The document discusses key financial metrics including rate of return, average, variance, standard deviation, covariance, correlation, portfolio risk and portfolio return. It provides formulas and examples of how to calculate each metric using daily stock price data for National Refinery Limited and MCB Bank Limited. The document demonstrates how to analyze the relationship between two investments by calculating their covariance, correlation, and using the metrics to determine an efficient portfolio.

1. Presented By:
Robiha Yaseen
Faiza Manzoor

10.  The rate of return is the amount you receive after the
cost of an initial investment, calculated in the form of a
percentage. The percentage can be reflected as a
positive, which is considered a gain or profit. When the
percentage is negative, it reflects a loss. This
information is very useful in determining whether or not
the initial investment you made was a good one.
 Formula
RR = P1-P0 *100
P0

11.  The word “average” is used in everyday life to describe
where the middle number of a data set is. It’s the typical
number you would expect to find in a series of numbers.
In statistics, the average is called the “arithmetic mean,”
usually just shortened to the mean. Both the average
and the mean use the same.
 Formula

12.  Variance measures how far a data set is spread out.
The technical definition is “The average of the squared
differences from the mean,” but all it really does is to
give you a very general idea of the spread of your data.
A value of zero means that there is no variability; All the
numbers in the data set are the same.
 Formula:

13.  Standard deviation is a measure of dispersement in
statistics. “Dispersement” tells you how much your data
is spread out. Specifically, it shows you how much your
data is spread out around the mean or average.
 Formula:

14.  Covariance is a measure of how much two random
variables vary together. It’s similar to variance, but
where variance tells you how a single variable varies,
co variance tells you how two variables vary together.
 Formula:

15.  Correlation, in the finance and investment industries, is
a statistic that measures the degree to which two
securities move in relation to each other. Correlations
are used in advanced portfolio management computed
as the correlation coefficient, which has value that must
fall between -1 and 1.
 Formula:

16.  Each investment carries a risk of loss. The higher the
potential returns, the higher the risk. If you hold a
portfolio with many investments, each of those
investments carries its own risk. All of the investment
risks combined result in an overall risk you have
exposed your portfolio to. You must monitor your
portfolio risk to make sure you have a variety of
investments whose high and low risks offset each other
 Formula:

17.  Portfolio return is the monetary return experienced by a
holder of a portfolio. Portfolio returns can be calculated
on a daily or long-term basis to serve as a method of
assessing a particular investment strategy. Dividends
and capital appreciation are the main components of
portfolio returns.
 Formula
RP = w1R1 + w2R2

18. Day Code Company Open High Low Close Avg. Turnover LDCP
29-Jun-18NRL National Refinery Limited 444.95 450 435 443.01 441.5 179,700 443.52
28-Jun-18NRL National Refinery Limited 443.11 450 433 443.52 441.53 194,800 443.11
27-Jun-18NRL National Refinery Limited 440 445 435 443.11 441.8 196,850 438.24
26-Jun-18NRL National Refinery Limited 427.5 440.46 427.05 438.24 435.36 126,200 424.38
25-Jun-18NRL National Refinery Limited 425 440 409 424.38 421.84 197,300 421.63
22-Jun-18NRL National Refinery Limited 421 425.46 416.1 421.63 421.86 94,650 419.88
21-Jun-18NRL National Refinery Limited 415 425 406.1 419.88 417.72 148,700 414.16
20-Jun-18NRL National Refinery Limited 418.01 423.79 403 414.16 415.97 243,750 416.93
19-Jun-18NRL National Refinery Limited 416 422 412.01 416.93 416.42 183,800 415.94
14-Jun-18NRL National Refinery Limited 416.49 420 409 415.94 412.89 130,400 416.31
13-Jun-18NRL National Refinery Limited 405.8 422 403 416.31 414.27 131,850 402.3
12-Jun-18NRL National Refinery Limited 402.05 411.84 400.65 402.3 404.36 56,050 409.91
11-Jun-18NRL National Refinery Limited 424.9 426.84 407.01 409.91 412.76 101,700 427.22
7-Jun-18NRL National Refinery Limited 427.63 445.24 420.84 427.22 439.48 539,700 424.04
6-Jun-18NRL National Refinery Limited 405.22 424.04 403.22 424.04 417.96 191,850 403.85
5-Jun-18NRL National Refinery Limited 394.47 405.8 389.22 403.85 398.17 152,150 394.47
4-Jun-18NRL National Refinery Limited 389.85 400.99 380 394.47 394.04 370,650 381.9
1-Jun-18NRL National Refinery Limited 365 381.9 362 381.9 374.48 187,150 363.72
31-May-18NRL National Refinery Limited 350.15 366.7 348 363.72 360.92 507,000 352.22
30-May-18NRL National Refinery Limited 347.95 355 336 352.22 346.99 163,700 344.98
29-May-18NRL National Refinery Limited 339.4 346 337.5 344.98 343.38 73,450 336.18
28-May-18NRL National Refinery Limited 327.4 341.12 327.4 336.18 336.7 54,000 327.95
25-May-18NRL National Refinery Limited 332.5 332.5 327.4 327.95 328.88 18,250 332.32
24-May-18NRL National Refinery Limited 336 336.01 331.4 332.32 333.36 14,550 337.4

