Chapter 11 FIN 3000 PDF

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Chapter 11 FIN 3000...

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Tophedgef undmanagerSal l yBuffitbel i ev est hatas t oc kwi t ht hes amemar k et r i s kast heS&P500wi l ls el laty ear endatapr i c eof$50.Thes t oc kwi l lpaya di v i dendaty ear endof$2.As sumet hatr i s k f r eeTr eas ur ysec ur i t i escur r ent l yoffer ani nt er es tr at eof2%. Av er ager at esofr et ur nonTr eas ur ybi l l s ,gov er nmentbonds ,andc ommons t oc k s , 1900–2015( fi gur esi nper c entpery ear )ar easf ol l ows .

Portfolio Treasury bills Treasury bonds Common stocks

Average Annual Average Premium (Extra Rate of Return return (%) versus Treasury bills) (%) 3.8 5.3 1.5 11. 7.6 4

Whati st hedi s c ountr at eont hes t oc k ? Whatpr i c es houl dshebewi l l i ngt opayf ort hes t ockt oday ? Basedont hehi st or i cal r i skpr emi um oft heS&P500( 7. 6%)andar i sk f r eer at eof2. 0%,onewoul dpr edi ct anexpect edr at eofr et ur nof9. 60%.I ft hest ockhast hesamesy st emat i cr i sk,i tal soshoul dpr ovi det hi s expect edr et ur n.Ther ef or e,t hest ockpr i ceequal st hepr esentval ueofcashflowsf ora1yearhor i zon.

P0 =

$2 + = $50 $47.45 1.096

As sumet hes ear et hes t oc kmar k etandTr eas ur ybi l lr et ur nsf ora5y earper i od: Yea r 201 1 201 2 201 3 201 4 201 5

Stock Market Return (%)

T-Bill Return (%)

0.98

0.03

16.06

0.05

33.06

0.07

12.71

0.05

0.67

0.21

a. Whatwast her i s kpr emi um oncommons t oc ki neac hy ear ?

Year 2011 2012 2013 2014 2015

Stock Market Return 0.0098 0.1606 0.3306 0.1271 0.0067

T-Bill Return Risk 0.0003 0.0005 0.0007 0.0005 0.0021 Average risk premium

Premium 0.0095 0.1601 0.3299 0.1266 0.0046

Deviation from Mean –0.1166 0.0340 0.2038 0.0005 1.1215

Squared Deviation 0.0136 0.0012 0.0415 0.0000 0.0148

0.1261 Variance Standard deviation

0.0142 0.1192

b.Whatwast heav er ager i s kpr emi um? Theaver ager i skpr emi um was12. 61%.

c.Whatwast hes t andar ddev i at i onoft her i s kpr emi um? Thevar i ance( t heaver agesquar eddevi at i onf r om t hemean)was1. 42%.Ther ef or e:St andar ddevi at i on= 1192,or11. 92%. 0. 01421/2 =0.

As t oc ki ss el l i ngt odayf or$40pers har e.Att heendoft hey ear ,i tpay sadi v i dend of$2pers har eandsel l sf or$44. a. Whati st het ot alr at eofr et ur nont hes t oc k ? Total percentage (Capital gain + Dividend) / Initial = return share price =[($44 – 40) + $2] / $40 =0.15, or 15%

b.Whatar et hedi v i dend per c ent agec api t algai n? Dividend Dividend / Initial sh = yield price =$2 / $40 =0.05, or 5%

y i el dand Capital gains Capital gain / Initial = yield share price =($44 – 40) / $40 =0.10, or 10%

c.Nows uppos et hey ear ends t ockpr i ceaf t ert hedi vi dendi spai di s$36.Whatar e t hedi v i dendy i el dandper cent agec api t algai ni nt hi sc ase ? Dividend Dividend / Initial shar = yield price =$2 / $40 =0.05, or 15%

Dividend Capital gain / Initial = yield share price =($36 – 40) / $40 =–0.10, or –10%

Youpur c has e100s har esofs t oc kf or$40as har e.Thes t oc kpay sa$2pers har e di v i dendaty ear end. a. Whati st her at eofr et ur nony ouri nv es t menti ft heendof y ears t ockpr i cei s( i ) $38;( i i )$40;( i i i )$42? Rate of return

