bkm 10e chap005 sm final

8/12/2019 BKM 10e Chap005 SM Final

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CHAPTER 5: INTRODUCTION TO RISK, RETURN, ANDTHE HISTORICAL RECORD

CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND

THE HISTORICAL RECORD

PROBLEM SETS

1. The Fisher equati! "re#i$ts that the !%i!a& rate 'i&& equa& the equi&i(riu%rea& rate "&us the e)"e$te# i!*&ati! rate. He!$e, i* the i!*&ati! rate i!$reases*r% + t 5 'hi&e there is ! $ha!-e i! the rea& rate, the! the !%i!a& rate'i&& i!$rease ( /. O! the ther ha!#, it is "ssi(&e that a! i!$rease i! thee)"e$te# i!*&ati! rate 'u (e a$$%"a!ie# ( a $ha!-e i! the rea& rate *i!terest. 0hi&e it is $!$eia(&e that the !%i!a& i!terest rate $u re%ai!$!sta!t as the i!*&ati! rate i!$rease#, i%"&i!- that the rea& rate #e$rease# asi!*&ati! i!$rease#, this is !t a &i2e& s$e!ari.

/. I* 'e assu%e that the #istri(uti! * retur!s re%ai!s reas!a(& sta(&e er thee!tire histr, the! a &!-er sa%"&e "eri# 3i.e., a &ar-er sa%"&e4 i!$reases the"re$isi! * the esti%ate * the e)"e$te# rate * retur! this is a $!seque!$e* the *a$t that the sta!#ar# errr #e$reases as the sa%"&e si6e i!$reases.H'eer, i* 'e assu%e that the %ea! * the #istri(uti! * retur!s is $ha!-i!-er ti%e (ut 'e are !t i! a "siti! t #eter%i!e the !ature * this $ha!-e,the! the e)"e$te# retur! %ust (e esti%ate# *r% a %re re$e!t "art * thehistri$a& "eri#. I! this s$e!ari, 'e %ust #eter%i!e h' *ar (a$2,histri$a&&, t - i! se&e$ti!- the re&ea!t sa%"&e. Here, it is &i2e& t (e#isa#a!ta-eus t use the e!tire #ata set (a$2 t 1778.

+. The true state%e!ts are 3$4 a!# 3e4. The e)"&a!ati!s *&&'.

State%e!t 3$4: Let 9 the a!!ua& sta!#ar# #eiati! * the ris2

i!est%e!ts a!# 1 9 the sta!#ar# #eiati! * the *irst i!est%e!t a&ter!atie

er the t'ear "eri#. The!:

= /1

There*re, the a!!ua&i6e# sta!#ar# #eiati! *r the *irst i!est%e!ta&ter!atie is equa& t:


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State%e!t 3e4: The *irst i!est%e!t a&ter!atie is %re attra$tie t i!estrs'ith &'er #e-rees * ris2 aersi!. The *irst a&ter!atie 3e!tai&i!- a seque!$e* t' i#e!ti$a&& #istri(ute# a!# u!$rre&ate# ris2 i!est%e!ts4 is ris2iertha! the se$!# a&ter!atie 3the ris2 i!est%e!t *&&'e# ( a ris2*reei!est%e!t4. There*re, the *irst a&ter!atie is %re attra$tie t i!estrs 'ith&'er #e-rees * ris2 aersi!. Nti$e, h'eer, that i* u %ista2e!&

(e&iee# that ti%e #iersi*i$ati! $a! re#u$e the tta& ris2 * a seque!$e *ris2 i!est%e!ts, u 'u hae (ee! te%"te# t $!$&u#e that the *irsta&ter!atie is &ess ris2 a!# there*re %re attra$tie t %re ris2aersei!estrs. This is $&ear& !t the $ase the t'ear sta!#ar# #eiati! * the*irst a&ter!atie is -reater tha! the t'ear sta!#ar# #eiati! * the se$!#a&ter!atie.

