Portfolio Performance Analysis

This assignment involves evaluating the performance of a hypothetical portfolio by comparing it to a benchmark index (ASX200). Key metrics used include tracking error, beta, correlation, R-squared, and Root Mean Squared Error (RMSE) for various assets within the portfolio. The analysis aims to assess how closely the portfolio tracks the index's returns and understand the risk associated with its investments.

Running Header: PORTFOLIO ANALYSIS
1
Portfolio analysis
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Portfolio analysis 2
1.
a) Continuously compounding of returns
b) Vector of expected returns
From the derived annualized returns, it can be seen that the stocks have a positive return with all
the ten stocks and the market index having an annualized expected return that ranges from 0.7 to
1.3. From the variance-covariance matrix, it can be seen that the covariance between the stocks
and the index is positive indicating a positive relationship. On the other hand, the variances of
the stocks are also high. Thus, it can be seen that the stocks are highly volatile since the variance
range from 0.5 to 1.1.
c) Table 1: Stock betas
Stock betas
CBA WBC ANZ BHP NAB CSL TLS WES WOW MQG
Beta 1.012 0.990 0.919 0.759 0.909 1.313 1.054 0.943 0.855 1.251
The table above shows that the 10 stocks have a high volatility. Moreover, CBA, CSL, TLS, and
MQG have a volatility that is more than the market as they are more than 1.
d) Table 2: Total risk decomposition
CBA WBC ANZ BHP NAB CSL TLS WES WOW MQG
Variance
1.011 0.968 0.827 0.537 0.813 1.658 1.095 0.880 0.698 1.520
Systematic risk
1.014 0.971 0.837 0.571 0.819 1.709 1.100 0.881 0.724 1.550
Unsystematic
risk
-0.002 -0.003 -0.010 -0.035 -0.006 -0.050 -0.005 -0.001 -0.027 -0.029
R^2
0.413 0.828 0.794 0.247 0.152 0.014 0.134 0.055 0.734 0.456

Portfolio analysis 3
The systematic risk and the variance of the stocks are almost similar. It, therefore, suggests that
the risks of the assets are attributed to macroeconomic factors which affect all assets (Gencay,
2005). On the other hand, the unsystematic risks are very low suggesting that there is no risk of
anything going wrong with the company of the industry (Estrada, 2002).
The R square of the stocks varies across the stocks. Stocks with an R squared that is between
0.85and 1, have a performance which is in line with the market. Stocks with R squared less than
0.7 do not perform in line with the index. They include CBA, BHP, NAB, CSL, TLS, WES, and
MQG.
e) Figure 1: Capital Market Line
0.733000000000001 0.933000000000001 1.133 1.333
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.277
Capital Market Line
Standard deviation
Returns
f) Figure 2: Security Market Line

Portfolio analysis 4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
MQG
WOW
WES
TLS
CSL
NABANZ
WBC
CBA
Based on figure 1, it can be seen no stock undervalued stock as they are below the security
market line. Thus, it none offers a greater return compared to its risk. On the other hand, all the
remaining stocks are overvalued and will thus offer a small return.
2.
a) The weight of the ten stocks which minimize the variance of the portfolio is as shown
below:
CBA WBC ANZ BHP NAB CSL TLS WES WOW MQG
Variance
1.011 0.968 0.827 0.537 0.813 1.658 1.095 0.880 0.698 1.520
weight 1
0.67 0.02 0.11 0.35 0.13 -0.29 -0.05 0.09 0.21 -0.25
weighted variance
0.681 0.022 0.093 0.187 0.103 -0.479 -0.051 0.081 0.146 -0.377
beta
1.012 0.990 0.919 0.759 0.909 1.313 1.054 0.943 0.855 1.251
weighted beta 0.681 0.023 0.104 0.264 0.115 -0.380 -0.049 0.086 0.179 -0.310

Portfolio analysis 5
From the weights, it can be seen that all the stocks had a reduction in variance expect for CBA.
On the other hand, none of the stock had an exposure that is exactly one but CBA, CSL, and TSL
had an exposure that was close to the index.
The weights were derived from the variances covariance matrix using the solver add-in in excels.
Arbitral weights were assigned to the stocks at first. The solver then minimized the variance,
subject to the arbitral weights. However, it should be noted that the arbitral weights had to sum
up to 1. The weighted variance was obtained by multiplying the derived weights to the variance.
A similar approach was also used for the weighted beta values.
b) Table 4: RMSE minimization
CBA WBC ANZ BHP NAB CSL TLS WES
WO
W MQG
weight 1
0.67 0.02 0.11 0.35 0.13 -0.29 -0.05 0.09 0.21 -0.25
Expected returns
1.004 0.981 0.901 0.705 0.896 1.274 1.044 0.938 0.817 1.223
Weighted returns
0.676 0.022 0.102 0.245 0.113 -0.368 -0.049 0.086 0.171 -0.303
Returns
1.004 0.981 0.901 0.705 0.896 1.274 1.044 0.938 0.817 1.223
difference
0.108 0.919 0.638 0.212 0.612 2.698 1.194 0.726 0.418 2.329
factor T
0.004 0.037 0.026 0.008 0.024 0.108 0.048 0.029 0.017 0.093
RMSE
0.066 0.192 0.160 0.092 0.157 0.329 0.218 0.170 0.129 0.305
To minimize the RMSE, the weights were multiplied with the weighted returns to get the
weighted returns. The weighted returns were then minimized by the expected return to get the
difference. The differences were then divided by 25 to get the factor T. to obtain the minimized
the RMSE, the square root of the factor T were obtained.

