Test2SolutionSketches Fall2011 Updated

7/25/2019 Test2SolutionSketches Fall2011 Updated

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Solution sketchesTest 2, Fall 2011


2/27

Level of diculty On multiple choice questions

!asy" denotes that a#out $0%100&

of students 'et this question co((ect )edium" denotes that a#out *0%$0&

of students 'et this question co((ect

+a(d" denotes that a#out 0%*0& ofstudents 'et this question co((ect


3/27

Level of diculty On -(o#lems

. take a 10& sample !asy" denotes that the ave(a'e sco(e

is $0%100& of the points possi#le )edium" denotes that the ave(a'e

sco(e is *0%$0& of the points possi#le +a(d" denotes that that ave(a'e

sco(e is 0%*0& of the points possi#le


4/27

/hat is the #eta of a

stock isk%f(ee (ate is *& stock has an e3pected (etu(n of 1& !3pected (etu(n on the ma(ket is 11& /hat is #eta

1& 4 *& 5 6 711& 8 *&9

6 4 1:* !asy question


5/27

/hat is the standa(d

deviation Sample of a stock;s

(etu(ns 1&, ith a sample9 ?a(iance is 0:002====

Standa(d deviation is thesqua(e (oot of theva(iance 0:0@==

The closest ans>e( is


6/27

Aeomet(ic ave(a'e /hat is the 'eomet(ic ave(a'e of

annual (etu(ns of


7/27

Ba(ina Bo(ona, (eal

payment of C .nEation >ill #e $& pe( yea( fo( the

(st yea(s .nEation >ill #e 12& pe( yea( afte(

the (st yea(s Gominal payment

C


8/27

-e(petuity pe(petuity makes payments of

C1,000 eve(y t>o yea(s, startingone

yearfrom today: .f the eHectiveannual inte(est (ate is @&, >hat is thep(esent value of this pe(petuity

/hat is the eHective (ate eve(y 2yea(s 1:0@28 1 4 1$:$1&


9/27

-e(petuity /hat is a pe(petuity >o(th if C1,000

is paid eve(y t>o yea(s, starting

two years from today C1,000I:1$$1 4 Co /e need to inc(ease the value of each

payment


10/27

-e(petuity /e need to nd out ho> much this

pe(petuity is >o(th if each

payment is made one yea( soone( C


11/27

. p(o#lem .f . invest C1,000 today in a p(oKect and

(eceive C1,$00 ve yea(s f(om today in(etu(n, my annual inte(nal (ate of (etu(nis :

Fo( >hat annual discount (ate >ill the-? of the costs and #enets #e equal

C1,000 71 5 .9


12/27

Mou loan a f(iend Cill #e made 10 yea(s f(om today,ho> much >ill this payment have to#e to completely pay #ack the loan


13/27

Mou loan a f(iend C


14/27

-ay#ack pe(iod method .n you( (st Ko#, suppose that you #oss tells you to

use the pay#ack pe(iod method 7undiscounted9,>ith the cutoH date = yea(s, = months f(om no>:

.n othe( >o(ds, the pay#ack pe(iod is = yea(s, =months: The eHective annual discount (ate is *&:/hich of the follo>in' oHe(s should you accept ifyou use this method C1,00 eve(y t>o yea(s fo(eve(, >ith the (st payment

made t>o yea(s f(om today C0,000 eve(y yea( fo(eve(, >ith the (st payment made

fou( yea(s f(om today Cith the (st payment made today Cith the (st payment made one

yea( f(om no> one%time payment of C1,000,000 ve yea(s f(om today


15/27

-ay#ack pe(iod method .f >e only look at the (st = yea(s, =

months, ho> much is each oHe( >o(th

Go discountin' used in the calculations +a(d p(o#lem

Got meant to #e a ha(d p(o#lem

)ake su(e that you unde(stand thete(minolo'y used in the #ook and inlectu(es


16/27

-ay#ack pe(iod methodN

+o> much afte( = yea(s C


17/27

Summa(y of )B questions < easy questions 1 medium question 1 ha(d question 1 ve(y ha(d question


18/27

-(o#lemN Packie Packson Packie Packson has >on the nal (ound of a ne> ctional

'ame sho>, -ay /hat Mou Ban Ho(d:" Packie 'ets to take

out a =0%yea(, 3ed%(ate mo(t'a'e fo( Cith the

mo(t'a'e company so that an additional payment is made

*0 months 7o( < yea(s9 afte( Packie takes out the mo(t'a'e:+o> much >ill this payment #e if >e assume that Packie

makes all =*0 monthly payments and that the #alance of

the loan >ill #e Qe(o afte( =0 yea(s ound you( ans>e( to

the nea(est dolla(:


19/27

-(o#lemN Packie Packson )onthly r4 0:00< 4 0:


20/27

-(o#lemN Packie Packson -? of additional payment

C


21/27

-(o#lemN -(ince -itche( -(ince -itche( is inte(ested in #uyin' a stock: .n

o(de( to dete(mine if this stock is >o(th #uyin',he assumes an annual eHective discount (ate

of 10&: fte( a tho(ou'h analysis of the stock,he assumes that the company >ill pay its ne3tdividend of C1 pe( sha(e one yea( f(om today:Fo( t>o yea(s afte( the ne3t dividend payment,the dividend >ill inc(ease #y 1hat is thep(esent value of each sha(e of this stockound you( ans>e( to the nea(est cent:


22/27

-(o#lemN -(ince -itche( -? of payment in yea( 1

1 I 1:1 4 C0:@0@

-? of payment in yea( 2 1:1


23/27

-(o#lemN @2 days of

inte(estToday is Govem#e( 1J, 2011: .f you

deposit C10,000 in the #ank today

and the stated annual inte(est (ateis J:=&, ho> much inte(est >ill youea(n afte( @2 days 7ssume =*e( to the nea(estcent:


24/27

-(o#lemN @2 days of

inte(est Vaily inte(est (ate

J:=& I =*< 4 0:0002 4 0:02& Got 0:2& 7common mistake9

Total #alance afte( @2 days C10,00071:00029@24 C10,1$


25/27

-(o#lemN Stock Stock has an e3pected annual (etu(n of ell la#eled, includin' indicatin'

nume(ical values on each a3is fo( each of the follo>in' pointsN -ut an " #ythe point on the '(aph fo( Stock and a U" #y the point on the '(aph fo(Stock U: 7+intN Mou may >ant to see the '(aph on the cove( sheet to see that itis >ell la#eled:9

7#9 7= points9 V(a> a line o( cu(ve to denote possi#le e3pected (etu(n%standa(ddeviation com#inations of all of the possi#le po(tfolios >ith positive amountsof #oth Stock and Stock U: ssume that the co((elation #et>een Stock and

Stock U is 80: you d(a> this: +o>eve(, . am onlylookin' fo( the shape of the line o( cu(ve, so it does not need to #e e3act:9

7c9 71 point9 La#el the minimum va(iance point )?: 7Gote that you do notnecessa(ily need to calculate the e3act point of minimum va(iance:9

7d9 7= points9 Blea(ly sho> o( e3plain >hat the ecient set is: 7GoteN Theecient set is also (efe((ed to as the ecient f(ontie(:9


26/27

-(o#lemN Stock

std: dev: of

po(tfolio;s(etu(n

e3pected(etu(n onpo(tfolio

1


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Summa(y of -(o#lems

= points of !asy p(o#lems 21 points of !asy%)edium

p(o#lems points of )edium p(o#lems = points of +a(d p(o#lems

Test2SolutionSketches Fall2011 Updated

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