;. Fr the %!e %ar2et *u!#, ur hi!-"eri# retur! *r the !e)t ear#e"e!#s ! the &ee& * +8#a i!terest rates ea$h %!th 'he! the *u!# r&&ser %aturi!- se$urities. The !eear sai!-s #e"sit **ers a "er ear, 'hi$h is 158(asis "i!ts hi-her tha! the rate ! the !eear sai!-s #e"sit h'eer, u$u ear! a !eear HPR %u$h &ess tha! ,the! the "ri$e * the (!# 'i&& *a&&, a!# the resu&ti!- $a"ita& &ss 'i&& 'i"e uts%e r a&& * the > retur! u 'u hae ear!e# i* (!# ies ha#re%ai!e# u!$ha!-e# er the $urse * the ear.

5. a. I* (usi!esses re#u$e their $a"ita& s"e!#i!-, the! the are &i2e& t#e$rease their #e%a!# *r *u!#s. This 'i&& shi*t the #e%a!# $ure i!Fi-ure 5.1 t the &e*t a!# re#u$e the equi&i(riu% rea& rate * i!terest.

(. I!$rease# huseh sai!- 'i&& shi*t the su""& * *u!#s $ure t theri-ht a!# $ause rea& i!terest rates t *a&&.

$. O"e! %ar2et "ur$hases * U.S. Treasur se$urities ( the Fe#era&Resere ?ar# are equia&e!t t a! i!$rease i! the su""& * *u!#s 3ashi*t * the su""& $ure t the ri-ht4. The FED (us treasuries 'ith

$ash *r% its '! a$$u!t r it issues $erti*i$ates 'hi$h tra#e &i2e$ash. As a resu&t, there is a! i!$rease i! the %!e su""&, a!# theequi&i(riu% rea& rate * i!terest 'i&& *a&&.

5/


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=. a. The @I!*&ati!P&us CD is the sa*er i!est%e!t (e$ause it -uara!tees the"ur$hasi!- "'er * the i!est%e!t. Usi!- the a""r)i%ati! that the rea&rate equa&s the !%i!a& rate %i!us the i!*&ati! rate, the CD "ri#es a rea&rate * 1.5 re-ar#&ess * the i!*&ati! rate.

(. The e)"e$te# retur! #e"e!#s ! the e)"e$te# rate * i!*&ati! er the !e)t

ear. I* the e)"e$te# rate * i!*&ati! is &ess tha! +.5 the! the $!e!ti!a&CD **ers a hi-her rea& retur! tha! the i!*&ati!"&us CD i* the e)"e$te# rate* i!*&ati! is -reater tha! +.5, the! the ""site is true.

$. I* u e)"e$t the rate * i!*&ati! t (e + er the !e)t ear, the! the$!e!ti!a& CD **ers u a! e)"e$te# rea& rate * retur! * /, 'hi$h is8.5 hi-her tha! the rea& rate ! the i!*&ati!"rte$te# CD. ?ut u!&ess u2!' that i!*&ati! 'i&& (e + 'ith $ertai!t, the $!e!ti!a& CD is a&sris2ier. The questi! * 'hi$h is the (etter i!est%e!t the! #e"e!#s ! urattitu#e t'ar#s ris2 ersus retur!. Bu %i-ht $hse t #iersi* a!# i!est"art * ur *u!#s i! ea$h.

#. N. 0e $a!!t assu%e that the e!tire #i**ere!$e (et'ee! the ris2*ree!%i!a& rate 3! $!e!ti!a& CDs4 * 5 a!# the rea& ris2*ree rate 3!i!*&ati!"rte$te# CDs4 * 1.5 is the e)"e$te# rate * i!*&ati!. Part * the#i**ere!$e is "r(a(& a ris2 "re%iu% ass$iate# 'ith the u!$ertai!tsurru!#i!- the rea& rate * retur! ! the $!e!ti!a& CDs. This i%"&ies thatthe e)"e$te# rate * i!*&ati! is &ess tha! +.5 "er ear.


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>. E3q4 9 38 8./54 31 8./54 3/ 8.584 9 1./5

q9 8./5 38 G 1./54/ 8./5 31 G 1./54/ 8.58 3/ G 1./54/1/9 8.7/>/

18. 3a4 0ith "r(a(i&it 8.>5;;, the a&ue * a !r%a&& #istri(ute#aria(&e 'i&& *a&& 'ithi! / sta!#ar# #eiati!s * the %ea! that is,(et'ee! G;8 a!# 78. Si%"& a## a!# su(tra$t / sta!#ar##eiati!s t a!# *r% the %ea!.

