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Chapter 4 Return and Risk: Analyzing The Historical Record

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Musa Tahirli

1. This document discusses risk and return analysis using historical data. It provides examples of how the returns on various investments like money market funds, bonds, and GICs can vary depending on interest rate changes. 2. Key factors like business spending, household saving, and central bank actions are described as shifting supply and demand curves for funds, thereby impacting equilibrium interest rates. 3. Different types of GICs are compared in terms of their risk and expected returns under varying inflation scenarios. Diversification across investments is suggested. 4. Historical risk premiums and variations in returns over time are analyzed for stocks, bonds, and market indexes to estimate expected returns and risk.

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Chapter 4 Return and Risk: Analyzing The Historical Record

Uploaded by

Musa Tahirli
42 views4 pages
1. This document discusses risk and return analysis using historical data. It provides examples of how the returns on various investments like money market funds, bonds, and GICs can vary depending on interest rate changes. 2. Key factors like business spending, household saving, and central bank actions are described as shifting supply and demand curves for funds, thereby impacting equilibrium interest rates. 3. Different types of GICs are compared in terms of their risk and expected returns under varying inflation scenarios. Diversification across investments is suggested. 4. Historical risk premiums and variations in returns over time are analyzed for stocks, bonds, and market indexes to estimate expected returns and risk.

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1. This document discusses risk and return analysis using historical data. It provides examples of how the returns on various investments like money market funds, bonds, and GICs can vary depending on interest rate changes. 2. Key factors like business spending, household saving, and central bank actions are described as shifting supply and demand curves for funds, thereby impacting equilibrium interest rates. 3. Different types of GICs are compared in terms of their risk and expected returns under varying inflation scenarios. Diversification across investments is suggested. 4. Historical risk premiums and variations in returns over time are analyzed for stocks, bonds, and market indexes to estimate expected returns and risk.

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Download as DOC, PDF, TXT or read online from Scribd
Download as doc, pdf, or txt
42 views4 pages

Chapter 4 Return and Risk: Analyzing The Historical Record

Uploaded by

Musa Tahirli
1. This document discusses risk and return analysis using historical data. It provides examples of how the returns on various investments like money market funds, bonds, and GICs can vary depending on interest rate changes. 2. Key factors like business spending, household saving, and central bank actions are described as shifting supply and demand curves for funds, thereby impacting equilibrium interest rates. 3. Different types of GICs are compared in terms of their risk and expected returns under varying inflation scenarios. Diversification across investments is suggested. 4. Historical risk premiums and variations in returns over time are analyzed for stocks, bonds, and market indexes to estimate expected returns and risk.

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CHAPTER4

RETURNANDRISK:ANALYZINGTHEHISTORICALRECORD
1.

Yourholdingperiodreturnforthenextyearonthemoneymarketfunddependsonwhat
30dayinterestrateswillbeeachmonthwhenitistimetorollovermaturingsecurities.
Theoneyearsavingsdepositwilloffera7.5%holdingperiodreturnfortheyear.Ifyou
forecasttherateonmoneymarketinstrumentstorisesignificantlyabovethecurrentyield
of6%,thenthemoneymarketfundmightresultinahigherHPRfortheyear.Whilethe
20yearGovernmentofCanadabondsisofferingayieldtomaturityof9%peryear,
whichis150basispointshigherthantherateontheoneyearsavingsdepositatthebank,
youcouldwindupwithaoneyearHPRofmuchlessthan7.5%onthebondiflongterm
interestratesriseduringtheyear.IftheGovernmentofCanadabondsyieldsriseabove
9%duringtheyear,thenthepriceofthebondwillfall,andthecapitallosswillwipeout
someorallofthe9%returnyouwouldhavereceivedifbondyieldshadremained
unchangedoverthecourseoftheyear.

2.a.

Ifbusinessesincreasetheircapitalspendingtheyarelikelytoincreasetheirdemandfor
funds.ThiswillshiftthedemandcurveinFigure5.1totherightandincreasethe
equilibriumrealrateofinterest.

b.

Increasedhouseholdsavingwillshiftthesupplyoffundscurvetotherightandcausereal
interestratestofall.

c.

AnopenmarketsaleofTreasurysecuritiesbytheBankofCanadaisequivalenttoa
reductioninthesupplyoffunds(ashiftofthesupplycurvetotheleft).Theequilibrium
realrateofinterestwillrise.

3.a.

TheInflationPlusGICissaferbecauseitguaranteesthepurchasingpowerofthe
investment.Usingtheapproximationthattherealrateequalsthenominalrateminusthe
inflationrate,theGICprovidesarealrateof3.5%regardlessoftheinflationrate.

b.

Theexpectedreturndependsontheexpectedrateofinflationoverthenextyear.Ifthe
rateofinflationislessthan3.5%thentheconventionalGICwillofferahigherrealreturn
thantheInflationPlusGIC;ifinflationismorethan3.5%,theoppositewillbetrue.

c.

