!

!

"

# "$

% # #&%##' ! "

( )

#

$ %

&

$

' (

) ( " "

' (

*

+ ,

- . " ! / ,

& ,

$ " $ ( (

"$ *

!

" " !

0 $ "

1 2 "" " ( + '

%

3 ,4,

)"

0,4564 ,

1,762""",

Amos Lim

Amos LimReinvestment risk: Risk that future coupons from a bond will not be reinvested at the prevailing interest rate when the bond was initially purchased.

+,% -./

$./,42"

/-!4""/-!4"/-!4"/-4$#.!//7"

Amos LimTIPS: Treasury Inflation Protected Security. It is a treasury security that is indexed to inflation to protect investors from the negative effects of inflation.

Amos LimB, because (1) 10y T-bond is more liquid, more reflective of stocks; and (2) Expected holding period of a stock for investment is on average 8-10y (matching discount rate to expected holding period).

Amos Lim

Amos LimDone

0,% "

Amos LimFocus on 10y rate, as more appropriate for computing risk-free rate.For the same reason, we use Germany, as it has the lowest risk.

Amos LimDone

1,% 2

4$08!"

"9,:;

..,(

)"2",4""2"",

)

..,"07++

8 (

$

%"#"$ *33

& -

'

F2%-

Amos LimThese methods are historical approaches.

+3#9%

!"

#$%!!%&%'

()

*&$%+%

*),&)-)#)-.)/-(

Amos LimUS T-Bond i/r: 4.29%Brazil USD Sovereign Bond i/r: 10.30%Therefore default spread = 6.01%

Amos Lim

Amos Lim

03 "$

4",2,

0,)- 01#! /.("

!&%2

3 *4)-#)-5/)-(4)-

!4)-. )-4)/-

#3&% &)-&167&/)-(

Amos LimHowever, what should be the time frame under consideration for the risk premium?Daily Return: Too volatileAnnual Return: May not have enough observationsIn practice, we use weekly return

Amos Lim

Amos Lim

Amos Lim

Amos Lim

13 9:.;%

-""",5-188D6

"

18 #9:%(4)-18*.4)-8 .4)-

#$%&'()*$+#',#$)*'-.$/0'

Amos LimThis variable factors in the effect of country risk premium

Amos LimBond market must be liquid, as otherwise the data gathered will not reflect the true standard deviation. This is especially a problem for Asian Bond Markets.

Amos Lim

Amos Lim

Amos Lim

Amos Lim

!"# $

%&!

'% '! ()"*% +,"- *% *%& . -& + +/0 /"&"1& +/!& & "20 +$ $!% +$0& 3& +

&"4&%

& &5& 6 +5 '!& ' '"7 % " 6% 1& ,% &8 + / / +/& 9 3&&5& +

+& 5&) & "%",&5&6 ' '5&!"7& + +1&

, -50! 26 2! +%6 &&

/% 7 7 + 60 + 6&":; +90&

! +*& +.% - 2& +

? G " ! . / . /

G & ! " " ,

. 9G

. -" $

" " ,

2 - @ "$ * "0

Amos LimBecause of (1) compounding, and (2) arithmetic mean weighs gains in each period equally.

Amos LimFirms that go bankrupt are delisted, and contribute nothing to estimates of return. This creates an upward bias in indexes.

In practice, analysts usually make adjustments for the bankruptcies by:- treating small cap bankruptcies as -30% return- treating large cap bankruptcies as -50% return

Amos LimE.g. subprime mortgage crisis

Amos Lim

?>

?>

", " ?>

8&&% *#" $& % A&%$*/ A&%

8&&% *#" +

7&"& ! 2"%62" ! +

8&&% & >6%&% &%7&6&& & ++

&"%&"&B 0 &C

7/ ?*(2@? 17/ @?1/@*'

?+@?+@?@+

", " ?>

! -#' F! 6 ! ?-

C " ?-

! C

$ B C

$ $

$ $

19

&9)* *'

1"$

0 -#' . -# '/

0"'

-"#4

Amos LimCAPM has only one factor: the market

Multi factor models, on the other hand

Arbitrage Pricing

Amos LimBuild-up approach

# % * %*'

6 @ - "

"

"

#

"G + + ' #

G ' #

0

? 9 "$ .'/

! "6"& ' D E F"& ' A ?G

G ! =8! 4!" !