11. Fr% Ta(&e 5.;, the aera-e ris2 "re%iu% *r the "eri# /=>/81/ 'as:1/.+; "er ear.

A##i!- 1/.+; t the + ris2*ree i!terest rate, the e)"e$te# a!!ua& HPR *rthe ?i-Ma&ue "rt*&i is: +.88 1/.+; 9 15.+;.

1/.

(01/1928-06/1970)Small Big

Low 2 High Low 2 High

Average 1.03% 1.21% 1.6%

0.78% 0.88% 1.18%

S! 8.""% 8.7%10.3"

%".89% 6.91% 9.11%

S#ew1.670

1.667

32.306

0.006

71.62"

11.63

8

$r&o'i'

13.1"0"

13."28

17.2137

6.2"6

16.230"

13.6729

(07/1970-12/2012)

Small Big

Low 2 High Low 2 High

Average 0.91% 1.33% 1.6%

0.93% 1.02% 1.13%

S! 7.00% ".9% ".66%.81% ."0% .78%

S#ew

-0.327

8

-0."13

"

-0.32

3

-0.313

6

-0.3"0

8

-0.9"

$r&o'i'

1.7962

3.1917

3.8320

1.8"16

2.07"6

2.8629

No. The distributions from (01/192806/1970) and (07/197012/2012) periods

have distinct characteristics due to systematic shocks to the economy and

subsequent government intervention. While the returns from the two periods do not

differ greatly, their respective distributions tell a different story. The standard5;


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deviation for all six portfolios is larger in the first period. Skew is also positive, but

negative in the second, showing a greater likelihood of higher-than-normal returns

in the right tail. Kurtosis is also markedly larger in the first period.

1+. a 77.5,8577.8+./5 =.


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E$!% Pr(a(i&it Dii#e!# HPR E)$e&&e!t 8./5 J 1+1.88 1, r +.;>. The $$ ris2 "re%iu% 'i&& equa& .8/ .8+;> 9 .8;;+, r;.;++.

$. The a""r"riate *r%u&a is ,

'here . Usi!- s&er r -a& see2, setti!- the

tar-et $e&& t the 2!'! e**e$tie $$ rate ( $ha!-i!- the u!2!'! aria!$e

3$$4 rate, the equia&e!t sta!#ar# #eiati! 3$$4 is 17.8+ 3e)$e& %a ie

s&i-ht& #i**ere!t s&uti!s4.

#. The e)"e$te# a&ue * the e)$ess retur! 'i&& -r' ( 1/8 %!ths 31/%!ths er a 18ear hri6!4. There*re the e)$ess retur! 'i&& (e 1/8 ;.;++ 9 5+1.>. The e)"e$te# SD -r's ( the square rt * ti%e

resu&ti!- i! 17.8+ 9 1>


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CFA PROBLEMS

1. The e)"e$te# #&&ar retur! ! the i!est%e!t i! equities is J17,888 38.= J58,888 8.;

J+8,8884 $%"are# t the J5,888 e)"e$te# retur! *r T(i&&s. There*re, the e)"e$te#ris2 "re%iu% is J1+,888.

/. E3r4 9 8./ 3/54 8.+ 18 8.5 /; 918

+. E3rX4 9 8./ 3/84 8.5 17 8.+ 58 9/8

E3rY4 9 8./ 3154 8.5 /8 8.+ 18 918

;. X/9 8./ 3G /8 G /84/ 8.5 317 G /84/ 8.+ 358 G /84/ 9 5>/

X9 /;.++

Y/9 8./ 3G 15 G 184/ 8.5 3/8 G 184/ 8.+ 318 G 184/ 9 1 /84 38.1 184 91>J1,>88 i! retur!s

=. The "r(a(i&it that the e$!% 'i&& (e !eutra& is 8.58, r 58. ie! a

!eutra& e$!%, the st$2 'i&& e)"erie!$e "r "er*r%a!$e +8 * theti%e. The "r(a(i&it * (th "r st$2 "er*r%a!$e a!# a !eutra& e$!%is there*re:

8.+8 8.58 9 8.15 9 15

bkm 10e chap005 sm final

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