Finance ii week 1 introduction personal introduction

Finance II
Week 1
Question 5a
A portfolio consists of three stocks, 30% is invested in the
first stock, 25% in the second stock and 45% in the third.
The yearly average return is 10% for the first stock, 12%
for the second and 13% for the third. The below table gives
the historical Variance-Covariance matrix of the (yearly) stock
returns:
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 6
a
b
c
Question 7
a
b
Question 8
a
b
c
0.10 0.04 0.03
0.04 0.20 0.04
0.03 0.04 0.60
I
Compute the average return of the portfolio.
¯
R
p
=
N X
i =1
w
i
·
¯
R
i
= 0 . 3 · 10%+0 . 25 · 12%+0 . 45 · 13% = 11 . 85%

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 5b
The below table gives the historical Variance-Covariance ma-
trix of the (yearly) stock returns:
0.10 0.04 0.03
0.04 0.20 0.04
0.03 0.04 0.60
I
¯
R
p
= 11 . 85%
I
Compute the yearly variance and volatility of the
portfolio return.
Question 6
a
b
c
Question 7
a
b
Question 8
a
b
c

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 5
a
b
Question 6
a
b
c
Question 7
Question 8
a
b
c
Question 5b
The below table gives the historical Variance-Covariance ma-
trix of the (yearly) stock returns:
0.10 0.04 0.03
0.04 0.20 0.04
0.03 0.04 0.60
I
Compute the yearly variance and volatility of the
portfolio return.
Var
p
=
N
X
i =1
w
2
i
Var ( R
i
) + 2
N - 1
X
i =1
N
X
j = i +1
w
i
w
j
cov ( R
i
, R
j
)

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 6
a
b
c
Question 7
a
b
Question 8
a
b
c
Question 5b
The below table gives the historical Variance-Covariance ma-
trix of the (yearly) stock returns:
0.10 0.04 0.03
0.04 0.20 0.04
0.03 0.04 0.60
I
¯
R
p
= 11 . 85%
I
Var
p
= 0 . 166
I
Compute the yearly variance and volatility of the
portfolio return.
σ
p
=
p
Var
p
=
√
0 . 166 = 40 . 76%

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 6
a
b
c
Question 7
a
b
Question 8
a
b
c
Question 6
A portfolio consists of 8 stocks. The following is known about
the weights w
i
, the volatilities and the correlations:
I
w
1
= w
2
= 0 . 2
I
w
3
= w
4
= w
5
= w
6
= w
7
= w
8
= 0 . 1
I
ρ
ij
= 0 . 3 , i 6 = j
I
σ
i
= 40%

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 6
a
b
c
Question 7
Question 6a
I
w
1
= w
2
= 0 . 2
I
w
3
= w
4
= w
5
= w
6
= w
7
= w
8
= 0 . 1
I
ρ
ij
= 0 . 3 , i 6 = j
I
σ
i
= 40% , σ
2
i
= (40%)
2
= 0 . 16
I
Cov
ij
= ρ
ij
σ
i
σ
j
= 0 . 3 · 40% · 40% = 0 . 048
I
Compute the variance and volatility of the portfolio
return
Var
p
=
N
X
i =1
w
2
i
Var ( R
i
) + 2
N - 1
X
i =1
N
X
j = i +1
w
i
w
j
cov ( R
i
, R
j
)

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2
Question 3
a
b
c
d
Question 5
a
b
Question 6
a
b
c
Question 7
a
b
Question 8
a
b
c
Question 6b
Now suppose all the weights are the same. Again compute
the variance and volatility of the portfolio return.

Finance II
Week 1
Introduction
Personal Introduction
Course Introduction
Question 1
Question 2