This report is aimed at performing risk and return analysis of stocks and portfolio applying various statistical measures such as arithmetic mean, geometric mean, regression, variance, covariance, and correlation. Arithmetic mean and geometric mean are used to compute average returns and variance is the indicator of risk. The covariance and correlation are considered to be effect in finding out the relationship between the returns of two stocks. This identification of relation is necessary to formulate an optimum portfolio. In this report, three stocks namely Google, Amazon, and Rio Tinto have been selected for analysis. Further, a portfolio having composition of these stocks with equal weights has also been formed to analyze the risk and return in relation to portfolio. Apart from this, this report also highlights the significance of portfolio in terms risk diversification.
Alphabet Inc also popularly known as Google is a USA based company engaged in the business of online advertising and branding. The company was founded in the year 1998 and since then it grown manifold spreading business in every corner of world. The stock of Alphabet Inc is listed on Nasdaq. The financial performance of the company is improving rapidly. In the year 2017, the company reported revenues of $110,855 million and net profit of $12,662 million (Yahoo finance, 2018).
Amazon is the world leader in online retail sales of consumer goods. The company having its headquarters in United States operates globally in many countries. Apart from retailing of consumer goods, the company also provides web services through one its segments namely Amazon Web Services. The company was founded in the year 1994 and since then it has expanded surprisingly to reach the customers in every part of the world. The stock of company is listed on Nasdaq. In the year 2017, the company reported revenues of $177,866 million and net profit of $3,033 million (Yahoo finance, 2018).
Rio Tinto is a giant company engaged in the business of exploration of minerals such as iron ore, coal, gold, copper and diamond. The company was founded in way back 1873 and since then it has operated successfully. The company has its headquarters in UK and it operates globally in many countries. The company’s stock is listed on New York Stock Exchange in USA. As per the financial statements of 2017, it generates revenues of $40,030 million with net profit of $8,762 million (Yahoo finance, 2018).
Taking the price data of past 28 weeks (Excel attached), arithmetic and geometric mean of returns have been computed. The arithmetic mean shows simple average of the returns over the period. The geometric mean is improved version to calculate the average of data series. Both the arithmetic mean and geometric mean are used to assess the performance of stocks and portfolios. Applying the arithmetic mean and geometric mean on the historical data set one can get the basis to predict the future trend in returns on the stocks (Kevin, 2015). In the current report, the arithmetic mean and geometric mean have been computed in relation to three selected stocks and the market index, the results of which are presented as below:
|
S&P 500 |
|
Amazon |
Rio Tinto |
||
|
Arithmetic mean |
0.20% |
0.45% |
1.50% |
0.81% |
|
|
Geometric mean |
0.17% |
0.37% |
1.42% |
0.73% |
Further, apart from the analysis of return, the analysis of risk is of equally importance. Hence, in order to address the risk, variance, covariance, and correlation of stocks have been computed (Baker & English, 2011). The variance indicates the total risk of stock which comprises of systematic as well as unsystematic risk. The covariance and correlation shows relationship between the returns of two assets. The summary of results of data analysis of the present case is shown below:
|
Variance |
0.06% |
0.17% |
0.18% |
0.17% |
|
|
Co-variance Matrix |
|||||
|
S&P 500 |
|
Amazon |
Rio Tinto |
||
|
S&P 500 |
1 |
||||
|
|
0.0852% |
1 |
|||
|
Amazon |
0.0569% |
0.1093% |
1 |
||
|
Rio Tinto |
0.0683% |
0.0982% |
0.0541% |
1 |
|
|
Correlation coefficients |
|||||
|
S&P 500 |
|
Amazon |
Rio Tinto |
||
|
S&P 500 |
1.00 |
||||
|
|
90.1967% |
1.00 |
|||
|
Amazon |
57.9792% |
65.5352% |
1.00 |
||
|
Rio Tinto |
61.4784% |
32.1401% |
32.1401% |
1.00 |
From the figures presented above, it could be observed that S&P 500 (market index) is showing arithmetic mean and geometric mean of 0.20% and 0.17% respectively. This shows that the market earns on an average a return of 0.20% over a period of week. Further, the selected stocks are also showing positive mean values which indicate that these stocks are providing satisfactory return to the investors. All three stocks are generating higher returns as compared to the stock market. Among the stocks, Amazon could be observed to be generating the highest returns. Further, observed that Google has been the lowest earner among the stock but it is earning returns higher than the market.
A trend in the stock prices of Google over the period of past 28 weeks is shown in the chart given below:
It could be observed that the stock performed exceptionally well in the month of January 2018. The stock prices reached to the peak during the month of January. The company’s financial performance in the fourth quarter of 2017 attracted the investors in January 2018 and this caused the share price to go record high (Statt, 2018). However, the rising trend could sustain for long and the stock started slopping downward in the immediately next month. Google though performed well in the fourth quarter as compared to the previous quarter but it was not better than the industry average. This caused change in the market sentiments and stock went down.
