Homework IPM March 2016

8/19/2019 Homework IPM March 2016

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Chapter 3

26a. Given the $15,000 invested funds and assuming the gain or loss on the short

position is (–500 × ∆ P , !e "an "al"ulate the rate of return using the follo!ing

formula#ate of return % (–500 × ∆ P &15,000

'hus, the rate of return in ea"h of the three s"enarios is#

(i ate of return % (–500 × $4&$15,000 % –0.1333 % –13.33

(ii ate of return % (–500 × $0&$15,000 % 0

(iii ate of return % )–500 × (–$*+&$15,000 % 0.1333 % 13.33

'otal assets on margin are the sum of the initial margin and the pro"eeds fromthe sale of the sto"#

$20,000 - $15,000 % $35,000. ia/ilities are 500 P . margin "all !ill /eissued !hen#

$35,000－500P

500P % 0.25 or 25 !hen P % $56 or higher.

/. ith a $1 dividend, the short position must no! pa on the /orro!ed shares#

($1&share × 500 shares % $500. ate of return is no!#

)(–500 × ∆ P – 500+&15,000

(i ate of return %)(–500 × $* – $500+&$15,000 % –0.166 % –16.6

(ii ate of return % )(–500 × $0 – $500+&$15,000 % –0.0333 % –3.33

(iii ate of return % )(–500 × (–$* – $500+&$15,000 % 0.1000 % 10.00

'otal assets are $35,000, and lia/ilities are (500 P - 500. margin "all !ill /e issued !hen#

$35,000－500P－500

500P % 0.25 or 25 !hen P % $55.20 or higher.

Global Questions

a. Capital gains# *,000 (2* 4 100020 41000

nterest paments# 600 (10,000 4 6

7o total profits % 3,*00 ("apital gains – interest paments

ate of return on o!n "apital % 3,*00&10,000 %3*.

/. ogi" same as a/ove. ate of return on o!n "apital# *8

Feedback: Because of higher leverage, in spite of higher interest rate costs

". e must have "apital gains % interest paments % 600. 7o, appro4imatel 920.60


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Chapter *

13. Given that net asset value e:uals assets minus lia/ilities e4pressed on a pershare

/asis, !e first add up the value of the shares to get the maret value of the portfolio#

7to" ;alue 10,850,000C *,100,000? @,150,000

'otal $30,*00,000

Ano!ing that the a""rued management fee, !hi"h adBusts the value of the portfolio,

totals $20,000, and the num/er of the shares outstanding is 3,000,000, !e "an use the ; e:uation#

et asset value %Market value of assets － Market value of liabilities

S hares outstanding

%

$30,*00,000 $20,000

3,000,000

−

% $10.13

1*. 'he value of sto"s sold and repla"ed % $@1,500,000.

'urnover rate %Value of stocks sold or replaced

Value of assets

%

$@1,500,000

$30,*00,000

% 0.301 % 30.10

Chapter 5

12.a. llo"ating 80 of the "apital in the ris portfolio P , and 20 in risfree

asset, the "lient has an e4pe"ted return on the "omplete portfolio "al"ulated /adding up the e4pe"ted return of the ris proportion ( y and the e4pe"tedreturn of the proportion (1 y of the risfree investment#

D(r C % y × D(r E - (1 – y × r f

% (0.8 × 0.12 - (0.2 × 0.0* % 0.10*0 or 10.*0 per ear

'he standard deviation of the portfolio e:uals the standard deviation of the


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ris fund times the fra"tion of the "omplete portfolio invested in the risfund#

σC % ×σE % 0.8 × 0.28 % 0.22*0 or 22.*0 per ear

/. 'he investment proportions of the "lientFs overall portfolio "an /e "al"ulated

/ the proportion of ris portfolio in the "omplete portfolio times the proportion allo"ated in ea"h sto".

Security

nvestmentEroportions

'>ills 20.0

7to" 0.8 × 20 % 16.0

7to" > 0.8 × 30 % 2*.0

7to" C 0.8 × 50 % *0.0

". e "al"ulate the re!ardtovaria/ilit ratio (7harpe ratio using D:uation 5.1*.

=or the ris portfolio#

7 %Portfolio Risk Premium

S tandard eviation of Portfolio !"cess Return

% !#rP － r f

P %

0%&' － 0%0(

0%') % 0.285

=or the "lientFs overall portfolio#

7 %

!#r* － r f

* % 0%&0(0 － 0%0(

0%''(0 % 0.285

d.


