Stock Returns Coursework Example

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Course:
Date:
Question 6
Average returns.
Company A
= 5.23+8.91+7.32-15.81-8.32+25.98
6
=3.885%

Company B
=13.51-9.35+2.44+3.12+14.81+18.36
6
=7.148%
Standard deviation.
Company A
YEAR ANNUAL RETURN DEVIATION FROM +3.885% SQUARE DEVIATION
1 5.23 1.345 1.8090
2 8.91 5.025 25.2506
3 7.32 3.435 11.7992
4 -15.81 -19.695 387.8930
5 -8.32 -12.205 148.9620
6 25.98 22.095 488.1890
Variance = ∑ (AR-µR) ^2
N
Where: AR = Annual return
µR = average return
N = number of years

Variance = 1.8090+25.2506+11.7992+387.8930+148.9620+488.1890
6
=177.3171
Standard deviation = √Variance
Standard deviation = √177.3171
= 13.3160
Company B
YEAR ANNUAL RETURN DEVIATION FROM+7.148% SQUARE DEVIATION
1 13.51 6.362 40.4750
2 -9.35 -16.498 272.1840
3 2.44 -4.708 22.1653
4 3.12 -4.208 16.2248
5 14.81 7.662 58.7062
6 18.36 11.212 125.7089
Variance = ∑ (AR-µR) ^2
N
Where: AR = Annual return
µR = average return
N = number of years
Variance = 40.4750+272.1840+22.1653+16.2248+58.7062+125.7089
6
=89.2440
Standard deviation = √Variance
Standard deviation = √89.2440
= 9.4469
Average return of the portfolio:
YEAR Company A Company B Total returns for the portfolio
1 5.23 13.51 18.74
2 8.91 -9.35 -0.44
3 7.32 2.44 9.76
4 -15.81 3.12 -12.69
5 -8.32 14.81 6.49
6 25.98 18.36 44.34
Average return of the portfolio= 18.74-0.44+9.76-12.69+6.49+44.34
6
=11.03%
Standard deviation of the portfolio:
Total returns for the portfolio Deviation from +11.03% Square deviation
18.74 7.71 59.4441
-0.44 -11.47 131.5609
9.76 -1.27 1.6129
-12.69 -23.72 562.6384
6.49 -4.54 26.6116
44.34 33.31 1109.5561
Variance = ∑ (AR-µR) ^2
N
Where: AR = Annual return
µR = average return
N = number of years
Variance= 59.4441+131.5609+1.6129+562.6384+26.6116+1109.5561
6
= 314.2373
Standard deviation = √Variance
Standard deviation= √314.2373
= 17.7267
Wa.ARa + Wb.ARb
(0.6*3.885) + (0.4*7.148)
2.331 + 2.8592
=5.1902%
Question 7
Calculations:
Weight = Specific shares
Total shares
Position = the closer the beta is to 1, the higher it ranks.
Merck & Co., Inc.
Position: 2
Weight:
150/800= 0.1875
W*Beta:
0.1875*1.62=0.3038
Domino’s pizza.
Position: 3
Weight:
200/800=0.25
W*Beta:
0.25*1.8=0.45
Macy’s Inc.
Position: 1
Weight:
300/800=0.375
W*Beta:
0.375*1.42=0.5325
Tesla.
Position: 4
Weight:
150/800=0.1875
W*Beta:
0.1875*2.51=0.4706
Shares Price Position Weight Beta W x Beta
Merck & Co., Inc. 150 61 2 0.1875 1.62 0.3038
Domino’s Pizza 200 152 3 0.25 1.8 0.4500
Macy’s, Inc. 300 36 1 0.375 1.42 0.5325
Tesla 150 202 4 0.1875 2.51 0.4706
Totals 800 4 1 1.7569 1.7569
Totals
Total shares = 800
Total positions = 4
Total weight = 1
Total W*Beta = 1.7659
Beta of the portfolio, βp= 1.7569
This is a high risk portfolio, this is because beta is greater than 1.
Expected Returns = RFR + βp (Rm – Rf)
= 6 + 1.7569 (11 – 6)
= 14.7845%
Risk of the portfolio=βp=1.

7659

References:
Capiński, Maciej J, and Ekkehard Kopp. Portfolio Theory and Risk Management. Cambridge University Press, 2014.