asset pro(y6 *'bills
erfectly price'inde(ed bond E t!e only risk free asset in real terms6*'bills are commonly viewed as Ft!eG risk'free asset6&oney market funds ' t!e most accessible risk'free asset for most investors>
Risky asset stock Bor a portfolio
Can represent t!e total investments in risky assets"(amine risk return tradeoff
2emonstrate !ow different de#rees of risk aversion will affectallocations between risky and risk free assets
Capital Allocation
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ortfolios of One Risky Asset
and One Risk'3ree AssetAssume a risky portfolio P defined by
E Br p 0 5;= and
*!e available risk'free asset !asr f 0 @= and
*!e proportions invested y= in P and B5' y = in r f
"(pected returns : standard deviation for combinations
0 complete or combined portfolio
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or If +
or If
or
If
Combinations ,it!out
Levera#e
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8/19/2019 5-Utility and Capital Allocation
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ossible Combinations
5D>;=
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CAL (Capital Allocation Line)
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Slide 19 W. Suo
%orrow at t!e Risk'3ree Rate and invest in stock 9sin# ;
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Slide 20 W. Suo
Optimal Allocation
iven an investor’s risk aversion+ !ow to determinet!e optimal allocation?
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Slide 21 W. Suo
CAL wit! Risk references
"Br
@= Lender
%orrower
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Slide 22 W. Suo
reater levels of risk aversion lead to lar#er
proportions of t!e risk free rateLower levels of risk aversion lead to lar#er proportions of t!e portfolio of risky assets,illin#ness to accept !i#! levels of risk for !i#!levels of returns would result in levera#edcombinations
Risk Aversion and Allocation
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Slide 23 W. Suo
&at!ematically J
*!e optimal investment in is
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l d W Suo
CAL with Higher
Borrowing Rate