Introduction:
The report is based on the efficient frontier where we, at first, have taken the raw data of the
stocks for 4 years from DSE and we selected the 2 stocks from Pharmaceutical industry and 1
stock was already been given by our honorable faculty member from RMG sector. Each of the
stocks varies different risks and returns. The stocks we have worked with are-
Envoy Textiles LTD.
GSK
Reneta Pharmeceuticals LTD.
After gathering the data, we have calculated the index model and from that we have calculated
the common week to week return and with the help of the average weekly return, we have
computed the annualized return as well. We also calculated the average week to week variance
and from that calculation, we also computed the annualized variance for every stock.
We have recognized the weights of each stocks with the help of Markowitz-Portfolio
Optimization. We additionally have summed the ordinary variance of each and every share and
from that we have computed the well-known deviation of the portfolio. We even sum the
portfolio return. We afterwards then recognized each weights the usage of output from Solver.
We calculated the risk-return portfolio by allocating the different weights to each stock, with the
calculation, we have produced a graph of an efficient frontier.
After calculating the covariance and correlation between each stocks, we have found that each of
stocks have a positive relation with each other stock. Which indicates that the variables are
showing similar kind of behavior.
Portfolio Risk and Return:
The return on portfolio refers to the gain or loss of a portfolio of investments containing several
types of investments. Portfolios aim to deliver returns based on the investment strategy's stated
objectives, as well as risk tolerance of the portfolio - targeted type of investor. The portfolio
return and risk is shown through the picture in below-
Portfolio Variance
Portfolio Standard Deviation
Portfolio Mean
Portfolio Return 0.009
0.00263
Portfolio Variance 5
The optimal return of the portfolio is 0.9% with 1.81% optimal risk. We have tried to find out
our optimal return and risks trough different combination of weights for the three stocks. We
used different combination of weights for the portfolio and found different set of risk and return
of the portfolio.
Efficient Frontier:
From the looks of the efficient frontier graph, we have recognized that the portfolio that has low
risks are dominated portfolio and the portfolio within the line of the efficient frontier are the
dominator portfolio.
According to the efficient frontier is the red area where our risk is 0.9% with return 1.81%. This
is the area where our risk will be the lowest with highest return. Any point apart from this point
will increase the risk of the portfolio.
Portfolio Standard Deviation
0.01
0.01
0.01
0.01
0.01
0.01
0
0
0
0
0
0 1 2 3 4 5 6 7 8 9
df
The efficient frontier rates portfolios (investments) on a scale of return (y-axis) versus risk (x-
axis). Compound Annual Growth Rate (CAGR) of an investment is commonly used as the return
component while standard deviation (annualized) depicts the risk metric. We calculated the
derivation of efficient frontier to minimize the variance of the portfolio. We calculated it through
the excel solver in which we set an objective which was to minimize the portfolio variance by
changing the stock weights.