Rio Tinto could be observed to be growing gradually over the period of past 6 months. The stock went high in the month of February and March because the company reported good financial performance in the preceding quarter. Then the stock dropped down in April 2018. The drop in stock in April could be attributed to the overall mining industry downturn due to slow increase in demand of minerals.
The variance of S&P 500 (Market index) is 0.06% which is lower than the variance of stocks. The variance of Google, Amazon and Rio Tinto, is 0.17%, 0.18%, and 0.17% respectively. This shows that the risk of stocks taken individually is higher than the risk of market.
The covariance of stocks and market and covariance among the stocks is positive. However, the covariance values are lower than 1 which indicates that the covariance is less than perfect positive. This indicates an opportunity to diversify and reduce the risk by forming a portfolio of stocks (Baker & English, 2011).
In order to form a portfolio, the investment has been made Google, Amazon, and Rio Tinto in equal proportions. The return and variance of equally weighted portfolio has been computed as shown below:
|
Stocks |
||||
|
|
Amazon |
Rio Tinto |
||
|
Weights |
33.3333% |
33.3333% |
33.3333% |
|
|
Weekly Average Returns |
0.4512% |
1.5039% |
0.8146% |
|
|
Variance |
0.1670% |
0.1802% |
0.1698% |
|
|
Covariance |
0.1093% |
0.0683% |
0.0982% |
|
|
Portfolio return |
0.9232% |
|||
|
Variance |
0.0614% |
It could be observed that the portfolio weekly return is worked out to be 0.9232% and variance is 0.0614%.
The return of portfolio is greater than the return on market index which implies that the portfolio is performing better than the market. Further, comparing the return of portfolio with the stocks individually, it could be observed that the portfolio is earning higher returns than Google (0.45%) and Rio Tinto (0.81%). However, Amazon with a return of 1.50% is outperforming the portfolio.
The variance of portfolio is 0.0614% which is equal to the variance of S&P 500 indicating that the portfolio is not riskier than market. It has been observed that the risk is reduced significantly by forming a portfolio. The individual variances of stocks are very high comparing with the variance of portfolio. Thus, overall it could be inferred that the risk and return has been optimized by forming the portfolio of stocks (Pandya, 2013).
Part-III (a)
The risk free rate of return has been computed using the 26 weeks yield on 180 days Treasury bill. The average of weekly yield is worked out to be 1.56%. Since, it is annualized therefore; it has been converted into weekly yield which works out to be 0.0286%. Please refer attached excel for calculations and data.
Part-III (b)
The summary of results of regression analysis applied on the discrete returns of stocks is shown as below:
The security characteristics line is the graphical presentation of the systematic risk of a security and the return earned on that security. The slope of security characteristics line is known as beta and the point of interception is called alpha. Beta represents the portion of security’s return earned driven by the market movements while the alpha is constant. Thus, in plotting the security market, two important elements are necessary these are alpha and beta (Chance & Brooks, 2015). The computation of these elements is shown in the table given below:
|
Security Characteristic Line |
|||||||
|
|
Amazon |
Rio Tinto |
|||||
|
Y (return of stock) |
0.4512% |
1.5039% |
0.8146% |
||||
|
X (return of s&p 500) |
0.2005% |
||||||
|
b (beta) |
1.5343 |
1.0244 |
1.0544 |
||||
|
a (alpha) |
0.0076 |
0.0171 |
0.0103 |
||||
|
Characteristic Line of stocks |
|||||||
|
|
Y= -0.0076+1.5343*0.2005% |
||||||
|
Amazon |
Y= -0.0171+1.0244*0.2005% |
||||||
|
Rio Tinto |
Y= -0.0103-1.0544*0.2005% |
||||||
|
Characteristic Line of portfolio |
|||||||
|
Y (return of portfolio) |
0.9232% |
||||||
|
X (return of s&p 500) |
0.2005% |
||||||
|
b (beta) |
1.19 |
||||||
|
a (alpha) |
0.0116 |
||||||
|
Y= -0.0116+1.19*0.2005% |
Thus, the beta of Google, Amazon, and Rio Tinto has been found to be 1.53, 1.02, and 1.05 times respectively. Beta shows the relative volatility of the stocks to the market as a whole (Chance & Brooks, 2015).
The graphical representation of security characteristics line showing the prediction of Y is as below:
It could be observed that the characteristics line of Google predicting Y is quite volatile which shows that the volatility of the stock relative to the market is high. High volatility of the stock relative to the market means high beta.
The characteristics line of Amazon is less volatile as compared to Google which shows that Amazon has lower beta than Google. The Beta of Google is 1.54 times as against the beta of 1.02 times of Amazon.
The characteristics line of Rio Tinto is similar to that of Amazon. This implies that the volatility level of returns of Amazon and Rio Tinto is similar. The beta values of Amazon and Rio Tinto are also similar.