19. Day Code Company Open High Low Close Avg. Turnover LDCP
29-Jun-18MCB MCB Bank Limited 197.51 200.25 197 197.77 198.19 431,200 199.45
28-Jun-18MCB MCB Bank Limited 199 200.77 198.1 199.45 199.81 332,500 199.18
27-Jun-18MCB MCB Bank Limited 200.77 202.5 199 199.18 199.84 515,800 199.59
26-Jun-18MCB MCB Bank Limited 201 201.94 198.6 199.59 199.72 432,500 200.39
25-Jun-18MCB MCB Bank Limited 196.11 201 196.11 200.39 199.53 597,000 197.78
22-Jun-18MCB MCB Bank Limited 197.41 201 196.8 197.78 198.65 462,300 198.19
21-Jun-18MCB MCB Bank Limited 198 201.4 196.06 198.19 199.23 725,200 198.25
20-Jun-18MCB MCB Bank Limited 201.25 202 198.05 198.25 199.09 1,034,100 201.46
19-Jun-18MCB MCB Bank Limited 206.13 206.99 200.8 201.46 202.09 1,528,700 206.12
14-Jun-18MCB MCB Bank Limited 207 208 205 206.12 206.06 542,700 207.71
13-Jun-18MCB MCB Bank Limited 207 208 205.5 207.71 207.01 322,500 206.89
12-Jun-18MCB MCB Bank Limited 211 213 206.01 206.89 207.46 195,900 211.81
11-Jun-18MCB MCB Bank Limited 214 214.5 210.55 211.81 212.64 529,200 213.32
7-Jun-18MCB MCB Bank Limited 215.1 216 213 213.32 214.38 214,800 214.85
6-Jun-18MCB MCB Bank Limited 211.5 216 210.5 214.85 214.51 780,100 212.82
5-Jun-18MCB MCB Bank Limited 207.44 213.85 207 212.82 212.11 632,500 208.94
4-Jun-18MCB MCB Bank Limited 206 209.8 204.6 208.94 206.44 602,100 205.67
1-Jun-18MCB MCB Bank Limited 202.44 207 202.44 205.67 205.4 646,800 204.19
31-May-18MCB MCB Bank Limited 201.5 205 201 204.19 203.92 1,008,600 200.14
30-May-18MCB MCB Bank Limited 204.5 204.5 199.99 200.14 200.98 637,300 203.95
29-May-18MCB MCB Bank Limited 200 204 200 203.95 203.11 563,700 198.59
28-May-18MCB MCB Bank Limited 201.9 204.5 197.2 198.59 201.56 274,100 199.98
25-May-18MCB MCB Bank Limited 198.21 202 198 199.98 199.7 263,200 199.42
24-May-18MCB MCB Bank Limited 202 203 198 199.42 200.42 2,069,500 202.48