=

Capital gain + Dividend Initial share price

=

($38 − 40) + $2 $40

= 0%

( i i ) Rate of return

=

($40 − 40) 0.05, or + $2 = 5% $40

( i i i ) Rate of return

($42 − 40) + 0.10, or $2 = = 10% $40

b.Whati sy ourr eal ( i nfl at i onadj us t ed)r at eofr et ur ni ft hei nfl at i onr at ei s4%? (i)

Rate of return

=

1 + Nominal rate of return 1 + Inflation rate

−1 =

1 + Nominal rate of return 1 + Inflation rate

−1 =

1 + Nominal rate of return 1 + Inflation rate

−1 =

1+0

= −1 = −0.0385, or −3.85%

1 + 0.04

(ii)

Rate of return

=

1.05

= −1 = 0.0096, or 0.96%

1.04

(iii)

Rate of return

=

1.10

= −1 = 0.0577, or 5.77%

1.04

The Costaguanan stock market provided a rate of return of 95%. The inflation rate in Costaguana during the year was 80%. In Ruritania, in contrast, the stock market return was only 12%, but the inflation rate was only 2%. Calculate the real rate of return for both the Costaguana and the Ruritania stock markets. Rate of

=1 + Nominal rate of −

return

return 1 + Inflation rate

1

1.9 Costaguana: Real 5 − 1 = 0.0833, or = 1.8 8.33% return 0

1.1 2 − 1 = 0.0980, or = 9.80% 1.0 2 TheRur i t ani apr ovi dest hehi gherr ealr at eofr et ur ndespi t et hel owernomi nal r at eofr et ur n.

Ruritania: Real return

As t oc kwi l lpr ov i dear at eofr et ur nofei t her−18% or26%. I fbot hpos s i bi l i t i esar eequal l yl i k el y ,c al cul at et hes t oc k ' sexpec t edr et ur nand s t andar ddevi at i on. Expect edr et ur n=( –18% +26)/2=4% 2 2 Var i ance=[ ( –0. 18–0. 04) +( 0. 26–0. 04) ]/2=0. 0484 St andar ddevi at i on=0. 04841/2 =0. 22,or22%

Thei nfl at i onr at ei nt heUni t edSt at eshasav er aged3% ay earsi nc e1900.Us et he dat ai nt het abl ebel owt oans wert hef ol l owi ngques t i on: Av er ager at esofr et ur nonTr eas ur ybi l l s ,gov er nmentbonds ,andc ommons t oc k s , 1900–2015.

Portfolio Treasury bills Treasury bonds Common stocks

Average Annual Rate of Return (%)

Average Premium (Extra return versus Treasury bills) (%)

3.8 5.3

1.5

11.4

7.6

Whatwast heav er ager eal r at eofr et ur nonTr eas ur ybi l l s ,Tr eas ur ybonds ,and c ommons t ock si nt hatper i od? 1 + Nominal rate of return 1 + Inflation rate

Real rate of return =

Asset Class Treasury bills Treasury bonds Common stocks

Nominal Rate of Inflation Return Rate

−1

Real Rate of Return

3.80%

3.00%

0.78%

5.30%

3.00%

2.23%

11.40%

3.00%

8.16%

Cons i dert hef ol l owi ngs c enar i oanal y s i s :

Scenario Recession Normal economy Boom

Rate of Return Probabili Stock Bond ty s s 0.20 −5% 14% 0.60

15

8

0.20

25

4

b.Cal c ul at et heex pec t edr at eofr et ur nands t andar ddev i at i onf oreac hi nv es t ment . rst ock=[ 0. 2×( −5%) ]+( 0. 6×15%)+( 0. 2×25%)=13. 0% rbonds=( 0. 2×14%)+( 0. 6×8%)+( 0. 2×4%)=8. 4% 2 2 2 Var i ance( bonds)=[ 0. 2×( 14−8. 4) ]+[ 0. 6×( 8−8. 4) ]+[ 0. 2×( 4−8. 4) ]=10. 24 1/2 St andar ddevi at i on=10. 24 =3. 2% St ockshavebot hhi gherexpect edr et ur nandhi ghervol at i l i t y .Mor er i sk aver sei nv est or swi l l choosebonds, whi l et hosewhoar el essr i sk aver semi ghtchoosest ocks .

