Risk and Return Report: Calculation, Estimation, and Discussion

This report presents calculations of average rate of return for individual stocks, rate of return on asset portfolio, estimation of risk for individual stocks and asset portfolio, coefficient correlation between returns of two common stocks, and discussion of Modern Portfolio Theory. The report also includes a discussion of the application of Markowitz's Portfolio Theory in obtaining the best portfolio in the stock market. The report concludes with a simplified perspective of the Markowitz Portfolio Theory and a characteristics analysis of behavioural portfolio theory in the Markowitz portfolio theory framework.

PROJECT THREE RISK
AND RETURN REPORT

Table of Contents
1. Calculation of average rate of return for each individual stocks.............................................3
2. Rate of return on asset portfolio each year..............................................................................3
3. Average return on the portfolio from 2003 to 2007................................................................3
4. Estimation of risk for each individual stock............................................................................3
5. Calculation of the risk for the asset portfolio..........................................................................4
6. Coefficient correlation between returns of two common stocks.............................................5
7. Discussion of Modern Portfolio Theory..................................................................................5
REFERENCES................................................................................................................................7

1. Calculation of average rate of return for each individual stocks
Year GM common stock
returns
Ford Common Stock
return
2003 -10% -3%
2004 18.50% 21.29%
2005 36.87% 44.25%
2006 14.33% 3.67%
2007 33% 28.30%
Sum of returns 93% 95%
No. of Years 5.00 5.00
Average return 18.54% 18.90%
2. Rate of return on asset portfolio each year
Year GM
common
stock
returns (a)
Weight
(b)
Ford Common
Stock return
(c)
Weight
(d)
Rate of return on asset
Portfolio (a * b) + (c * d)
2003 -10% 0.40 -3% 0.60 -5.80%
2004 18.50% 0.40 21.29% 0.60 20.17%
2005 36.87% 0.40 44.25% 0.60 41.30%
2006 14.33% 0.40 3.67% 0.60 7.93%
2007 33% 0.40 28.30% 0.60 30.18%
3. Average return on the portfolio from 2003 to 2007
Average return of portfolio = Sum of returns on the portfolio / Number of years
Average Portfolio return = -5.80% + 20.17% + 41.30% + 7.93% + 30.18% / 5
Average Portfolio return = 93.78 / 5 = 18.756%
4. Estimation of risk for each individual stock
Risk can be estimated through calculating standard deviation of returns for each stock, such as
the following:
For GM common stock returns

Year GM common
stock returns
x = (Actual
return - Average
return)
x2
2003 -10% -28.54% 8.15%
2004 18.50% -0.04% 0.00%
2005 36.87% 18.33% 3.36%
2006 14.33% -4.21% 0.18%
2007 33% 14.46% 2.09%
∑(x-Mean)2 13.77%
Average return = Sum of returns / Number of years = 93% / 5 = 18.54%
σ = √∑ (x - Mean)2 / 5 = √ 13.77 / 5 = √2.754
σ = 16.6%
For Ford common stock returns
Year Ford
Common
Stock return
x = (Actual
return - Average
return)
x2
2003 -3% -21.9% 4.80%
2004 21.29% 2.4% 0.06%
2005 44.25% 25.3% 6.43%
2006 3.67% -15.2% 2.32%
2007 28.30% 9.4% 0.88%
∑(x - Mean)2 14.48%
Average return = Sum of returns / Number of years = 95% / 5 = 18.90%
σ = √∑ (x - Mean)2 / 5 = √ 14.48 / 5 = √2.896
σ = 17.0%
5. Calculation of the risk for the asset portfolio
σp = √ w12 * σ12 + w22 * σ22 + 2 * w1 * w2 * ρ 1,2 * σ1 * σ2
σp = Portfolio standard deviation or risk
w12 = Weight of asset 1 (GM common stock) = 40% or 0.4
w22 = Weight of asset 2 (Ford common stock) = 60% or 0.6
σ12 = Standard deviation of asset 1 (GM common stock) = 16.6%