Ifyouexpecttherateofinflationtobe4%overthenextyear,thentheconventionalGIC
offersyouanexpectedrealrateofreturnof3%,whichis0.5%lowerthantherealrateon
theinflationprotectedGIC.Butunlessyouknowthatinflationwillbe3%with
41

certainty,theconventionalGICisalsoriskier.Thequestionofwhichisthebetter
investmentthendependsonyourattitudetowardsriskversusreturn.Youmightchoose
todiversifyandinvestpartofyourfundsineach.
d.

No.Wecannotassumethattheentiredifferencebetweenthenominalriskfreerate(on
conventionalGICs)of7%andtherealriskfreerate(oninflationprotectedGICs)of
3.5%istheexpectedrateofinflation.Partofthedifferenceisprobablyariskpremium
associatedwiththeuncertaintysurroundingtherealrateofreturnontheconventional
GICs.Thisimpliesthattheexpectedrateofinflationislessthan3.5%peryear.

4.

E(r)=.3544%+.3014%+.35(16%)=14%.
Variance=.35(4414)2 +.30(1414)2 +.35(1614)2 =630

Standarddeviation=25.10%
Themeanisunchanged,butthestandarddeviationhasincreased,astheprobabilitiesof
thehighandlowreturnshaveincreased.

5.

Probabilitydistributionofpriceand1yearholdingperiodreturnon30yearCanada
bonds(whichwillhave29yearstomaturityatyearsend):
Economy
Boom
NormalGrowth
Recession

Probability

YTM

Price

.20
.50
.30

11.0%
8.0
7.0

$74.05
100.00
112.28

Capitalgain Coupon
$25.95
0.00
12.28

$8.00
8.00
8.00

HPR
17.95%
8.00%
20.28%

6.

TheaverageriskpremiumonS&P/TSXcompositestocksfortheperiod19572006was
4.72%peryear.Addingthistoariskfreerateof6%givesanexpectedreturnof10.72%
peryearfortheS&P/TSXIndexportfolio.

7.

Theaveragerateofreturnandstandarddeviationarequitedifferentinthesubperiods:
Mean
19572009
19571984
19852009

STOCKS
Std.Dev.

10.72%
10.82
10.61

17.12%
17.72
16.79
42

Mean

BONDS
Std.Dev.

8.69%
6.82
10.78

9.78%
10.39
8.99

8.a

Iwouldprefertousetheriskpremiumsandstandarddeviationsestimatedovertheperiod
19571984,becausethecurrentinflationaryexpectationsareclosertothoseof19571984
thantothemoreinflationarylaterperiod.
Realholdingperiodreturn = 1 =
= = .0588=5.88%

b.

TheapproximationgivesarealHPRof80%70%=10%,whichisclearlytoohigh.

9.

E(q)=0x.25+1x.25+2x.5=1.25;E(q2)=1x.25+22x.50=2.25Var(q)=2.251.252=0.6875

10.

a.(correspondstoplusorminustwostandarddeviations)

11.

20%,10%

12.

24%,13%

13.

19%

14.

$13,000Expecteddollarreturnonequityinvestmentis$18,000versus$5,000returnon
Tbills]

15.

10%

16.

11.4

17.

Theprobabilitythattheeconomywillbeneutralis0.50,or50%.Givenaneutral
economy,thestockwillexperiencepoorperformance30%ofthetime.Theprobability
ofbothpoorstockperformanceandaneutraleconomyistherefore:
0.30x0.50=0.15=15%

18.a. ProbabilityDistributionofHPRontheStockMarketandPut
Stateofthe
Economy
Boom
NormalGrowth
Recession

Probability
.25
.50
.25

STOCK

Endingprice
+$4dividend HPR
$144
114
84

44%
14%
16%
43

PUT

Ending
Value
HPR
0
0
$30

100%
100%
150%

Rememberthatthecostofthestockis$100pershare,andthatoftheputis$12.
b.

Thecostofoneshareofstockplusaputis$112.TheprobabilitydistributionofHPRon
thestockmarketplusputis:
Stateofthe
Economy
Boom
NormalGrowth
Recession

Probability
.25
.50
.25

Stock+Put+$4dividend
EndingValue HPR
$144
28.6%
114
1.8
114
1.8

(144112)/112
(114112)/112

c.

BuyingtheputoptionguaranteesyouaminimumHPRof1.8%regardlessofwhat
happenstothestock'sprice.Thus,itoffersinsuranceagainstapricedecline.

19.

TheprobabilitydistributionofthedollarreturnonCDpluscalloptionis:
Economy
CombinedValue
Boom
NormalGrowth
Recession

Probability EndingValueCDEndingValueCall
.25$
.50
.25

114(107.55x1.06)
114
114

44

$30
0
0

$144
114
114

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