Descriptive Analysis Of A Portfolio With Four Stocks Listed On The London Stock Exchange

Overview and descriptive analysis

The purpose of this section is to create a portfolio using four stocks listed in the London stock exchange using the FTSE All-shares index as the market portfolio. The stocks that were chosen for the purpose of investment included Ashtead Group Plc, JD sports fashion, AstraZeneca Plc and Glencore PLC. The company are selected on the basis of positive share price performance in the recent five years and belong to a multiple sector which ensures that the diversification of the portfolio is maintained. The following part summarizes the nature of business of the above-mentioned stocks:

Ashtead Plc – It is an equipment rental company which is based in United Kingdom and operating under the brand name of Sunbelt rentals in United States, Canada and the United Kingdom. The company is involved in renting various construction, industrial and general equipment across different areas and to a diverse group of customers. The company share price has risen significantly in the past ten years which has supported our decision to include the stock in our portfolio. It has roughly 861 locations in the United States, 77 locations in Canada, and 188 locations in the United Kingdom. Lifting, powering, generating, moving, digging, compacting, drilling, supporting, scrubbing, pumping, directing, heating, and ventilating are all possible with the equipment that the company operates and rents to the public. The business model of the company includes purchasing a range of equipment from various business dealers and then renting it to the common public on a short term basis.

JD sports fashion Plc – The company is based in United Kingdom and is a multichannel retailer of branded sports and casual fashion apparels including global brands like Nike, Puma and adidas. The brands of the company also include The North Face, Pink Soda, and Supply & Demand. It operates in the segment of sports and fashion and has a diverse base of customer around the country to whom it sells its brands like JD, Chausport, Size, Scotts, Blacks, Millets, Sprinter, Tessuti, Tiso, Nicholas Deakins, Kukri, Focus, Source Lab, Naylors, and Go Outdoors brands through the online channels.

AstraZeneca Plc – AstraZeneca Plc (AstraZeneca) is a biopharmaceutical firm that specializes in the development, manufacture, and marketing of prescription medications. It works on products for pulmonary, cardiac, renal, and biochemical ailments, as well as cancer, autoimmune, infection, and brain disorders. Biologics, prescription medications, and vaccinations are among the company’s major products which its sells across the globe. The company has a business model where it contracts local based wholly owned local marketing companies, distribution channels and representative offices. The market for the company includes Europe, America, Asia, Africa and Australia. 

Ashtead Plc

Glencore Plc – It is a metal, mineral and energy company headquartered in Switzerland where it is engaged in producing and marketing the mentioned commodities. The company caters to the sector of auto, steel, power generation and supply, manufacturing of battery and oil companies. Marketing, Industrial, Corporate and Other are the segments in which it works and it is involved in sale and purchasing of physical commodities and providing several value-added services to the customers. The industrial section is focused towards selling of commodities beyond the cost of production or sales.

The following section includes a descriptive analysis of the companies including metrics like returns, variance, standard deviation, semi-deviation, and other central dispersion measures like skewness and kurtosis.

• Returns – The daily returns of the stock are calculated using the formula [1+ (next period price/previous period price)-1 which converts the returns into factors. The factors are then multiplied with each other to get the daily returns of the stock price which is present in the table below:

Daily average returns
AHT.L	JD. L	AZN.L	GLEN.L
230.6721%	166.0839%	62.3770%	74.2964%

The stock of Ashtead Plc has provided the highest daily returns compared to all other stocks in the portfolio followed by JD sports fashion Plc. The least amount of returns is provided by the stock of AstraZeneca Plc with a daily average return of 62.3370%. The daily returns calculated are annualized using the formula (1+R) ^ (252/no of observations) where the number of observations were the total number of returns. The following table summarizes the annualized daily returns provided by each stock.

Annualized returns
AHT.L	JD.L	AZN.L	GLEN.L
47.31%	37.30%	17.00%	19.72%

Variance – The variance is a metric that measures how close values are to the data’s mean. It’s an important metric for assessing the risks in a portfolio based on the individual returns of the assets (Laha, Arbaiya and Linb 2020). The variance of the stock is calculated using the (Varianace.S) function in excel. The following table represents the daily variance of each stock:

Daily variance
AHT.L	JD.L	AZN.L	GLEN.L
0.0618%	0.0852%	0.0274%	10.7065%

Glencore Plc has the highest daily variance coefficient as the stock price has been very volatile during the past three years. The stock is very risky for investment due to the high variance associated with it.