σ22 = Standard deviation of asset 2 (Ford common stock) = 17.0%
ρ 1,2 = Coefficient correlation between the returns of two stock = -1
σp = √ (0.4)2 * (16.6)2 + (0.6)2 * (17)2 + 2 * 0.4 * 0.6 * -1 * 16.6 * 17
σp = √ 0.16 * 275.56 + 0.36 * 289 – 135.456
σp = √ 44.09 + 104.04 – 135.456
σp = √12.674 = 3.56%
6. Coefficient correlation between returns of two common stocks
Year GM
common
stock
returns (x)
Ford
Common
Stock return
(y)
xy x2 y2
2003 -10% -3% 0.30% 1.00% 0.09%
2004 18.50% 21.29% 3.94% 3.42% 4.53%
2005 36.87% 44.25% 16.31% 13.59% 19.58%
2006 14.33% 3.67% 0.53% 2.05% 0.13%
2007 33% 28.30% 9.34% 10.89% 8.01%
Sum (∑) 93% 95% 30% 31% 32%
Coefficient correlation = n(∑xy) – (∑x) (∑y) / √ [n∑x2 – (∑x)2] [n∑y2 – (∑y)2]
= 5 * (30) – (93) * (95) / √ [5* 31 – (93)2] [5 * 32 – (95)2]
= 150 – 8835 / √ [155 - 8649] [160 - 9025]
= -8685 / √ [-8494] [-8865]
= -8685 / √75,299,310
= -8685 / 8677.52
= -1
7. Discussion of Modern Portfolio Theory
Modern Portfolio Theory or MPT was given by Harry Markowitz which is popularly
known as a method for choosing investments in an attempt to maximize overall returns at an

acceptable level risk level. The main component of this theory is diversification of investment
into different classes of assets because of their differentiating risk and returns. Many investments
are high return and high risk while other are low risk and low return and as per the argument of
Markowitz, investors could get better results by selecting an optimal mix of two assets or stocks
on the basis of their individual level of risk tolerance. Accordingly, with the help of MPT,
investors are able to construct efficient and diversified portfolios by ensuring maximum returns
at a level of risk acceptable to them (Chao, Tao and Zeng, 2019).
As per the arguments given in MPT, the risk and return associated with a particular investment
or stock should not be viewed alone however it needs to be evaluated in terms of their impact on
overall risk and return associated with the portfolio.
Within the modern portfolio theory, it has been assumed that investors are generally risk – averse
where the condition is such that investors prefer less – risky portfolio to that of riskier one at a
given level of return. Due to the prevalence of risk aversion, investments are made in multiple
assets or stocks through portfolio construction (Kumar, 2018).
With regard to portfolio constituting GM common stock and Ford common stock, the portfolio
risk and return comes out as 3.56% and 18.756% respectively, where 40% and 60% weights are
given to GM and Ford stocks respectively. GM common stock is found to be low risk and low
return stock while Ford common stock is found to be high risk and high return stock. Also, the
correlation coefficient between the stock returns comes out as -1 which indicates that the two
stock returns are negatively related where rise in returns of one would lead to fall in other with
the same proportion (Mittal, Bhattacharya and Mandal, 2021). If investor go for raising the
proportion of GM common stock in the portfolio against Ford common stock, then the overall
portfolio risk and return will fall because it is a low risk and low return investment avenue.
For instance, if 60% and 40% weights would be allotted to GM and Ford common stock, the
resultant risk and return would be 3.16% and 18.68% respectively which lower than the previous
portfolio having 40% and 60% of GM and Ford common stock.

REFERENCES
Chao, X., Tao, X. and Zeng, L., 2019. Application of Markowitz's Portfolio Theory in Obtaining
the Best Portfolio in the Stock Market. Advances in Social Science, Education and
Humanities Research, 309.
Kumar, V., 2018. A Simplified Perspective of the Markowitz Portfolio Theory. International
Journal of Research and Analytical Reviews, 5(3), pp.193-6.
Mittal, S., Bhattacharya, S. and Mandal, S., 2021. Characteristics analysis of behavioural
portfolio theory in the Markowitz portfolio theory framework. Managerial Finance.