H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
BERKELEY
UGBA 103
A
VINASH
V
ERMA
S
OLUTION
TO
H
OMEWORK
8
1.
(a)
Identify two publicly traded stocks,
(b)
download the
daily
data on historical price of the identified
stocks from
www.finance.yahoo.com
,
(c)
make sure that the price histories are contemporaneous for the most
recent 515 observations (for
every
trading day for which you have
adjusted closing price
1
available for one
stock, you should also have
adjusted closing price
available for the other stock),
(d)
compute daily return for
the most recent 514 trading days,
(e)
compute annualized standard deviation of returns on each stock,
(f)
compute the correlation coefficient between the returns on the two stocks,
(g)
compute the riskminimizing
portfolio weight on the two stocks for a twosecurity portfolio,
(h)
work out the dollar amount that will be
invested in each stock for a portfolio of $100 million, and
(i)
compute the standard deviation of the value of
the portfolio one year from now.
No single correct answer> Students get full credit so long as they:
used adjusted closing price and not the closing price,
computed returns correctly,
computed the standard deviation correctly,
annualized the standard deviation,
computed the correlation correctly,
used the formulas
x
1
2
2
12
1
2
2
2
12
2
*
=

+

σ
and
x
x
2
1
1
*
*
=

correctly,
computed
SD(R
p
)
correctly
by
using
the
formula
2
1
12
2
1
2
2
2
2
2
1
2
1
2
2
ρ
x
x
x
x
p
+
+
=
,
and finally,
computed SD(V(portfolio)) correctly as $100m*SD(R
p
).
2.
Ms. Adelgundes Krzyzanowska has $60 million invested as follows: $12 million in ABC Corporation, $42
million in XYZ Inc., and the remainder in the risk free asset. You are given that the standard deviation of
annualized returns on ABC, XYZ, and Ms. Adelgundes Krzyzanowska’s portfolio as a whole, is 25%, 21%,
and 18%, respectively. Solve for the correlation between returns on ABC and returns on XYZ.
Denoting ABC as Security