Question

Question 1
Richard must decide how to allocate the capital in his portfolio.
Richard has		$63,000	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.
a) How much will he invest in each stock?
(1 Mark)
b) The expected return of Richard's porfolio is:
(Round your answer to one one-hundreth of a percent)
c) The standard deviation of Richard's portfolio return is:
(1 Mark)(Round your answer to one one-hundredth of a percent)
Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)
1	-5.940	-18.120	5.690	-2.440
2	8.970	26.610	-6.238	5.015
3	12.320	36.660	-8.918	6.690
4	14.320	42.660	-10.518	7.690
5	-16.240	-49.020	13.930	-7.590
6	15.980	47.640	-11.846	8.520
7	4.880	14.340	-2.966	2.970
8	13.220	39.360	-9.638	7.140
9	9.260	27.480	-6.470	5.160
10	9.970	29.610	-7.038	5.515
11	-5.230	-15.990	5.122	-2.085
12	-8.240	-25.020	7.530	-3.590

Answer 1

Answer :

1) Funds Available = $63000 i.e to be invested 25% in each stock.

So, Amount invested in each stock = 63000*25%

                                                        = 15750

So, Richard will invest $15,750 in each of the 4 stocks.

2) the expected return of Richard's portfolio is weighted average of the investment made in each stock.

First we need to calculate the return of each of the stock mentioned as-

Simple average of the last 12 years of return is calculated as = sum of return of Stock / 12

A = 53.27/12 = 4.43%

B = 156.21/12 = 13.01%

C = -31.36/12 = -2.61%

D = 32.995/12 = 2.75%

Weighted average return of Richard's portfolio = 25%* 4.43% + 25%*13.01% + 25%*(-2.61) + 25%*2.75%

                                                                            = 4.4%

c) the Standard Deviation of Richard's portfolio is weighted average Standard Deviation of the investment made in each stock.

So, First we need to calculate the Standard Deviation of the Stock.

Steps to Calculate Standard Deviation :

Step 1: First calculate Mean of the given return.

Step 2: Subtract each of the return by the mean calculated in Step 1

Step 3: Make squares of each of the deviation calculated in step 2 and add them,

Step 4: Divide the sum of squares of Deviations by Total number of items(years or months) -1 i.e when the data provides return for 12 years, the sum of squares of Deviations should be divided by 11(12-1).

Step 5: the square root of Step 4 is the standard Deviation.

			Step 2	Step 3
	Year	Stock A (%)	return- mean	Deviation ^2	Stock B (%)	return- mean	Deviation ^2	Stock C (%)	return- mean	Deviation ^2	Stock D (%)	return- mean	Deviation ^2
	1	-5.94	-10.3791667	107.727101	-18.12	-31.138	969.543906	5.69	8.30333333	68.9453444	-2.44	-5.18958333	26.9317752
	2	8.97	8.97	80.4609	26.61	26.61	708.0921	-6.238	-6.238	38.912644	5.015	5.015	25.150225
	3	12.32	12.32	151.7824	36.66	36.66	1343.9556	-8.918	-8.918	79.530724	6.69	6.69	44.7561
	4	14.32	14.32	205.0624	42.66	42.66	1819.8756	-10.518	-10.518	110.628324	7.69	7.69	59.1361
	5	-16.24	-16.24	263.7376	-49.02	-49.02	2402.9604	13.93	13.93	194.0449	-7.59	-7.59	57.6081
	6	15.98	15.98	255.3604	47.64	47.64	2269.5696	-11.846	-11.846	140.327716	8.52	8.52	72.5904
	7	4.88	4.88	23.8144	14.34	14.34	205.6356	-2.966	-2.966	8.797156	2.97	2.97	8.8209
	8	13.22	13.22	174.7684	39.36	39.36	1549.2096	-9.638	-9.638	92.891044	7.14	7.14	50.9796
	9	9.26	9.26	85.7476	27.48	27.48	755.1504	-6.47	-6.47	41.8609	5.16	5.16	26.6256
	10	9.97	9.97	99.4009	29.61	29.61	876.7521	-7.038	-7.038	49.533444	5.515	5.515	30.415225
	11	-5.23	-5.23	27.3529	-15.99	-15.99	255.6801	5.122	5.122	26.234884	-2.085	-2.085	4.347225
	12	-8.24	-8.24	67.8976	-25.02	-25.02	626.0004	7.53	7.53	56.7009	-3.59	-3.59	12.8881
	Sum	53.27		1543.1126	156.21		13782.4254	-31.36		908.40798	32.995		420.24935
Step 1	Mean	4.439167			13.0175			-2.61333			2.749583
Step 4				140.2829637			1252.947764			82.58254368			38.20448638
Step 5	Standard Deviation			11.84411093			35.39700219			9.087493806			6.180977785

     

Stock	Standard Deviation	Weights given	Weighted Average Standard Deviation
A	11.84	25%	2.96
B	35.40	25%	8.85
C	9.09	25%	2.27
D	6.18	25%	1.55
Portfolio			15.63