25503 Investment Analysis For Variance Assessment Answers

Questions:

(a) Calculate and report a time-series plot of the tracker portfolio value from Jan 4 to June 28, 2017, along with the performance of the ASX200 index, clearly indicating which series is which. You should also normalise the values of both time series so that their values are 100 on Jan 4, 2017.

(b) Report the simple annualised return of the tracker portfolio and the ASX200 index over the investment period.

Answers:

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

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.

Table 4: RMSE minimization

CBA	WBC	ANZ	BHP	NAB	CSL	TLS	WES	WOW	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.

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

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.

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