Expected Rate of Return Standard Deviation Stocks Bonds

+/-1%

13.0 %

+/-1%

8.4 %

+/-1%

+/-1%

9.8 % 3.2 %

Thecommons t oc kofLeani ngTowerofPi t aI nc . ,ar es t aur antchai n,wi l lgener at e pay offst oi nv es t or snexty ear ,whi c hdependont hes t at eoft heec onomy ,as f ol l ows :

Boom Normal economy Recession

Divide Stock nd Price $ 8 $ 240 4

90

0

0

Thecompanygoesoutofbusi nes si far ec es si onhi t s .As sumef ors i mpl i c i t yt hat t het hr eepos s i bl es t at esoft heeconomyar eequal l yl i k el y .Thes t ocki ssel l i ng t odayf or$80. a-1. Cal c ul at et her at eofr et ur nt oLeani ngTowerofPi t as har ehol der sf oreac h ec onomi cs t at e. $8 + ($240 − 80) $80

Boom:

=2.1000, or 210.00%

$4 + ($90 − 80) $80

Normal:

Recession:

=0.1750, or 17.50%

$0 + ($0 − 80) =−1.0000, or −100% $80

a2.Cal c ul at et heex pect edr at eofr et ur nands t andar ddev i at i onofr et ur nt o Leani ngTowerofPi t as har ehol der s . r=

210 + 17.5 + (−100) 3

=0.4250, or 42.50%

Variance1 × (2.10 − 1 × (0.175 − 1 × (−1.00 − 2 0.425)2+ 0.425)2= = 3 0.425) + 3 3 1/2 St andar ddevi at i on=1. 6329 =1. 2779,or127. 79%

1.63 29

Thecommons t oc kofEs capi s tFi l mss el l sf or$25as har eandoffer st hef ol l owi ng pay offsnex ty ear :

Boom Normal

Divide nd $ 0 1

Stock Price $ 18 26

economy Recession

3

34

Thecommons t oc kofLeani ngTowerofPi t aI nc .i ssel l i ngf or$80andoffer st hes e pay offsnex ty ear :

Boom Normal economy Recession

Divide Stock Price nd $ 8 $ 240 4

90

0

0

a-1. Cal c ul at et her at eofr et ur nofEs capi s tFi l msf oreac heconomi cs t at e. Boom r et ur n=[ $0+( $18–25) ]/$25=–0. 28,or–28% Nor mal r et ur n=[ $1+( $26–25) }/$25=0. 08,or8% Recessi onr et ur n=[ $3+( $34–25) ]/$25=0. 48,or48%

a2.Cal c ul at et heex pect edr et ur nands t andar ddev i at i onofEs capi s ti fal lt hr ee ec onomi cs c enar i osar eequal l yl i k el yt oocc ur . Expected return = (–28% + 8 + 48) / 3 = 9.33% Variance = 1/3 × (–0.28 – 0.0933)2+ 1/3 × (0.08 – 0.0933)2+ 1/3 × (0.48 – 0.0933)2= 0.096356 Standard deviation = 0.0963561/2 = 0.3104, or 31.04%

b1.Cal c ul at et her at eofr et ur nofapor t f ol i ohal fi nv es t edi nEsc api s tandhal fi n Leani ngTowerofPi t af oreac hec onomi cs t at e. Boom r et ur n =( –28% +210)/2=91% Nor mal r et ur n =( 8% +17. 5)/2=12. 75% Recessi onr et ur n =( 48% +–100)/2=–26%

b2.Cal c ul at et heex pec t edr at eofr et ur nands t andar ddevi at i onofapor t f ol i ohal f i nv es t edi nEsc api s tandhal fi nLeani ngTowerofPi t a.Al l t hr eeeconomi cs cenar i os ar eequal l yl i k el yt oocc ur . Expected return = (91% + 12.75 + –26) / 3 = 25.92% Variance = 1/3 × (0.91 – 0.2592)2+ 1/3 × (0.1275 – 0.2592)2+ 1/3 × (–0.26 – 0.2592)2= 0.236818 2 St andar ddevi at i on=0. 2368181/ =0. 4866,or48. 66%

