Analysis of Risk and Return for a Stock Portfolio (Finance)

This report presents a comprehensive analysis of risk and return for a stock portfolio comprising General Motors (GM) and Ford (F) common stocks. The analysis begins by calculating the average rate of return for each stock individually, followed by the determination of the annual rate of return for a portfolio with a 50/50 allocation between GM and Ford. The average return of the portfolio over the period from 2003 to 2007 is then computed. Furthermore, the individual risk of each stock is estimated, along with the calculation of the risk for the asset portfolio as a whole, including covariance and standard deviation. The coefficient correlation between the returns of the two stocks is also determined. Finally, the report critically discusses the modern portfolio theory, pioneered by Harry Markowitz, in relation to the findings, offering investment advice to a client regarding the profitability and diversification of their asset portfolio, considering the risks and returns associated with each stock and the portfolio as a whole. The report concludes with a discussion on the implications of the findings for portfolio management and investment strategy, including the role of diversification and correlation in managing risk.

INDICATIVE ASSESSMENT

TABLE OF CONTENTS
RISK AND RETURN......................................................................................................................1
Tasks............................................................................................................................................1
1) Estimate the average rate of return of each stock individually................................................1
2) If your client invested in a stock portfolio comprising 50% of GM common stocks and 50%
of Ford common stocks, what would have been the rate of return on the asset portfolio each
year?.............................................................................................................................................1
3) What would have been the average return on the portfolio during the period from 2003 to
2007..............................................................................................................................................2
4) Estimate the (individual) risk of each stock. ..........................................................................2
5) Calculate the risk for the asset portfolio (both common stocks taken together).....................3
6) What is the coefficient correlation between the returns of the two common stocks?.............4
7) Critically discuss the modern portfolio theory, which was pioneered by Harry Markowitz,
in relation to your findings and advise your client accordingly in layman’s terms on the
profitability of your client’s asset portfolio.................................................................................4
REFERENCES................................................................................................................................6