Further, Jensen’s Alpha has also been computed to assess the performance of stocks and portfolio. The Jensen’s alpha is computed by deducting the risk free rate of return from the CAPM return of the stock and dividing the resultant figure by standard deviation. The summary of results of which are shown below:
|
Jensen’s Alpha |
||||
|
CAPM-RF |
||||
|
|
Amazon |
Rio Tinto |
Portfolio |
|
|
CAMP |
0.2926% |
0.2047% |
0.2099% |
0.2336% |
|
RF (risk free rate) |
0.0282% |
0.0282% |
0.0282% |
0.0282% |
|
Jensen’s Alpha |
0.2644% |
0.1765% |
0.1817% |
0.2055% |
Apart from the above, the analysis of risk has been done in more detail by segregating the total risk into systematic and unsystematic components (Kevin, 2015). The summary of results has been shown as under:
|
Total risk, systematic and unsystematic risk |
||||
|
|
Amazon |
Rio Tinto |
Portfolio |
|
|
Total risk (weekly) |
0.17% |
0.18% |
0.17% |
0.06% |
|
Total risk (annualized) |
9.43% |
10.21% |
9.59% |
3.16% |
|
Systematic risk (beta)^2 |
235.41% |
104.94% |
111.18% |
142.17% |
|
Unsystematic risk |
-225.98% |
-94.73% |
-101.59% |
-139.00% |
The beta shows systematic risk of stocks (Kevin, 2015). It could be observed that beta of Google (1.53) is higher than the beta values of other two stocks namely Amazon (1.02) and Rio Tinto (1.05). This analysis shows that Google is riskier than other two stocks.
The bifurcation of total risk into systematic and unsystematic shows that the unsystematic risk is negligible. The entire risk of stocks and portfolio is absorbed by the systematic risk factor only. Thus, the unsystematic risk (company specific risk) is not a material concern for the investors.
Further, Jensen’s alpha has been observed to be 0.2644%, 0.1765%, and 0.1817% in case of Google, Amazon, and Rio Tinto. This shows that stock of Google better performer comparing to other two stocks. Further, the Jensen’s alpha of portfolio has been found to be 0.2055% which indicates that the portfolio is performing even better than the individual stocks (Kevin, 2015).
The analysis of risk and return of a stock is critical for the investor to decide whether to invest in that stock or not (Kevin, 2015). For this purpose, an analysis of risk and return through various statistical measures such as arithmetic mean, geometric mean, variance, covariance, and correlation has been done. The analysis of return using the historical data gives a solid basis to predict the future trend in the stock’s performance. Therefore, the analysis in relation to the return of stocks and portfolios is of great value to an investor. Further, the statistical measures applied to assess the risk also provide a great help to the investor to make a choice for investment.
In order to form a portfolio, it is of paramount importance to know the relationship between the returns of stocks. The portfolio comprising stocks with less perfect positive correlation would result in risk diversification. Therefore, it is important to analyze the relationships between the returns of two stocks to optimize the return and risk through formation of portfolio. Apart from this, an analysis of total risk segregating it into systematic and unsystematic has been done in this report which is also important for an investor. The investor should know the degree of risk caused by the systematic and unsystematic risk factors. This knowledge would be helpful in designing in a perfect portfolio with optimum risk and return.
Thus, the analysis done in relation to the risk and return in this report is highly useful for the investors. However, this analysis is subject to certain limitations. For instance, future aspect of the performance of stocks is ignored in this analysis as it confines to historical data only. Further, this analysis is purely based on the data and figures and it ignores the other factors such as reputation of company in market. Moreover, this analysis also does not provide insight into the financial performance of the company as it confines only to the analysis of stock prices.
Therefore, in order to get insight of the financial performance, ratio analysis or trend analysis of financial performance over the period of past few years is desirable. Further, an analysis industry in relation to future performance could also be conducted to get overview of the industry wide growth or downturn.
References
Baker, K.H. & English, P. 2011. Capital Budgeting Valuation: Financial Analysis for Today’s Investment Projects. John Wiley & Sons.
Chance, D.M. & Brooks, R. 2015. Introduction to Derivatives and Risk Management. Cengage Learning.
Kevin, S. 2015. Security Analysis And Portfolio Management. PHI Learning Pvt. Ltd.
Pandya, F.H. 2013. Security Analysis and Portfolio Management. Jaico Publishing House.
Statt, N. 2018. Alphabet profit miss sends stock down, but Google ad and cloud sales remain strong. Accessed May 14, 2018 https://www.theverge.com/2018/2/1/16961214/alphabet-google-q4-2017-earnings-report-announcement-youtube
Yahoo finance. 2018. Alphabet Inc: Financial. Accessed May 14, 2018 https://finance.yahoo.com/quote/GOOG/financials?p=GOOG
Yahoo finance. 2018. Amazon Inc: Financial. Accessed May 14, 2018 https://finance.yahoo.com/quote/AMZN/profile?p=AMZN
Yahoo finance. 2018. Rio Tinto Plc: Financials. Accessed May 14, 2018 https://finance.yahoo.com/quote/RIO/financials?p=RIO
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