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E(r)

7

27

14

17P

CAL(slope=.3704)%

%18.9

client

13.

d. D(r C % y × D(r E - (1 – y × r f

% y × 0.12 - (1 – y × 0.0* % 0.11 or 11 per ear

7olving for y, !e get y %0%&&

－ 0%0(

0%&0 % 0.85

'herefore, in order to a"hieve an e4pe"ted rate of return of 11, the "lientmust invest 8.5 of total funds in the ris portfolio and 12.5 in '/ills.

e. 'he investment proportions of the "lientFs overall portfolio "an /e "al"ulated / the proportion of ris asset in the !hole portfolio times the proportionallo"ated in ea"h sto".

SecuritynvestmentEroportions

'>ills 12.5

7to" 0.85 × 20 % 1.50

7to" > 0.85 × 30 % 26.25

7to" C 0.85 × 50 % *3.5

f. 'he standard deviation of the "omplete portfolio is the standard deviation ofthe ris portfolio times the fra"tion of the portfolio invested in the ris asset#

σC % y ×σE % 0.85 × 0.28 % 0.2*50 or 2*.5 per ear


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Chapter 6

C= 2ns!er#=und ? represents the single /est addition to "omplement 7tephensons "urrent

portfolio, given his sele"tion "riteria. =irst, =und ?Fs e4pe"ted return (1*.0 per"enthas the potential to in"rease the portfolioFs return some!hat. 7e"ond, =und ?Fsrelativel lo! "orrelation !ith his "urrent portfolio (- .65 indi"ates that =und ? !ill

provide greater diversifi"ation /enefits than an of the other alternatives e4"ept =und>. 'he result of adding =und ? should /e a portfolio !ith appro4imatel the samee4pe"ted return and some!hat lo!er volatilit "ompared to the original portfolio.

'he other three funds have short"omings in terms of either e4pe"ted returnenhan"ement or volatilit redu"tion through diversifi"ation /enefits. =und offers the

potential for in"reasing the portfolioFs return, /ut is too highl "orrelated to providesu/stantial volatilit redu"tion /enefits through diversifi"ation. =und > provides

su/stantial volatilit redu"tion through diversifi"ation /enefits, /ut is e4pe"ted togenerate a return !ell /elo! the "urrent portfolioFs return. =und C has the greatest

potential to in"rease the portfolioFs return, /ut is too highl "orrelated to providesu/stantial volatilit redu"tion /enefits through diversifi"ation.

C= 3 ns!er#

a. 7u/s"ript HE refers to the original portfolio, >C to the ne! sto",and E to the ne! portfolio.

i. D(r E % !HE D(r HE - !>C D(r >C % ( .@ × .6 - ( .1 × 1.25 % .280

ii. CovHE , >C % Corr HE , >C × σHE × σ>C % .*0 × 2.3 × 2.@5 % 2.@66

iii. σ E % )!HE 2 σHE 2 - !>C 2 σ>C 2 - 2 !HE !>C (CovHE , >C+1&2

% )( .@2 × 2.32 - ( .12 × 2.@52 - (2 × .@ × .1 × 2.@66+1&2

% 2.262

/. 7u/s"ript HE refers to the original portfolio, G7 to government se"urities, and E to the ne! portfolio.

i. D(r E % !HE D(r HE - !G7 D(r G7 % ( .@ × .6 - ( .1 × .*2 % .6*50

ii. CovHE , G7 % Corr HE , G7 × σHE × σG7 % 0 × 2.3 × 0 % 0

iii. σ E % )!HE 2 σHE 2 - !G7 2 σG7 2 - 2 !HE !G7 (CovHE , G7+1&2

% )( .@2 × 2.32 - ( .12 × 0 - (2 × .@ × .1 × 0+1&2

% 2.1330


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". dding the risfree government se"urities !ould result in a lo!er /eta forthe ne! portfolio. 'he ne! portfolio /eta !ill /e a !eighted average of theindividual se"urit /etas in the portfolioI the presen"e of the risfreese"urities !ould lo!er that !eighted average.

