BANKING DEPARTMENT
MSC BANKING AND FINANCIAL ECONOMICS (HARARE COHORT)
COURSE:
FINANCIAL ECONOMICS (CBA5104)
LECTURER: MR P NKALA
ASSIGNMENT:
DUE :
NUMBER ONE (INDIVIDUAL)
31/03/16
NAME OF STUDENT
:
AARON KUUDZEREMA
STUDENT NUMBER
:
N01522588D
ADDRESS
:
NSSA HOUSE, KARIBA
TELEPHONE
:
0261 2145210
CELLPHONE
:
0773 501 255/0712 289 276
1 (a) Describe how you will select shares for a portfolio that will produce an efficient
frontier. (10 marks).
Firstly you calculate the rate of return given by;
shares is and
r=
p1− p
po
o
where
po the start price of
p1 is the closing price of shares.
The efficient frontier represents that set of portfolios that has the maximum rate of return for
every given level of risk, or the minimum risk for every level of return. To come up with an
efficient frontier we examine two asset combinations and derive a curve assuming all possible
weights. The envelope curve that contains the best of all these possible combinations is
referred to as efficient frontier. Every portfolio that lies on the efficient frontier has either a
higher rate of return for equal risk or lower risk for an equal rate of return than some portfolio
beneath the frontier. As an investor, you will target a point along the frontier based on your
utility function and your attitude toward risk. No portfolio on the efficient frontier can
dominate any other portfolio on the efficient frontier. All the portfolios have different return
and risk measures, with expected rates of return that increase with higher risk. The slope of
the efficient frontier decreases steadily as you move upward. This implies that adding equal
increments of risk as you move up the efficient frontier gives you diminishing increments of
expected return. Different weight or amounts of a portfolio held in various assets yield a
curve of potential combinations. Correlation coefficients among assets are the critical factor
one must consider when selecting investments because one has to maintain the rate of return
while reducing the risk level of the portfolio by combining assets that have low positive or
negative correlation.
B) For the year 2011 to 2012 select a portfolio of 3 shares from ZSE that will produce an
efficient frontier. (15 marks)
Innscor
Month
Dec 10
Jan 11
Feb 11
Mar 11
Apr 11
May 11
Jun 11
Jul 11
Aug 11
Sep 11
Oct 11
Nov 11
Dec 11
Jan 12
Feb 12
Mar 12
Apr 12
May 12
Jun 12
Jul 12
Aug 12
Sep 12
Oct 12
Nov 12
Dec 12
The standard deviation for each series is the square root of the variance of each as follows;
σi =
√ 13.288 = 3.64%
σo =
√ 7.1363 = 2.67%
σn =
√ 12.0154 = 3.67
Thus, based on the covariance between two series and the individual standard deviations, we
can calculate the correlations between returns for Innscor, Old Mutual and Nat foods as;
r io =
r¿=
Covio
−3.73
+
=−3.73 /9.7188 = -0.38
σ i σ o ( 3.64)(2.67)
Cov ¿
6.29
+
=6.29 /13.3588 = 0.47
σ i σ n (3.64)(3.67)
r on =
Covon
1.59
+
=1.59 /9.7989 = 0.16
σ o σ n (2.67)(3.67)
Correlation of +1.0 would indicate perfect positive correlation, and value of -1.0 would mean
that the returns moved in a completely opposite direction. Innscor and National Foods seem
to be positively correlated
r ¿ =¿ 0.47 though still the value are somehow low. A notable
result is that with low, zero or negative correlations, it is possible to derive portfolios that
have lower risk than either single assets. In this case
r io =-0.38 and
r on =0.16
respectively which reflects low correlations. By investing in these assets there is reduction in
risk and in essence is diversification.
c) If rf = 5%. Find the optimum portfolio (10 marks)
The correlations are as follows;
r io = -0.38; r ¿ = 0.47 and r on = 0.16
Closing prices of shares as at December 2012: Innscor =
70x541593440=379,115,408
Old Mutual = 152x54734804=83,196,902.08
Nat foods =
Total
132x68400108=90,288,142.56
=
552,600,452.60
Weight of each asset in portfolio
Innscor
=
69%
Old Mutual
=
15%
Nat foods
=
16%
R
R
E(¿¿
o)
E(¿¿
o)
R
W
E(
R
)
i
i
E( p )=
+
+
Wo ¿
Wn ¿
= (0.69 x 7.89) + (0.15 x 3.40) + (0.16 x 6.55) = 7.00
σ 2p =
W 2i σ 2i
W 2o σ 2o + W 2n σ 2n ¿ +
+
¿
(2 W i W o σ i σ o r io +2 W i W n σ i σ n r ¿ +
2W o W n σ o σ n r on )
=(0.692x3.642+0.152x2.672+0.16x3.672)+(2x0.69x0.15x3.64x2.67x0.38+2x0.69x0.16x3.64x3.67x0.47+2x0.15x0.16x2.67x3.67x0.16)1/2
= 7.51%
Reward to volatility ratio of the optimum CAL is
E ( RP )- r f
σp
= 7-5
7.51
= 0.27
d) Efficient frontier
10
OPTIMAL CAL
8
n
6
4
2
2
4
6
8
10
efficient frontier
References
Elton, Gruber, Brown, and Goetzmann 4-7 Modern Portfolio Theory and Investment
Analysis, 7th Edition