" ,

G " ? ! "

G ! " .,," " /

L .'/F%.'/

Amos LimIn practice, 10y T-bond

Amos LimMarket model

G $

G $ " 1!

G

B B # % * %*'

2M# :88 7I2 2

# 2

)

" 1 " !! "

0F=.0,8/

%C 9

$ "

"

" " MN

* ?

#%* 9

0

Amos LimS&P500: Top 500 MCap companies - bias toward large cap companies

NYSE Composite: Excludes a lot of large MCap stock that is in NASDAQ (e.g. Apple, Google.. )

Amos LimNeed to always have enough observations

Amos LimAdjusted beta is based on the assumption that historically superior/inferior growth rates cannot be sustained to infinity. If not adjusted, we are assuming that the company will perpetually grow at the same historical rate. 2/3 reflects the weight assigned to the present growth

Amos LimMany 0 observations due to no trade

?

$ "$

;*

.!*

*

>?

G -#' .!/

G -#'

G 4 "

G 8 "

G ?

( > ? (

> &+:1' A ? ? &??'0") . /) !

? ?

G 4 ! "6

? ? ? =8 4!"

? .9 . "/ ?

? @< . / ? "!! "!!

G 2 " " 5 ,

.9 & 'G ? , 25 .!5/ ,$ ,

G ", O ,

G *, ",

@< & 'G ? , " "!!,

G ", O ,

G *, . "!!/ ,

0 5&

6& D 77(D D ,2E

Amos Lim

Amos Lim

Amos LimReturns vary depending on whether growth (low BV:MCap) or value stock (high BV:MCap)

Amos Lim(In the long run)

Amos LimSuperior explanatory power than CAPM for explaining market performance. Accounts for (1) market factors, (2) Small cap stock outperform large cap stock, and (3) Value stock outperform growth stock.

Amos Lim

Amos Lim

Amos Lim

Amos Lim

Amos Lim

Amos LimFun fact: SMB & HML hypotheses were tested by comparing portfolios using a zero-investment portfolio

Amos Lim

Amos Lim

> &0:1' A *A. 0") . /) !

?>? *A.

G ) 6G ? ? =8 4!"

G .9 L 4

G P5 L 4

G @< L 4

G P L 4

G

", ?A?

0 5& 6& D 77(D D ,2

+?@ +?++@ F?@

*! .> " 5,

7 "

22;3$!! ' ;,$&!,&!

" B J

0"

! =,8;

:,8;

0,18

25 1,1;

25 " 8,01

% =,9;

% " 8,=D

* ; "

- "

Amos LimDone

%K8@" ",?A?

6>?%#8 8".>!.#>>(>!1 !!

: ;" " " " ? : ;" " @"" " : ;

"""""""""""""" " : ;" " : ;

Amos Lim4th factor: Contrarian portfolios tend to outperform momentum portfolios

Amos LimMomentum: Stocks that performed well in the previous year will perform well next yearContrarian: Stocks that performed well in the previous year will not perform well next year

Amos Lim

"L%*

"&M'

> &1:1' A &%*'0") . /) !

455(4-

?! &")))""' !

2

#@)# !$)

Amos LimMacro model

Amos Lim

%*&%*'

)6$$% !&.QR/,

46

&"&"&8!&"""!&"&"1/""!&"&"#""!&"

Amos LimText

%*&%*'

26 4.) ?7 4)

1 4)

+

%*&%*'

3

$"=;"9;6

'" L2L? 4-A -4-

+

+

Amos Lim

%*&%*'

$$% "D;"0;6

'$% L2$% L? L0;? D;L? =;

+

@?+

%*&%*'

$!&.QR/"08;""6

'& L2L? L8;? 08;L? 08;

@?+

@?@?+

%*&%*'

)9;6

@?@?+

@?@?+

9 ) * * &9)* *' 4 " 6

9)* * $ D ) > E :

" ,

1

G 2 ! " 5" N

G $ " " . =!D ; 2/ " .I4'/ ! ",

? I4' " BB

? 4 5 N "

