Sample Paper 1

Sample Test 1

Question 1 – Find the portfolio volatility given the following information (5 Marks)

	Price	Quantity	Volatility (%)
X – Apple	370	100	30%
Y – Microsoft	27	200	28%
Z – Citigroup	25	250	50%
K – GE	15	300	40%

Correlation Matrix –

	X	Y	Z	K
X	1
Y	0.5	1
Z	0.4	0.42	1
K	0.5	0.45	0.55	1

Solution –

	X	Y	Z	K	Total
Price	370	27	25	15
Quantity	100	200	250	300
Position	37000	5400	6250	4500	53150
Stdev / Volatility	30%	28%	50%	40%
Weights	69.61%	10.16%	11.76%	8.47%	100.00%

Using Matrix Method –

69.61%

10.16%

11.76%

8.47%

X

0.090	0.042	0.060	0.060
0.042	0.078	0.059	0.050
0.060	0.059	0.250	0.110
0.060	0.050	0.110	0.160

X

69.61%

10.16%

11.76%

8.47%

=

0.0790555

0.048385

0.086454

0.07337

X

69.61%

10.16%

11.76%

8.47%

=

Variance	0.0763281
Volatility of the Portfolio	27.628%

Question 2 – Find the following statistics from the returns (use log returns) of the time series data given.

AM, GM, Mode, Variance, Std Dev, Skewness, Kurtosis, Volatility (Daily), Covariance Matrix, correlation Matrix (2+3 = 5 Marks)

Answer 2 –

Open Excel and Go to Data - Data Analysis – Now use Descriptive Statistics option to generate all except covariance and correlation matrix. Here, the daily volatility is the Std Dev.

Select the covariance and correlation option to generate the respective matrices.

How to install Data Analysis – Go to excel options, select Add-ins and install Data analysis tool pack.

Covariance Matrix -

	Apple	Microsoft	Citigroup	GE
Apple	0.000337
Microsoft	0.000165	0.000331
Citigroup	0.000379	0.00041	0.002797
General Electric	0.000236	0.000208	0.000743	0.000652

Correlation Matrix -

	Apple	Microsoft	Citigroup	GE
Apple	1
Microsoft	0.494069	1
Citigroup	0.390779	0.426386	1
General Electric	0.504043	0.446948	0.550105	1

	Apple	Microsoft	Citigroup	GE
Mean	0.002018	0.000457	-0.00152	7.43E-06
Standard Error	0.000696	0.00069	0.002006	0.000969
Median	0.00189	0.000907	0	0.000785
Mode	#N/A	0	0	0
Standard Deviation	0.018363	0.01821	0.052925	0.025555
Sample Variance	0.000337	0.000332	0.002801	0.000653
Kurtosis	1.640945	6.308376	18.25128	6.573781
Skewness	0.025563	-0.31394	-0.95872	0.285687
Range	0.155956	0.224887	0.817993	0.29403
Minimum	-0.0819	-0.12502	-0.49496	-0.11389
Maximum	0.074056	0.099871	0.323036	0.180142
Sum	1.404854	0.317978	-1.06139	0.005175
Count	696	696	696	696
Volatility (daily)	0.018363	0.01821	0.052925	0.025555