Examiners' commentaries 2011

92 Corporate finance
8
Approaching the question
I II III IV IV VI VII
Year Fly-away, % Stay-athome,
%
I - mean II - mean III x III IV x IV III x IV
2010 0 14 –4 9 16 81 –36
2009 –4 –2 –8 –7 64 49 56
2008 8 0 4 –5 16 25 –20
2007 10 –5 6 –10 36 100 –60
2006 6 18 2 13 4 169 26
Sum 20 25 136 424 –34
Mean 4 5
Variance 34 106
Covariance –8.5
Stdev 5.83 10.30
Portfolio variance = 0.5 0.5 34 + 0.5 0.5 106 0.5 0.5 –8.5 = 30.75
Portfolio risk = square root of the variance = 5.55
Note that the above figures are adjusted for the small sample error.
b. Suppose the returns on Stock x, y and z are determined by the following twofactor
model:
r
r
r
x
y
z
=
=
=
0.
2
0.
16
0.
5
+ 2 F − F
1
1
+ 1.
2 F
1
+ F + F
2
2
+
=
= 10%
0.
5
F
6%
2
=
8%
i. Determine the portfolio weights you need to place on x, y and z in order
to replicate the portfolio returns on F and F respectively. 1 2 (10 marks)
ii. The return on Stock M is known to follow the following factor model
r = 0.2 + 1.6F + 1.8F m 1 2
It is currently traded with a return of 10%. Explain if any arbitrage
opportunity arises in this case.
Reading for the question
Subject guide, pp.46–50.
Approaching the question
(5 marks)
Let x, y and z as the weight in X, Y and Z.
For
( 1)
( 2)
( 3)
( 2)
( 2)
F
1
x + y + z = 1
2 x +
− x +
−
−
( 1)
( 3)
1.
2
⇒ y = 10
⇒ z = −7
0.
5
⇒ x = −2
y + z = 1
y + z = 0
⇒ x + 0.
2 y = 0
⇒ 3 x +
0.
7
y = 1