Question

Monthly returns for two stocks are given below:

Month	1	2	3	4	5	6	7	8	9	10	11	12
rA	4.10%	1.12%	1.66%	−0.18%	−4.71%	−0.60%	−0.91%	1.02%	1.69%	−0.51%	1.42%	2.52%
rB	−3.36%	−1.93%	−0.45%	0.34%	4.27%	8.48%	1.86%	4.10%	6.41%	−5.24%	−1.06%	1.40%

(a) Calculate the correlation between the returns of these two stocks. Consider a portfolio of the two stocks weighted 60:40 at t = 0.

(b) Calculate the returns on the rebalanced portfolio for each month and plot the portfolio return and the stock returns as shown in the graph in Section 7.4.2.

(c) Calculate the returns on an unrebalanced portfolio and plot the portfolio return and the stock returns.

Answer 1

month	rA	rB
1	4.10%	-3.36%
2	1.12%	-1.93%
3	1.66%	-0.45%
4	-0.18%	0.34%
5	-4.71%	4.27%
6	-0.60%	8.48%
7	-0.91%	1.86%
8	1.02%	4.10%
9	1.69%	6.41%
10	-0.51%	-5.24%
11	1.42%	-1.06%
12	2.52%	1.40%

Correlation between Stock A and Stock B is -0.32924 (use excel function Corre)

Portfolio of two stocks weighted 60:40

(0.04*0.6- 0.03*0.4 = 0.01116)

month	rA	rB	Portfolio (60:40)
1	0.04	-0.03	0.01116
2	0.01	-0.02	-0.001
3	0.02	0.00	0.00816
4	0.00	0.00	0.00028
5	-0.05	0.04	-0.01118
6	-0.01	0.08	0.03032
7	-0.01	0.02	0.00198
8	0.01	0.04	0.02252
9	0.02	0.06	0.03578
10	-0.01	-0.05	-0.02402
11	0.01	-0.01	0.00428
12	0.03	0.01	0.02072

month	rA	rB	Portfolio Returns(60:40)
1	4.10%	-3.36%	1.12%
2	1.12%	-1.93%	-0.10%
3	1.66%	-0.45%	0.82%
4	-0.18%	0.34%	0.03%
5	-4.71%	4.27%	-1.12%
6	-0.60%	8.48%	3.03%
7	-0.91%	1.86%	0.20%
8	1.02%	4.10%	2.25%
9	1.69%	6.41%	3.58%
10	-0.51%	-5.24%	-2.40%
11	1.42%	-1.06%	0.43%
12	2.52%	1.40%	2.07%

Total Portfolio Return : 9.90%

month	rA	rB	Portfolio Returns(50:50)
1	4.10%	-3.36%	0.37%
2	1.12%	-1.93%	-0.41%
3	1.66%	-0.45%	0.61%
4	-0.18%	0.34%	0.08%
5	-4.71%	4.27%	-0.22%
6	-0.60%	8.48%	3.94%
7	-0.91%	1.86%	0.48%
8	1.02%	4.10%	2.56%
9	1.69%	6.41%	4.05%
10	-0.51%	-5.24%	-2.88%
11	1.42%	-1.06%	0.18%
12	2.52%	1.40%	1.96%

Total Portfolio Return = 10.72%

thanks