Amos LimNote that this risk premium is for the difference in returns between equity and bonds

Amos Lim

Amos Lim

Amos Lim

9 ) * * &9)* *'

"A 9) *

"LA;4"LD,88;,

"I#/C

Amos LimCommon stock - Bond

Amos LimDone

#

; B>&>

; &9:%

; !>&

;

% # # $

*-

&"

&"'%

&" 4

'%

3>

3' ?$8 7&@ E3>3' 3>3'

"#

4""$",

4"6 C, %%,$

,

)3 !%&,,$:&%

C, ,, $ ,)B !$"$!,)D,

F

Amos LimIf >1 bond, need to use weighted average of YTM of bonds outstanding. Note that for bonds that are illiquid (and so PV, or mkt value, is unreliable or unavailable), you may have to infer the market value from comparable bonds or use the alternate method

Amos LimMore accurate if bonds issued all have the same rating

Amos Lim

Amos Lim

Amos Lim

Amos Lim

" +, % # # &)%

'

:? @ ; +?@

3 >

3 'G' ' ? $8 7 & @ 3 > 3 ' 3 > 3 '

F ? @? @ ? @

! =,8; :,8;

0,18

I4' ! " @0;H! "F4

D8;

4 =8;

Amos Lim6.1

Amos LimDone

"0,#%##%C9&)%

'

4N"D=":B,4""18Q0888,4"01"Q01B=,9:@D,4!@,=:00,=:,4"0,=:9:,4(=:,

Amos LimAdjusted Beta= 1.3585 (2/3) + 1 (1/3) = 1.239Bond YTM = .09019428.. 0.902 (Using FC)Ks 0.12545WACC =

Amos LimAns: 9.67%

Amos LimSemi-annual

Amos LimDone

"0,#%##%C9&. %

'

; 3! %E,! !!

/ !,.$" !!!"/ ! !)

; 3! %' /),93))

; 3! %E!$4)); 3 "+ A ": !)

3. !); 3! %

, !

%F)) 3 !F); 3! %E' !)

Amos LimAns: 9.55%

Amos Lim

".

4",$"

,

2# B .,0771H0776

,

#

4 --!,

188D0,88;" "

L> LD,1A;>0,88;L:,1A;

Amos LimNeed to use latest period, as deriving current market value

Amos Lim6.00% + 1.00% = 7.00%

Amos LimKs = (1.2 * 2/3 + 1/3) * 0.05 + 0.06 = 0.116666 0.117Preferred: 2 / 25 = 0.08Debt YTM:

-.> N07+1

+

5 )- )- )- )-5H )- )- )- )-5 )/- )- )- )-5. )- )- )- )/-5H )- )- )- )-5 )- )- )/- )-5. )- )- )- )-5H )- )- )- )//-5 )- )- )- )-

5. )/- )/- )- )-5H )- )- )- )-5 )- )- )/- )/-5. )- )- )- )-5H )- )- )- )-5 )/- )/- )/- )-5. )/- )- )- )-5H )- )- )- )-

""

$!&"'(

""

I.0/,".,,#%*CB??#6>B1>%*9) *

/.1/,$",

F 6642578&0,#1,%%/

Amos LimAdjusted Beta = 1.4 (2/3) + 1/3 = 1.266666 1.27CAPM Ks = 0.0275 + 1.27 * 0.0708 = 11.72%Macro: 0.0275 + 1.8 [0.01 - (-0.01)] + 0.7 (-0.02 - 0.025) + 1 (0.02 - 0.035) = 0.017FF4 Ks = 12 * {0.0275 / 12 + (1.068)(0.0059) + (-0.374)(0.0023) + (-0.814)(0.0041) + (-0.226)(0.0077)} = 12 * 0.0026 = 0.0319Bond YTM = 0.07% (Using FC)BYRP Ks = 0.07 + 0.04 = 0.11

Highest - Lowest = 0.1172 - 0.017 = .1002

Amos LimFor exams, use the simple average of all Ks that you can calculate.

Amos LimNote: FF4 Ks ignores compounding (/12 rather than 12. Just /12 in exams.