Cons i dert hef ol l owi ngs c enar i oanal y s i s :

Scenario Recession Normal economy Boom

Rate of Return Probabili Stock Bond ty s s 0.20 -5% 14% 0.60

15

8

0.20

25

4

As sumeapor t f ol i owi t hwei ght sof. 60i ns t oc k sand. 40i nbonds . a. Whati st her at eofr et ur nont hepor t f ol i oi neac hs cenar i o? Recession: (–0.05 × 0.6) + (0.14 × 0.4) = 0.026 or 2.6% Normal economy: (0.15 × 0.6) + (0.08 × 0.4) = 0.122 or 12.2% Boom: (0.25 × 0.6) + (0.04 × 0.4) = 0.166 or 16.6%

b.Whatar et heexpec t edr at eofr et ur nands t andar ddev i at i onoft hepor t f ol i o? Expected return = (0.2 × 0.026) + (0.6 × 0.122) + (0.2 × 0.166) = 0.1116 or 11.16% Variance = [0.2 × (0.026 – 0.1116)2] + [0.6 × (0.122 – 0.1116)2] + [0.2 × (0.166 – 0.1116)2] = 0.002125 Standard deviation = √0.002125 = 4.61%

a. Investors prefer diversified portfolios because they are less risky. b. If stocks were perfectly correlated, diversification would not reduce risk. Diversification with an indefinitely large number of securities completely c. eliminates risk. d. Diversification works only when returns are uncorrelated. The risk of a diversified portfolio depends on the specific risk of the individual e. stocks. The risk that you can’t avoid no matter how much you diversify is known as f. market risk. g. For a well-diversified portfolio, only market risk matters.

True True False False False True True

Her ear et her et ur nsont wos t oc k s . Digital Cheese

Executive Fruit

Januar +15 y Februa −3 ry March +5 April +7 May −4 June +3 July −2 August −8

+7 +1 +4 +13 +2 +5 −3 −2

a-1. Cal c ul at et hev ar i anc eands t andar ddev i at i onofeac hs t oc k . Digital Cheese Return 15.0 0 −3.0 0

Deviation From Mean 13.3 8 −4.6 3

March

5.00

3.38

April

7.00

5.38

−4.0 0 3.00 −2.0 0 −8.0 0

−5.6 3 1.38 −3.6 3 −9.6 3

January February

May June July August Ave Return Variance stnd.dev.

1.63

Squared Deviation From Mean 178. 29 21.3 9 11.3 9 28.8 9 31.6 4 1.89 13.3 4 92.6 4 379. 88

47.4 8 6.89

Executive Fruit Return

Deviation From Mean

January

7.00

3.63

February

1.00

−2.3 8

5.64

March

4.00

0.63

0.39

April

13.0 0

9.63

92.6 4

May

2.00

June

5.00 −3.0 0 −2.0 0

July August Ave Return Variance stnd.dev.

−1.3 8 1.63 6.38 −5.3 8

3.38 23.2 3 4.82

b.Nowc al c ul at et her et ur nsi neac hmont hofapor t f ol i ot hati nv es t sanequal amounteac hmont hi nt het wos t oc k s . Digital Cheese Return

Executive Fruit Return

Squared Deviation From Mean 13.1 4

50/50 Portfolio Return

Deviation From Mean

Squared Deviation From Mean

1.89 2.64 40.6 4 28.8 9 158. 76 185. 88

January February March April May June July August

15.00 −3.0 0 5.00 7.00 −4.0 0 3.00 −2.0 0 −8.0 0

7.00 1.00 4.00 13.00 2.00 5.00 −3.00 −2.00 Ave Return Variance stnd.dev.

11.00 −1.0 0 4.50 10.00 −1.0 0 4.00 −2.5 0 −5.0 0 2.50 30.06 5.48

8.50 −3.5 0 2.00 7.50 −3.5 0 1.50 −5.0 0 −7.5 0

72.25 12.25 4.00 56.25 12.25 2.25 25.00 56.25 240.5 0...