8. You have observed the following returns over time: YEAR
STOCK X
STOCK Y
MARKET
1997
14%
13%
12%
1998
19
7
10
1999
-16
-5
-12
2000
3
1
1
2001
20
11
15
Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent. a) What are the betas of Stocks X and Y? b) What are the required rates of return for Stocks X and Y? c) What is the required rate of return for a portfolio consisting of 80 percent of Stock X and 20 percent of Stock Y? d) If Stock X’s expected return is 22 percent, is Stock X under- or overvalued?
JAWAB : a. Stock X Β1997 = (R-Rf) / ( Rm-Rf) = (14-6) / (12-6) = 8/6 = 1,33%
Β1998 = (R-Rf) / ( Rm-Rf) = ( 19-6) / (10-6) = 13 / 4 = 3,25%
Β1999 = (R-Rf) / ( Rm-Rf)
= (-16-6) / (-12-6) = -22/-18 = 1,2%
Β2000 = (R-Rf) / ( Rm-Rf) = (3-6)/(1-6) = -3/-5 = 0,6%
Β2001 = (R-Rf) / ( Rm-Rf) =(20-6) / (15-6) = 14/9 = 1,55%
Stock Y Β1997 = (R-Rf) / ( Rm-Rf) = ( 13-6 ) / ( (12-6) = 7 / 6 = 1,16%
Β1998 = (R-Rf) / ( Rm-Rf) = (7-6) / (10-6) = 1 / 4 = 0,25%
Β1999 = (R-Rf) / ( Rm-Rf) = (-5-6) / (-12-6) = -11/ -18 = 0,611%
Β2000 = (R-Rf) / (Rm-Rf) = ( 1-6) / (1-6) = -5/-5 = 1%
Β2001 = (R-Rf) / ( Rm-Rf) = (11-6) / (15-6) = 5/9 = 0,55%
b. Stock X Return of stock = α + β stock . R market = 14 + (1,33 x 5) = 20,65% atau 0.21
Return of stock = α + β stock . R market = 19 + (3,25x5) = 35,25% atau 0.35
Return of stock = α + β stock . R market = -16 +( 1,2 x 5) = -10% atau -0.1
Return of stock = α + β stock . R market = 3 + ( 0,6x5) = 6% atau 0.06
Return of stock = α + β stock . R market
= 20 + ( 1,55x5) = 27,75% atau 0.28
Stock Y
Return of stock = α + β stock . R market = 13 + (1,16 x 5) = 18,8 % atau 0.188
Return of stock = α + β stock . R market = 7 + ( 0,25 x 5) =8,25 % atau 0.0825
Return of stock = α + β stock . R market = -5 + (0,611 x 5 ) = -1,945 % atau -19.45
Return of stock = α + β stock . R market = 1 + (1 x 5) = 6 % atau 0.06
Return of stock = α + β stock . R market = 11 + ( 0,55 x 5) = 13,75 % atau 0.1375 (*ket : untuk return of stock silahkan mau pilih dalam bentuk persen atau decimal )
c. 80% (0,8) stock X
14% x 0,8 = 0,112 19% x 0,8 = 0,152 -16% x 0,8 = -0,128 3% x 0,8 = 0,024 20% x 0,8 = 0,16 0,32
20% (0,2) stock Y
13% x 0,2 = 0,026 7% x 0,2 = 0,014 -5% x 0,2 = -0,01 1% x 0,2 =0,002 11% x 0,2 = 0,022 0,054
d. Jika Stock X 22 persen ,maka overvalued