RISK AND RETURN
Tasks
1) Estimate the average rate of return of each stock individually.
Year GM Ford
2003 -10 -3
2004 18.5 21.29
2005 36.87 44.25
2006 14.33 3.67
2007 33 28.3
92.7 94.51
Average rate
of return 18.54 18.902
The average return on GM stocks is 18.54% and average return on Ford stocks is 18.902.
Return is moreover same on both the stocks.
2) If your client invested in a stock portfolio comprising 50% of GM common stocks and 50% of
Ford common stocks, what would have been the rate of return on the asset portfolio each
year?
Portfolio return every year
Year GM Ford
0.5*GM return+0.5*Ford
return
2003 -10 -3 -6.50%
2004 18.5 21.29 19.90%
2005 36.87 44.25 40.56%
2006 14.33 3.67 9.00%
2007 33 28.3 30.65%
The portfolio return is calculated by considering the proportion of investments in each
stock. The last column of the above table shows the return from portfolio each year.
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3) What would have been the average return on the portfolio during the period from 2003 to
2007.
Year GM Ford
2003 -10 -3
2004 18.5 21.29
2005 36.87 44.25
2006 14.33 3.67
2007 33 28.3
92.7 94.51
Average rate
of return 18.54% 18.90%
Calculation of portfolio return for the five years
GM Ford
Average rate
of return 18.54 18.902
Portfolio 18.54*0.5 18.902*0.5
9.27 9.451
Return on
Portfolio 9.27+9.451
18.721
The above table shows the calculations for return on portfolio comprising of GM and
Ford stocks and it shows 18.72% return has been earned for the overall period.
4) Estimate the (individual) risk of each stock.
Risk of GM stocks
GM (x) x – x̅ (x – x̅ )^2
2003 -10 -28.54 814.5
2004 18.5 -0.04 0.00
2005 36.87 18.33 336.0
2006 14.33 -4.21 17.7
2007 33 14.46 209.1
92.7 1377.34
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Average rate of
return 18.54
Standard
Deviation 1377.34/5 275.47
Risk √275.47 16.60
The risk on Ford stocks is 16.60%
Risk of Ford stocks
Ford (y) y – ȳ (y – ȳ )^2
2003 -3 -21.902 479.7
2004 21.29 2.388 5.70
2005 44.25 25.348 642.5
2006 3.67 -15.232 232.0
2007 28.3 9.398 88.3
94.51 1448.26
Average rate of
return 18.902
Standard
Deviation 1448.26/5 289.65
Risk √289.65 17.02
The risk on Ford Stocks is 17.02%
5) Calculate the risk for the asset portfolio (both common stocks taken together)
GM (x) Ford (y) x – x̅ y – ȳ (x– x̅)(y– ȳ)
2003 -10 -3 -28.54 -21.902 625.08
2004 18.5 21.29 -0.04 2.388 -0.10
2005 36.87 44.25 18.33 25.348 464.63
2006 14.33 3.67 -4.21 -15.232 64.13
2007 33 28.3 14.46 9.398 135.90
92.7 94.51 1289.64
Risk of Asset
portfolio 1289.64/5
Covariance 257.93
The risk on portfolio comprising of both the stocks is represented by covariance which is
257.93
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6) What is the coefficient correlation between the returns of the two common stocks?
Coefficient
correlation σXY 257.93
σX*σY 16.60*17.02
257.93 0.913
282.47
The coefficient correlation between the two stocks is 0.913 which means there is positive
relationship correlation between the two stocks.
7) Critically discuss the modern portfolio theory, which was pioneered by Harry Markowitz, in
relation to your findings and advise your client accordingly in layman’s terms on the
profitability of your client’s asset portfolio
Modern portfolio theory is investment theory which allows the investors in assembling
the asset portfolio which maximises the expected return for given level of the risk. Theory
assumes investors are generally risk averse for given level of the expected returns, investors
would prefer less riskier portfolio. As per this theory investors must be compensated for the
higher risks through the higher expected returns (Runting and et.al., 2018). It employees core
idea of the diversification which states having portfolio of the assets of different class if less
riskier than holding portfolio of the similar assets. Investors could use the theory for choosing
investments for their portfolio. The MPT generally advocates buy & hold strategy with the
occasional rebalancing.
Theory assumes that the every investors aims at achieving highest long term return
without taking the extreme level of short term risks. Risks and rewards are correlated positively
in the investments, which means if investor opts for lower risk like cash or bond they could
expect the lower returns. Investors have to invest in the riskier and more volatile investments to
get higher returns (Alvarez, Larkin and Ropicki, 2017). However this option is not good for the
investors who are less risk averse and wants steady level of returns on their investments.
It states different strategies through which the assets could be allocated effectively to
overcome the risks and returns. Diversification refers to portfolio allocation strategy which aims
at minimising the idiosyncratic risks though holding the assets which are not perfect positive
correlated. Correlation is relationship between the two variables and is measures using
correlation coefficient that lies between -1< p <1.
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CC of -1 represents perfectly negative correlation between 2 assets. It reflects positive
movement is associated with negative movement of other. While CC of 1 represents perfectly
positive correlation which shows assets move in same direction in relation with market
movements. Positive correlation in assets within the portfolio increases risk of portfolio and
diversification holds assets to reduce the risk. In negative correlation less than -1 than a loss of
asset A will be offset by the gain of asset B which is the main advantage of the diversified
portfolio.
GM Ford
Return 18.54% 18.90%
Risk 16.60% 17.02%
Correlation coefficient 0.91
It could be evaluated in the portfolio of client that return is slightly higher in Ford where
the GM is also providing similar return with lower risks. The risks is higher in Ford with same
return. The correlation coefficient between two stocks is +0.91 which is positive correlation. It
shows that movement in stocks will be in direction of market (Shams and Esfandirari
Moghaddam, 2017). It should make diversified allocation of the assets so that the risk of one
stock is covered by the other.
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REFERENCES
Books and Journals
Runting, R.K., and et.al., 2018. Reducing risk in reserve selection using Modern Portfolio
Theory: Coastal planning under sea‐level rise. Journal of applied ecology. 55(5). pp.2193-
2203.
Alvarez, S., Larkin, S.L. and Ropicki, A., 2017. Optimizing provision of ecosystem services
using modern portfolio theory. Ecosystem services. 27. pp.25-37.
Shams, S. and Esfandirari Moghaddam, A.T., 2017. The impact of herding behavior on the
performance of investment companies based on modern and post modern portfolio
theory. Financial Research Journal. 19(1). pp.97-118.
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