Standard deviation – It is a statistical measure which measures the dispersion of a date set around a mean in a quantifiable manner. It can be defined as the square root of the variance that was obtained in the step above. The following table represents the daiky as well as annualized standard deviation of all the stocks analyzed:

Daily SD
AHT.L	JD. L	AZN.L	GLEN.L
2.4851%	2.9190%	1.6561%	32.7208%

Annualized SD
AHT.L	JD.L	AZN.L	GLEN.L
39.4495%	46.3381%	26.2891%	519.4274%

The highest daily standard deviation is experienced by the stock of Glencore Plc to the extent of 32.72%.

Semi-deviation – It is a statistical measure that helps us to measure the below mean fluctuations in the return on investment. It helps to understand the riskiness of an investment by assessing the worst-case performance of the stock. Semi-deviation of stocks has been calculated using the formula:

JD sports fashion Plc

Semi-deviation = n1? × rt? < Average∑n? (Average − rt?)2  

Where n stands for the total number of observations from the data analyzed, rt? represents the observed value and average is the mean value of the individual stock returns for three years. The following table represents the daily and annualized semi deviation of the stocks:

Semi Deviation
AHT.L	JD.L	AZN.L	GLEN.L
1.9162%	2.0747%	1.0927%	4.2335%

Annualized Semi-deviation
AHT.L	JD. L	AZN.L	GLEN.L
30.4195%	32.9341%	17.3464%	67.2046%

 The stock that would be contributing the most in case of worst-case performance of the portfolio would be the stock of Glencore Plc as suggested by the daily and annualized semi-deviation value of 4.23% and 67.20% respectively.

Normalcy in stock distribution – The normal distribution, also known as the Gaussian distribution, is a symmetric distribution centred on a data set’s mean value, implying that data is distributed evenly on both sides. A bell curve represents a normal distribution on a graph (Kim 2015). Skewness, on the other hand, investigates the tail of the distribution by discriminating between heavy and light tailed features, whereas skewness evaluates the symmetrical characteristics of a data set (Cain, Zhang and Yuan 2017). Using Skewness and kurtosis values of the stock, we can measure the normalcy of stock returns using a set of criteria and factors. A properly distributed data collection has a skewness of zero and a kurtosis of three (Mei 2017).

The skewness and kurtosis of the stock are represented in the table below:

Skewness
AHT.L	JD.L	AZN.L	GLEN.L
-0.410796	0.5514427	0.215367134	27.20697948

Kurtosis
AHT.L	JD. L	AZN.L	GLEN.L
16.743889	12.538841	4.076211623	753.6401777

Ashtead Plc has negatively skewed returns which implies that the stock generates frequent small gains and significant losses infrequently. The kurtosis of the stock suggests that distribution of a stock have heavier tails compared to a normal distribution.

The stocks of JD Sports fashion, AstraZeneca Plc and Glencore Plc has positively skewed returns which implies that the stock returns are not normally distributed with majority of the returns being on the negative side with few extreme outcomes on the positive side as it is suggested by the Kurtosis values of all the stocks.

Value at Risk (VaR) – It is a statistical concept which analyzes and quantifies the extent of possible losses experienced by a stock or a portfolio. The following table represents the 1%, 5% and 10 % Value at Risk calculated for all the stocks based on historical method:

The VaR of 1% represents the maximum losses experienced by individual stocks with 1% chances of exceeding the reported value. Similarly, 5% and 10% VaR represents the maximum possible losses experienced by each stock with 5% and 10% chances of exceeding the losses.

AstraZeneca Plc

Covariance is a statistical metric that compares the movements of two or more equities. Positive covariance between stocks indicates that stock returns are moving in the same direction, whilst negative covariance indicates that stock returns are moving in the opposite direction. It aids in evaluating the advantages of diversity gained in a portfolio, since investors prefer equities with negative covariance between themselves. The difference between the stock’s daily returns and the stock’s average return across both stocks is multiplied to get the stock’s covariance (Carnia 2019).

