Risk, Return, Standard Deviation of Walmart and MacDonald and their Portfolio. Yahoo Finance Data.(Corporate Finance)

The paper focuses on understanding the expected rate of return and the risk associated with an individual as well as the portfolios of the securities. Further, it intensifies its numerical analysis on statistical parameters like correlation coefficient, mean, standard deviation, coefficient of variation and their implication on portfolio. For the purpose, two companies are considered as a sample, they are Walmart(WMT) and Macdonald(MCD).  The data are pulled from finance.yahoo.com for previous 20 years and analysis is carried out.

Expected Rate of Return and Risk of a security.

The annual rate of return is a return expected by an investor from his investment. So, if an investor has invested P0 today and gets P1 at the end of the year along with dividend of D1. Than,

Expected Return E(r)= (P1-P0 + D1) / P0   eqn…………(i)

It can be written as = (P1-P0)/P0 + (D1/P0)

= Capital Gain + Dividend Yield

Whereas the risk associated with the return of a security is measured by standard deviation (σ)

Standard deviation(σ) = (1/N ∑ (ri-E(r)) ^2) ^(1/2)  eqn…………(ii)

Where ri is the return of each period and N is the number of data/samples.

E(r) is the mean of the data set, but for the purpose, we have use the Microsoft Excel to calculate the Standard deviation(σ). Let us begin with the annual return and standard deviation calculation for Macdonald(MCD)

Year	Close Price	Dividends	Return	Rate of Return
1998	$39.41
1999	$37.38	0.3828	-1.6485	-0.0418
2000	$29.35	0.4300	-7.5950	-0.1927
2001	$27.18	0.4500	-1.7200	-0.0436
2002	$14.24	0.4700	-12.4700	-0.3164
2003	$25.74	0.8000	12.3000	0.3121
2004	$32.39	1.1000	7.7500	0.1967
2005	$35.01	1.3400	3.9600	0.1005
2006	$44.35	2.0000	11.3400	0.2877
2007	$53.58	3.0000	12.2300	0.3103
2008	$58.02	3.2500	7.6900	0.1951
2009	$62.43	4.1000	8.5100	0.2159
2010	$73.67	4.5200	15.7600	0.3999
2011	$99.05	5.0600	30.4400	0.7724
2012	$95.29	5.7400	1.9800	0.0502
2013	$94.17	6.2400	5.1200	0.1299
2014	$92.44	8.1800	6.4500	0.1637
2015	$123.78	6.8800	38.2200	0.9698
2016	$122.57	7.2200	6.0100	0.1525
2017	$171.14	7.6600	56.2300	1.4268

Table 1: Calculation of Annual Return for MCD from 1998 to 2017

Similarly, the annualized rate of return for Walmart(WMT) is depicted below: -

Year	Price	Dividends	Return	Rate of Return
1998	43
1999	54.75	0.4	12.15	0.282558
2000	56.79	0.48	2.52	0.058605
2001	59.98	0.56	3.75	0.087209
2002	47.79	0.6	-11.59	-0.26953
2003	53.84	0.72	6.77	0.157442
2004	52.4	1.04	-0.4	-0.0093
2005	46.11	1.2	-5.09	-0.11837
2006	47.68	1.34	2.91	0.067674
2007	50.74	1.76	4.82	0.112093
2008	47.11	1.9	-1.73	-0.04023
2009	53.43	2.18	8.5	0.197674
2010	56.07	2.42	5.06	0.117674
2011	61.36	2.92	8.21	0.19093
2012	69.94	3.18	11.76	0.273488
2013	74.68	3.76	8.5	0.197674
2014	84.98	3.84	14.14	0.328837
2015	66.36	3.92	-14.7	-0.34186
2016	66.74	4	4.38	0.10186
2017	106.59	4.08	43.93	1.021628

Table 2: Calculation of Annual Return for WMT from 1998 to 2017

Till now, we have pulled the data from finance.yahho.com and calculated the annualized return now let us calculate the expected return of the data set and its standard deviation for each set of security data.