d. 'he "omment is not "orre"t. lthough the respe"tive standard deviations ande4pe"ted returns for the t!o se"urities under "onsideration are identi"al, the"orrelation "oeffi"ients /et!een ea"h se"urit and the original portfolio areunno!n, maing it impossi/le to dra! the "on"lusion stated. =or instan"e,if the "orrelation /et!een the original portfolio and JKL sto" is smallerthan that /et!een the original portfolio and >C sto", repla"ing >Csto"s !ith JKL sto"s !ould result in a lo!er standard deviation for the

portfolio as a !hole. n su"h a "ase, JKL so"s !ould /e the preferredinvestment, assuming all other fa"tors are e:ual.

e. Gra"e "learl e4pressed the sentiment that the ris of loss !as more

important to her than the opportunit for return. Msing varian"e (or standarddeviation as a measure of ris in her "ase has a serious limitation /e"ausestandard deviation does not distinguish /et!een positive and negative pri"emovements.

Chapter

25.a. 7in"e the maret portfolio, / definition, has a /eta of 1.0, its e4pe"ted rate

of return is 1*.

/. N % 0 means the sto" has no sstemati" ris.


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a. Using the SML, the expected rate of return for any portfolio P is:

D(r E % r f - β)D(r O – r f +

Substituting for portfolios A and B:

D(r % 6 - 0.8 × (12 – 6 % 10.8 Q 11

D(r > % 6 - 1.5 × (12 – 6 % 15.0 R 1*

Hence, Portfolio A is desirable and Portfolio B is not.

b. The slope of the CAL supported by a portfolio P is given by:

7 %!#rP － r f

P

Computing this slope for each of the three alternative portfolios, we have:

7 (7SE 500 % (12 − 6&20 % 6&20

7 ( % (11 − 6%)/10% = 5&10 R 7(7SE 500

7 (> % (1* − 6%)/31% = 8&31 Q 7(7SE 500


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ii. =or an investor !ho !ants to hold this sto" as a singlesto" portfolio, Aa should re"ommend 7to" K, /e"ause it has higherfore"asted return and lo!er standard deviation than 7to" J. 7to" KFs7harpe ratio is#

(0.1 – 0.05&0.25 % 0.*8

7to" JFs 7harpe ratio is onl#

(0.1* – 0.05&0.36 % 0.25

'he maret inde4 has an even more attra"tive 7harpe ratio#

(0.1* – 0.05&0.15 % 0.60


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/. 'he reason this is per"eived as an overrea"tion is /e"ause there are t!o eventso""urring. =irst, re"essions lead to redu"ed profits, impa"ting the numerator in afundamental analsis. 'his redu"ed "ash flo! represses sto" pri"es.7imultaneousl, the re"ession "auses ris premiums to rise, thus in"reasing thedenominator in the fundamental analsis "al"ulation. n in"rease in the

denominator further redu"es the pri"e. 'he result is the appearan"e of anoverrea"tion.

C= 11a. 7ome empiri"al eviden"e that supports the DO< is#

(i professional mone managers do not tpi"all earn higher returns than"ompara/le ris, passive inde4 strategiesI

(ii event studies tpi"all sho! that sto"s respond immediatel to the pu/li"release of relevant ne!sI

(iii most tests of te"hni"al analsis find that it is diffi"ult to identif pri"e

trends that "an /e e4ploited to earn superior risadBusted investment returns.

/. 7ome eviden"e that is diffi"ult to re"on"ile !ith the DO< "on"erns simple portfolio strategies that apparentl !ould have provided high risadBusted returnsin the past. 7ome e4amples of portfolios !ith attra"tive histori"al returns#

(i lo! E&D sto"sI(ii high /ootomaret ratio sto"sI(iii small firms in TanuarI(ivfirms !ith ver poor sto" pri"e performan"e in the last fe! months.

Hther eviden"e "on"erns postearningsannoun"ement sto" pri"e drift and

intermediateterm pri"e momentum.

". n investor might "hoose not to inde4 even if marets are effi"ient /e"ause he orshe ma !ant to tailor a portfolio to spe"ifi" ta4 "onsiderations or to spe"ifi" rismanagement issues, for e4ample, the need to hedge (or at least not add toe4posure to a parti"ular sour"e of ris (e.g., industr e4posure.

