De Todo

Covarianza

LINEA DEL MERCADO DE CAPITALES

sensibilidad

Ba=1.25+Bb

Chapter 10: Retarn and Rlsk: The Capital-Asset-PridngModel (CAPM)

10.4

Holdings of Atlas stock = 120 x $50 = $6,000 Holdings of Babcock stock = 150 x $20 = $3,000
Weight of Atlas stock = $6,000 159,000= 2 1 3 Weight of Babcock stock = S3,M)O1$9,000 = 1 1 3

b.c.

'

= (0.0208)'"

=0.4'(0.1)'+0.6'(0.2)'+2(0.4)(0.6)(0.1)(0.2)(-0.5)

-

0.1442 a 14.42%

= 0.01 12 ap = (0.0112)'"=0.1058 = 10.58% As the stocks arc mae ng.tivcly cmelated, the s h n d d deviation of thc patfolio dccmwc8.

Weighthfamnoft $8,000 1$20,000 = 0.4 Intelligent $12,000 1$20,000 0.6 8. RP ~0.4(0.1S)+0.6(0.20)~0.18~18% = 0.4' (0.08)' + 0.6' (0.2)' + 2 (0.4) (0.6) (0.38)(0.08) (0.20) up' = 0.0183424 = (0.0183424)'" -0.1354 = 13.54% a b. New weight: Macrosoft $8,000 1S12,000 = 0.667 - Intelligent $4.000 1$12,000 = 0.333 16.66% RP = 0.667 (0.15) + 0.333 (0.20)=0.1666= = 0.667' (0.08)' + 0.333' (0.2)' + 2 (0.667) (0.333) (0.38) (0.08) (0.20) a,' = 0.009984 (0.009984)'" = 0.09992 = 9.95% or

-

-

10.9

a.

RP
UP
I

b.

up -

RP

UpZ

c.

upNo, I would not hold 100% of stock A because the portfolio in b hrs higher expected return but less standard deviation than stock A.

=0.3 (0.10)+0.7(0.20)=0.17 = 17.0% = 0.3' (0.05)' + 0.7' (0.15)' = 0.01 125 = (0.01125)'" =0.10607 = 10.61% =0.9 (0.10) + 0.1 (0.20) = 0.1 I = 11.0% = 0.9' (0.05)' + 0.1' (0.15)' = 0.00225 = (0.00225)'" = 0.04743 = 4.74%

I may or may not hold 1Wh of stock B,depending on my pnf-.
10.10 The expected return on any portfolio must be less than or equal to the rrtum on the stock w t the highest mum. It cannot be greater than this stock's rchm becaw all sc b ih tc w t lower rctusns will pull down the value of the weighted a m p return. ih Similarly, the expected rctwn on any portfolio m s be greater than a c q d to the rrarm ut of the asset w t che lowestrctum. The Donfolio return cannot be less than t lowest ih -~~~ k ~-~~ return in the portfolio because all highe;earning stocks will pull up the value ofthe weighted avmge.
~~

10.11 a.

RB a' ,
UA

RA -

=0.4 (0.03) + 0.6 (0.15) 10.102 = 10.2% = 0.4 (0.065) + 0.6 (0.065) = 0.065 = 6.5% = 0.4 (0.03 0.102)'+ 0.6 (0.15 0.102)' = 0.003456 = (0.003456)'" = 0.05878 = 5.88%

-

-

U B ~ ~ O~ = O

b.

c.

0.417 (0.102) + 0.583 (0.065) = 0.0804 = 8.04% = X2a: = 0.0006 = (0.0006)'" = 0.0245 = 2.45% UP Amount borrowed = 4x $50 = 42,000 X~s$8,000/$6,000=4/3 x8=1-xAid 13 R P =(4/ 3) (0.102) +(-I / 3)(0.065) = 0.1143 = 11.43% = (4 13)' (0.003456) = 0,006144 ; UP' UP a (0.006144)'" 0.07838 = 7.84%
UP'

XA XB Rr

-

=1

= $2,500 1$6,000 = 0.417 0.417 = 0.583

--

10.12 Thewide fluctuations in the price of oil stocks do not indicate that oil ia .poor investmmt. If oil is purcbnecd u pat of a portfolio. what mattas is only itr k . S i t. the price captum beta plus idioaymatic risks, observing price volatility is not an adequate IEeSSM of the appropriDteness of adding oil to a portfolio. Ranm~bcr tobl tb.t variability should not be used whm deciding whether or not toput an asset into a large portfolio.

-., .State o c cm 0.25
0 20
~.--

R, -ZI
0.075 0.025 -0.075
=
= 0.0403

@I -% I~
0.005625 0.000625 0.005625

P x (Rl -El)]
0.0005625 0.0002500 0.0005625 0.0016250

0.10

Variance
Standard deviation
.-

--<

state occurs
0.25

R2 - E 2
0.075 0.025 -0.075
=

( ~ -2 2 ) I R
0.005625 0.000625 0.005625

~ x ( ~ ~ - i i t ) I0.0005625 0.0002500 0.0005625 0.0016250

0.20 0.10

Variance
Standard deviation

-- 0.0403
2

Statc occurs R, -Ti, 3
0.10 0.15
~

., -.

6.075 -0.025 0.075
= = 0.0403

0.005625 0.000625 0.005625

0.0005625 0.0002500 0.0005625 0.0016250

-

0.25

Variance
Standard deviation

c.

E(R)= .5 x ,175 + .5 x.175 = ,175 Var = . 5 x . 5 x . 0 4 0 3 x . 0 4 0 3 + . 5 x . 5...