MCD	WMT
-0.0418	0.2826
-0.1927	0.0586
-0.0436	0.0872
-0.3164	-0.2695
0.3121	0.1574
0.1967	-0.0093
0.1005	-0.1184
0.2877	0.0677
0.3103	0.1121
0.1951	-0.0402
0.2159	0.1977
0.3999	0.1177
0.7724	0.1909
0.0502	0.2735
0.1299	0.1977
0.1637	0.3288
0.9698	-0.3419
0.1525	0.1019
1.4268	1.0216

Table 3: Annual Return for MCD and WMT from 1998 to 2017

                         Summary of findings

Particulars	MCD	WMT
Expected ROR	0.2678	0.1272
Standard Deviation	0.4076	0.2785

Correlation between the return of WMT and MCD

The correlation coefficient gives the direction of the relation between the available data of the securities. This analysis helps us to know the direction of pattern between the flow of returns of WMT and MCD.

The correlation coefficient between WMT and MCD (ρ) = 0.472,

The correlation coefficient has major implication while investing in portfolio. The negative the correlation helps to drastically reduce the risk of portfolio whereas the positive won’t. we can infer from here that the return of WMT and MCD moves in the same direction, i.e. if the return of WMT increases, MCD returns also increases.

Risk and Return of the portfolio.

Every rational investor wishes to maximize his return and minimize his risk. Harry Markowitz propounded the portfolio theory which as per (Brealey, Myers, & Allen, 2016) suggests the best fit to reduce the risk and maximize return.

The portfolio return can be calculated as: -

Expected Return E(rp) = W1r1 + W2r2, eqn…………(iii), where

W1 is the proportion of the investment made in MCD and W2 is in WMT. Similarly, the risk of the portfolio is determined as: -

Variance of portfolio(Varp)

W1^2*Var(r1) + W2^2*Var(r2) +2ρ (1,2) * W1 *W2√(Var(r1)* Var(r2)), eqn…………(iv),Where

r1= return of MCD and r2 =return of WMT

Var(r1) and Var(r2) are the variance of r1 and r2

ρ(1,2) is the correlation coefficient between r1 and r2

W_1	W_2	Expected ROR	Standard Deviation	CV
0	1	0.127160343	0.278518109	2.19029064
0.1	0.9	0.141228394	0.27229861	1.9280727
0.2	0.8	0.155296444	0.271015946	1.74515229
0.3	0.7	0.169364495	0.27473927	1.62217748
0.4	0.6	0.183432545	0.283271254	1.54428023
0.5	0.5	0.197500596	0.296196648	1.49972534
0.6	0.4	0.211568647	0.312971594	1.479291
0.7	0.3	0.225636697	0.33301486	1.47588962
0.8	0.2	0.239704748	0.355774492	1.48421963
0.9	0.1	0.253772798	0.380763699	1.50041179
1	0	0.267840849	0.407572587	1.52169689

Table 3: Portfolio creation for MCD and WMT from 1998 to 2017

Here, the CV stands for Coefficient of Variation which is equal to the ratio of Standard deviation (σ) by return (r), i.e. (C.V) = σ/ r

Throughout the portfolio, we can see that the investment of 70% in MCD and 30% in WMT is the best possible investment alternative as it has the lowest level of risk measured by the standard deviation of portfolio to the expected return of the portfolio. The overall scenario can be depicted in the graph as: -

Figure 1:  Efficient frontier of the portfolio among MCD and WMT.

The horizontal axis is the standard deviation of portfolio which defines the risk and the vertical axis is the expected return.

From the graph plotted above, we can see that the risk and return changes with the alternation in the proportion of the investment made in the securities. As stated by (Raykar, 2017) high risk comes with the high return but the investor may have to go through prolonged phase of the uncertainty and volatilities. So, it depends upon the amount of risk taking capacity of the investor. The investor with high risk-taking capacity selects in the upwards points of the efficient frontier as shown in figure- 1 whereas those with less risk-taking capacity satiate in the lower points of the efficient frontier.

Conclusion

From the above data and its calculations, we can infer that the creation of portfolio for the investment better-offs an investor rather than making investment in a single security. The annualized return in MCD is greater than in WMT and in the same way the risk is also proportionately higher. But when the portfolio is constructed, the risk, as well as return, also decreased which is illustrated by the efficient frontier as in graph-1. And ultimately depending upon the voracity of risk-taking investors invests in alternatives.

References

Brealey, R. A., Myers, S. C., & Allen, F. (2016). Principles of Corporate Finance. McGraw Hill Education.

Raykar, S. G. (2017, September 27). A fund in high-risk and high-return category. Retrieved from www.economictimes.indiatimes.com: https://economictimes.indiatimes.com/mf/analysis/a-fund-in-high-risk-and-high-return-category/articleshow/60851912.cms