Chapter @

C= 1

ns!er#

i. Oental a""ounting is /est illustrated / 7tatement U3. 7ampsonFs re:uirementthat his in"ome needs /e met via interest in"ome and sto" dividends is ane4ample of mental a""ounting. Oental a""ounting holds that investorssegregate funds into mental a""ounts (e.g., dividends and "apital gains,maintain a set of separate mental a""ounts, and do not "om/ine out"omesI aloss in one a""ount is treated separatel from a loss in another a""ount.Oental a""ounting leads to an investor preferen"e for dividends over "apitalgains and to an ina/ilit or failure to "onsider total return.


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ii. Hver"onfiden"e (illusion of "ontrol is /est illustrated / 7tatement U6.7ampsonFs desire to sele"t investments that are in"onsistent !ith his overallstrateg indi"ates over"onfiden"e. Hver"onfident individuals often e4hi/itrisseeing /ehavior. Eeople are also more "onfident in the validit of their"on"lusions than is Bustified / their su""ess rate. Causes of over"onfiden"e

in"lude the illusion of "ontrol, selfenhan"ement tenden"ies, insensitivit to predi"tive a""ura", and mis"on"eptions of "han"e pro"esses.

iii.eferen"e dependen"e is /est illustrated / 7tatement U5. 7ampsonFs desire toretain poor performing investments and to tae :ui" profits on su""essfulinvestments suggests referen"e dependen"e. eferen"e dependen"e holds thatinvestment de"isions are "riti"all dependent on the de"isionmaerFsreferen"e point. n this "ase, the referen"e point is the original pur"hase pri"e.lternatives are evaluated not in terms of final out"omes /ut rather in terms ofgains and losses relative to this referen"e point. 'hus, preferen"es aresus"epti/le to manipulation simpl / "hanging the referen"e point.

C= 5 ns!er#

i. Overconfidence (Biased Expectations and Illusion of ontrol!# Eier"e is /asing herinvestment strateg for supporting her parents on her "onfiden"e in the e"onomi"fore"asts. 'his is a "ognitive error refle"ting over"onfiden"e in the form of /oth

/iased e4pe"tations and an illusion of "ontrol. Eier"e is liel more "onfident in thevalidit of those fore"asts than is Bustified / the a""ura" of prior fore"asts.nalstsF "onsensus fore"asts have proven routinel and !idel ina""urate. Eier"ealso appears to /e overl "onfident that the re"ent performan"e of the Eogo slande"onom is a good indi"ator of future performan"e. >ehavioral investors often

"on"lude that a short tra" re"ord is ample eviden"e to suggest future performan"e.

7tandard finan"e investors understand that individuals tpi"all have greater"onfiden"e in the validit of their "on"lusions than is Bustified / their su""essrate. 'he "ali/ration paradigm, !hi"h "ompares "onfiden"e to predi"tive a/ilit,suggests that there is signifi"antl lo!er pro/a/ilit of su""ess than the "onfiden"elevels reported / individuals. n addition, standard finan"e investors no! thatre"ent performan"e provides little information a/out future performan"e and arenot de"eived / this Vla! of small num/ers.W

ii. "oss #version ($isk %eeking!# Eier"e is e4hi/iting risk aversion in de"iding to sell the

Core >ond =und despite its gains and favora/le prospe"ts. 7he prefers a "ertain gainover a possi/l larger gain "oupled !ith a smaller "han"e of a loss. Eier"e ise4hi/iting loss aversion (ris seeing / holding the ond =und despiteits un"ertain prospe"ts. 7he prefers the modest possi/ilit of re"over "oupled !iththe "han"e of a larger loss over a "ertain loss. Eeople tend to e4hi/it ris seeing,rather than ris aversion, /ehavior !hen the pro/a/ilit of loss is large. 'here is"onsidera/le eviden"e indi"ating that ris aversion holds for gains and ris seeing

/ehavior holds for losses, and that attitudes to!ard ris var depending on parti"ulargoals and "ir"umstan"es.

7tandard finan"e investors are "onsistentl ris averse, and sstemati"all prefer a"ertain out"ome over a gam/le !ith the same e4pe"ted value. 7u"h investors alsotae a smmetri"al vie! of gains and losses of the same magnitude, and their


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sensitivit (aversion to "hanges in value is not a fun"tion of a spe"ified valuereferen"e point.

iii. $eference &ependence: Eier"eFs in"lination to sell her 7mall Compan =undon"e it returns to her original "ost is an e4ample of reference dependence.

Homework IPM March 2016

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