Correlation and covariance are similar in that they both assess the movement of two or more equities. The distinction between correlation and covariance is that correlation lends a numerical number to the strength of the link between two stock returns, but covariance does not. A correlation of more than 1 means that the stock returns moved in the same direction irrespective of negative or positive values. A negative correlation implies that the stocks move in opposite direction (Wang, Xei and Chen 2017). A zero or no correlation implies that the stocks that are being compared does not exhibits any sort of relationship. A correlation can be determined by dividing the covariance by the product of the standard deviation of both the stocks.

The following table represents the correlation and covariances between the stocks calculated using data analysis functions of excel:

All the stocks in the portfolio have positive covariance with each other although it is very low. The stocks of AstraZeneca PLC and JD Sports fashion PLC have exhibited the least covariance between each other, while the strongest covariance is exhibited by the stocks of JD Sports fashion Plc and Ashtead Plc.

The following table represents the correlation coefficient amongst the stocks included in the portfolio:

Although no stock in the portfolio is negatively linked with another, no stock in the portfolio has a correlation of more than one with the other, implying that the portfolio has achieved some portfolio diversity. The stocks of Glencore Plc and AstraZeneca Plc have the lowest correlation in the portfolio, with a correlation value of 0.011766. With a score of 0.51, the stocks of JD Sports fashion Plc and Ashtead Plc have the strongest positive correlation.

The movement of a stock in respect to the wider market is measured by its beta. A beta number greater than one indicates that the stock is extremely sensitive to the market and moves more than it does. A stock with a beta of less than one is less market sensitive and, if included in a portfolio, would operate as a diversifier. The stock beta values are determined by regressing each stock’s stock returns against the returns generated by the UK FTSE All share index for a three-year period beginning on January 1, 2019 and ending on January 31, 2021. The beta values generated in Excel using the correlation function are shown in the table below:

BETA values
AHT.L	JD.L	AZN.L	GLEN.L
0.72	0.59	0.38	0.04

Glencore Plc

All of the equities in the portfolio have betas of less than one, which benefits the portfolio by making it less sensitive to market movements. Including all four equities in the portfolio would be favorable to the overall performance of the portfolio. The stock of Glencore Plc, on the other hand, has the lowest beta, implying that it would give significant diversification benefits in a portfolio when compared to the other stocks. When compared to the other three companies in the portfolio, Ashtead Plc has the largest beta. The portfolio beta based on an equal weight assigned to all the stocks was around 0.43.

To analyze whether the stocks are over or underpriced, the Capital Asset Pricing Model has been used to determine the expected return from the stock based on the beta calculated in the step above. The CAPM method has three significant variables i.e. risk-free rate of return, market premium and beta of the stock, using which it estimates the required rate of return for a stock by an investor.

The risk-free rate was assumed to be equal to 2%, which was converted into daily return. The market return was calculated as the average daily return of the UK FTSE All Shares index for the past three years. The CAPM implied expected rate of return for the stocks are represented in the table below:

CAPM
AHT.L	JD.L	AZN.L	GLEN.L
0.0185%	0.0161%	0.0123%	0.0062%

The realized rate of return from the stock in the past three years are represented in the table below:

Realized return
AHT.L	JD.L	AZN.L	GLEN.L
0.1850%	0.1682%	0.0760%	1.1504%

After analyzing the CAPM implied required rate of return and the realized return of the stock it can be concluded that the stocks are underpriced as it has provided excess returns for the period analyzed. The excess returns provided by the stocks are represented in the table below:

Excess return
AHT.L	JD.L	AZN.L	GLEN.L
0.1666%	0.1521%	0.0636%	1.1441%

The most underpriced stock according to the analysis is the stock of Glencore Plc with an excess return of 1.1441 percent followed by the stock of Ashtead Plc with an excess return of 0.1666 percent.

This section contains the financial analysis of two stocks chosen out from the four stocks included in the section 1 to create a minimum variance portfolio for a client having a required rate of return of 10 percent. The two stocks that were chosen to be included in the portfolio were the stocks of Ashtead Plc and JD sports fashion Plc.

Ashtead Plc – The firm has performed well in the past, with an EPS growth rate of 12.6 percent in 2021 and an anticipated growth rate of roughly 37.5 percent in 2022, considerably ahead of the industry’s growth (Nasdaq.com 2022). The company’s cash flow growth has also been increasing, with a rate of 141.1 percent compared to the industry average of -0.6 percent.