20. Day Company Close Return Company Close Return
29-Jun-18National Refinery Limited 332.32 MCB Bank Limited 199.42
28-Jun-18National Refinery Limited 327.95 -1.31%MCB Bank Limited 199.98 0.3%
27-Jun-18National Refinery Limited 336.18 2.5%MCB Bank Limited 198.59 -0.7%
26-Jun-18National Refinery Limited 344.98 2.6%MCB Bank Limited 203.95 2.7%
25-Jun-18National Refinery Limited 352.22 2.10%MCB Bank Limited 200.14 -1.9%
22-Jun-18National Refinery Limited 363.72 3.3%MCB Bank Limited 204.19 2.0%
9.18% 2.4%

21. Weight 0.5
co-varince 0.03%
co-relation 23.26%
portfolio of risk 1.43%
portfolio of return 3.52%
% 40.82%
Mean 1.53%
Standard Deviation 1.62%
Mean 1.530%
Standard Deviation 1.688%

22. Day Company Close Return Company Close Return
21-Jun-18National Refinery Limited 381.9 MCB Bank Limited 205.67
20-Jun-18National Refinery Limited 394.47 3.29%MCB Bank Limited 208.94 1.6%
19-Jun-18National Refinery Limited 403.85 2.4%MCB Bank Limited 212.82 1.9%
14-Jun-18National Refinery Limited 424.04 5.0%MCB Bank Limited 214.85 1.0%
13-Jun-18National Refinery Limited 427.22 0.7%MCB Bank Limited 213.32 -0.7%
12-Jun-18National Refinery Limited 409.91 -4.1%MCB Bank Limited 211.81 -0.7%
7.37% 3.0%

23. Wieght 0.5
co-varince 0.10%
co-relation 72.84%
portfolio of risk 1.99%
portfolio of return 3.33%
Portfolio of Standard Deviation 0.60%
Mean 1.23%
Standard Deviation 3.11%
Mean 0.497%
Standard Deviation 1.106%

24. Day Company Close Return Company Close Return
11-Jun-18National Refinery Limited 402.3 MCB Bank Limited 206.89
7-Jun-18National Refinery Limited 416.31 3.5%MCB Bank Limited 207.71 0.4%
6-Jun-18National Refinery Limited 415.94 -0.1%MCB Bank Limited 206.12 -0.8%
5-Jun-18National Refinery Limited 416.93 0.2%MCB Bank Limited 201.46 -2.3%
4-Jun-18National Refinery Limited 414.16 -0.7%MCB Bank Limited 198.25 165.0%
1-Jun-18National Refinery Limited 419.88 1.4%MCB Bank Limited 198.19 0.0%
4.35% 162.34%

25. Weight 0.5
co-varience 0.02%
co-relation 0.51%
portfolio of risk 24.47%
portfolio of return 82.26%
Portfolio of Standard Deviation 73.80%
Mean 27.057%
Standard Deviation 66.272%
Mean 0.725%
Standard Deviation 1.487%

26. Day Company Close Return Company Close Return
31-May-18National Refinery Limited 421.63 MCB Bank Limited 197.78
30-May-18National Refinery Limited 424.38 0.7%MCB Bank Limited 200.39 1.3%
29-May-18National Refinery Limited 438.24 3.3%MCB Bank Limited 199.59 -0.4%
28-May-18National Refinery Limited 443.11 1.1%MCB Bank Limited 199.18 -0.2%
25-May-18National Refinery Limited 443.52 0.1%MCB Bank Limited 199.45 0.1%
24-May-18National Refinery Limited 443.01 -0.1%MCB Bank Limited 197.77 -0.8%
5.01% 1.5%

27. Mean 0.835%
Standard Deviation 1.217%
portfolio of risk 0.75%
portfolio of return 2.00%
Portfolio of Standard Deviation 0.37%
Mean 0.835%
Standard Deviation 1.217%
Mean 0.250%
Standard Deviation 0.870%