Question

Richard must decide how to allocate the capital in his portfolio. Richard has $23,000 available to invest. He finds the rates of return for four stocks for the past 12 years and the results are given         below. Richard plans to invest 25% of his funds in each stock.                 

Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)
1	-4.080	-0.930	1.260	-6.090
2	16.540	4.225	-3.895	24.840
3	24.360	6.180	-5.850	36.570
4	16.360	4.180	-3.850	24.570
5	-33.480	-8.280	8.610	-50.190
6	31.880	8.060	-7.730	47.850
7	9.080	2.360	-2.030	13.650
8	26.240	6.650	-6.320	39.390
9	10.320	2.670	-2.340	15.510
10	18.540	4.725	-4.395	27.840
11	-9.460	-2.275	2.605	-14.160
12	-17.480	-4.280	4.610	-26.190

Anna is a Vice President at the J Corporation. The company is considering investing in a new factory and Anna must decide whether it is a feasible project. In order to assess the viability of the project, Anna must first calculate the rate of return that equity holders expect from the company stock. The annual returns for J Corp. and for a market index are given below. Currently, the risk-free rate of return is 1.2% and the market risk-premium is      2.4%     

Year	J Corp. Return (%)	Market Return (%)
1	-4.32	-2.10
2	16.30	8.21
3	24.12	12.12
4	16.12	8.12
5	-33.72	-16.80
6	31.64	15.88
7	8.84	4.48
8	26.00	13.06
9	10.08	5.10
10	18.30	9.21
11	-9.70	-4.79
12	-17.72	-8.80

Richard has just received an unexpected bonus at work worth $5,750 and, given the J. Corp.'s reputation for excellent investment decision making, he will invest all of the bonus        in J Corp. stock. Given the rates of return for stocks A, B, C, and D presented in Question 1 and the rates of return for J Corp. stock and the market presented in Question 2, as well as the cash amounts he is investing in stocks A, B, C, and D as you determined in Question 1,                                                                                                                                                

a) What is the beta of Richard's portfolio?                                                                                            

(round to two decimal points)                                                                                   

b) Richard's portfolio is…                               Aggressive         

                                                                                Defensive          

                                                                                Neither

Answer 1

Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)	Market Return (%)	Beta of A	Beta of B	Beta of C	Beta of D
1	-4.08	-0.93	1.26	-6.09	-2.1	2.00	0.50	-0.50	3.00
2	16.54	4.225	-3.9	24.84	8.21
3	24.36	6.18	-5.85	36.57	12.12
4	16.36	4.18	-3.85	24.57	8.12
5	-33.5	-8.28	8.61	-50.2	-16.8
6	31.88	8.06	-7.73	47.85	15.88
7	9.08	2.36	-2.03	13.65	4.48
8	26.24	6.65	-6.32	39.39	13.06
9	10.32	2.67	-2.34	15.51	5.1
10	18.54	4.725	-4.4	27.84	9.21
11	-9.46	-2.28	2.605	-14.2	-4.79
12	-17.5	-4.28	4.61	-26.2	-8.8
Beta
year	J Corp. Return (%)	Market Return (%)
1	-4.32	-2.1
2	16.3	8.21						Formula for calculating return, %= today's return/previous return-1
3	24.12	12.12
4	16.12	8.12
5	-33.7	-16.8
6	31.64	15.88
7	8.84	4.48
8	26	13.06
9	10.08	5.1
10	18.3	9.21
11	-9.7	-4.79
12	-17.7	-8.8
Beta	2
Since the extra income of 5750 dollars are invested in Jcorp which is exactly same as the contribution in each stock
23000/4	=	5750
Beta of portfolio		=	(2+2+.5-.5+3)/5	1.40
So according to me Richard's portfolio is aggressive in nature since beta is far more than 1