Portfolio analysis 6
c) Table 5: Portfolio tracker 1 vs. portfolio tracker 2
Portfolio tracker 1
CBA WBC ANZ BHP NAB CSL TLS WES WOW MQG
Variance
1.011 0.968 0.827 0.537 0.813 1.658 1.095 0.880 0.698 1.520
weight 1
0.67 0.02 0.11 0.35 0.13 -0.29 -0.05 0.09 0.21 -0.25
weighted
variance
0.46 0.00 0.01 0.06 0.01 0.14 0.00 0.01 0.03 0.09
Expected
returns
1.004 0.981 0.901 0.705 0.896 1.274 1.044 0.938 0.817 1.223
Weighted
returns
0.68 0.02 0.10 0.25 0.11 -0.37 -0.05 0.09 0.17 -0.30
beta
1.01 0.99 0.92 0.76 0.91 1.31 1.05 0.94 0.86 1.25
covariance
1.00 0.98 0.90 0.71 0.89 1.26 1.04 0.93 0.82 1.22
Correlation
0.46 0.00 0.01 0.09 0.01 0.11 0.00 0.01 0.04 0.08
R^2
0.21 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.01
Portfolio tracker 2
CBA WBC ANZ BHP NAB CSL TLS WES WOW MQG
Weighted
returns
0.67 0.02 0.11 0.35 0.13 -0.29 -0.05 0.09 0.21 -0.25
Returns
1.004 0.981 0.901 0.705 0.896 1.274 1.044 0.938 0.817 1.223
weight
0.67 0.02 0.11 0.35 0.13 -0.29 -0.05 0.09 0.21 -0.25
Variance
1.011 0.968 0.827 0.537 0.813 1.658 1.095 0.880 0.698 1.520
weighted
variance
0.69 0.02 0.08 0.10 0.08 -0.79 -0.06 0.07 0.10 -0.57
beta
1.01 0.99 0.92 0.76 0.91 1.31 1.05 0.94 0.86 1.25
covariance
1.00 1.08 1.05 1.01 1.02 1.04 1.02 1.00 1.10 1.07
correlation
1.02 0.90 0.79 0.53 0.80 1.59 1.07 0.88 0.63 1.42
R^2
1.03 0.81 0.62 0.28 0.64 2.52 1.15 0.77 0.40 2.01

Portfolio analysis 7
The table above shows the results of the expected returns, variance, beta and the r-squared of the
two tracker portfolios. The most recommendable portfolio tracer is tracker 2 since it has a
minimized R squared that is close to 100.
3.
a) Time series
Figure 3: Tracker portfolio time series
1/4/2017 2/23/2017 4/14/2017 6/3/2017 7/23/2017
85.00
95.00
105.00
115.00
125.00
135.00
145.00
Tracker portfolio time series
CBA
WBC
ANZ
BHP
NAB
CSL
TLS
WES
WOW
MQG
Time
From the tracker time series, it can be seen that the annual returns of CSL are increasing over
time. However, the rest of the stocks seem to e relatively constant with minimal fluctuations over
time.
Figure 4: ASX200 time series

Portfolio analysis 8
1/5/2017 2/24/2017 4/15/2017 6/4/2017 7/24/2017
0.00
50.00
100.00
150.00
200.00
250.00
300.00
350.00
ASX200 time series
Figure 4 shows that the market index is very volatile as a trend cannot be identified. The returns
of the markets fluctuate frequently thus making it very volatile.
b) Annualized returns
Table 6: Annualized returns
CB
A
WB
C
AN
Z
BH
P
NA
B CSL TLS
WE
S
WO
W
MQ
G
ASX20
0
Expected
returns
0.99
2
0.98
6
0.96
1
0.95
7
1.00
4
1.22
2 0.887
1.00
2 1.059 0.995 1.005
Annualize
d returns
0.00
4
0.00
4
0.00
4
0.00
4
0.00
4
0.00
5 0.004
0.00
4 0.004 0.004 0.004
From table 6, it can be seen that the annualized returns of the portfolio and the index are positive.
c) Table 7: Tracker portfolio
Beta
CBA
WB
C ANZ BHP NAB CSL TLS WES
WO
W
MQ
G
ASX20
0

Portfolio analysis 9
Annualized
variance
0.01
2 0.047 0.042 0.056
0.03
2
0.16
7 0.075
0.02
0 0.014 0.009 0.004
Beta
0.38
7 0.167 0.167
-
0.045
0.24
1
0.04
9 -0.088
0.31
7 0.374 0.458 -
Correlatio
n
0.69
4 0.603 0.571
-
0.178
0.72
5
0.33
7 -0.405
0.75
6 0.743 0.731 1.000
R^2
0.48
2 0.363 0.326 0.032
0.52
5
0.11
4 0.164
0.57
1 0.552 0.534 1.000
RMSE
0.99
3 0.990 0.992 0.999
0.98
8
0.99
4 0.994
0.99
0 0.992 0.994 0.992
Table 7 shows that the values of the tracker portfolio are close to the value in tracker 2.
Reference
Estrada, J. (2002). Systematic risk in emerging markets: the D-CAPM. Emerging Markets
Review, 3(4), 365-379.
Gençay, R., Selcuk, F., & Whitcher, B. (2005). Multiscale systematic risk. Journal of
International Money and Finance, 24(1), pp.55-70.