Metrics Analysis

Financial analysts have given the company a high rating, and many stock analysts suggest it as a buy. With an annualized return of about 47 percent, the stock calculated in section 1 had the highest historical return of all. With a Sharpe ratio of roughly 1.14, the stock likewise has the highest Sharpe ratio among the four stocks. We have decided to add the stock in the portfolio based on the aforementioned considerations. Sports fashion Plc – According to (Simplywall.com 2022), the company’s earnings are predicted to increase by 33% in the next year, resulting in strong cash flows and a beneficial impact on the company’s share value. Despite the fact that the stock is now selling at a premium to its industry rivals, the good price performance of the firm, as shown by an annualized return of 37.30 percent estimated in section, suggests that it should be included in a portfolio. Furthermore, the stock’s Sharpe ratio is the second best among the four equities examined.

The most common form of investment technique in the asset management business is the minimal variance portfolio, which is a portfolio designed with the goal of maximizing returns while reducing risk. The minimum variance portfolio estimated using the solver function of the excel suggests an investment of 66.07 percent in the stock of Ashtead Plc and 33.93 percent in the stock of JD sports fashion. The variance of the portfolio is 0.134466 and the returns associated with this level of variance is 43.91 percent. The following efficient frontier graph represents all the combinations asset weights resulting in a range of portfolios:

The minimum variance portfolio which suggests investing 66.07 percent in the stock of Ashtead Plc and 33.93 percent in the stock of JD sport fashion is the optimal portfolio for the client. The mean of such a portfolio is 43.91 percent whereas the standard deviation of the portfolio is around 36.67 percent.

• Treynor ratio – It is also known as the reward to volatility ratio and it measures the excess return generated by the portfolio for each extra unit of risk undertaken by the portfolio (Stefanus and Robiyanto 2020). The excess returns are calculated comparing the portfolio return with the risk-free rate of return. The Treynor ratio of the minimum variance portfolio is around 0.623668.
• Jensen’s alpha – It is a risk adjusted performance which measures the excess return provided by the portfolio compared with the expected return predicted by the Capital Asset Pricing Model which utilizes the risk-free return, beta and average market return (Breloer, Huhn and Scholz 2016). The Jensen’s alpha of the MVP portfolio is around 37.21 percent.
• Sharpe ratio – The ratio which measures the excess return of a portfolio over and above the risk-free rate of return by taking into account the standard deviation of the portfolio is called Sharpe ratio. It measures the excess return earned by a portfolio by taking one extra unit of return. The Sharpe ratio of the portfolio is around 1.14 which is considered to be healthy.
• Information ratio – Information ratio measures the returns of portfolio over and above the returns of the benchmark which is generally an index comparing them with the volatility of the returns. The benchmark index here is the UK FTSE All Shares index the returns of which are compared with the portfolio return. The difference in the return is divided by the standard deviation of the excess returns to arrive at the information ratio. The information ratio of the portfolio is around 0.097277.
• M2 measure – It is the Modigliani risk adjusted performance measure calculated using the Sharpe ratio, standard deviation of the benchmark and the risk-free return. The M2 measure of the portfolio is around 0.03368.

References

Breloer, B., Lea Hühn, H. and Scholz, H., 2016. Jensen alpha and market climate. Journal of Asset Management, 17(3), pp.195-214.

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Carnia, E., 2019, October. Optimization of the mean-absolute deviation portfolio investment in some mining stocks using the singular covariance matrix method. In Journal of Physics: Conference Series (Vol. 1315, No. 1, p. 012002). IOP Publishing.

Is Now An Opportune Moment To Examine JD Sports Fashion plc (LON:JD.)? (2022). Available at: https://simplywall.st/stocks/gb/retail/lse-jd./jd-sports-fashion-shares/news/is-now-an-opportune-moment-to-examine-jd-sports-fashion-plc (Accessed: 9 March 2022).

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Nasdaq.com. 2022. Here is Why Growth Investors Should Buy Ashtead Group PLC (ASHTY) Now. [online] Available at: <https://www.nasdaq.com/articles/here-is-why-growth-investors-should-buy-ashtead-group-plc-ashty-now> [Accessed 9 March 2022].

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