Question

Calculate your portfolio return. (simple return AND annualized) and your portfolio beta. Did the portfolio beta match the actual results? Did your portfolio earn it's required rate of return?  

Company	Shares	Beging of Year Price	Dividend per share	End of Year Price	Beginning Value	Portvolio Wt	Capital Gain	Income	Total Return	% Return	Beta
Walt Disney Co.	52	108.97	0	146.21	$                   5,666.44	25.8%	$         1,936.48	$            -	$         1,936.48	34.17%	1.02
Ulta Beauty Inc	40	247.97	2	252.64	$                   9,918.80	45.1%	$            186.80	$    80.00	$             266.80	2.69%	1.12
Twitter Inc	30	28.81	0	30.21	$                      864.30	3.9%	$               42.00	$            -	$               42.00	4.86%	0.56
Apple Inc	25	157.92	3.04	266.92	$                   3,948.00	17.9%	$         2,725.00	$    76.00	$         2,801.00	70.95%	1.23
Starbucks	25	64.32	1.49	86.28	$                   1,608.00	7.3%	$            549.00	$    37.25	$             586.25	36.46%	0.52
SUM					$                22,005.54		$         5,439.28	$  193.25	$         5,632.53	25.60%	4.45
		Portfolio $ return	$5,632.53
		Portfolio % return	25.6
		Portfolio Beta	1.048146639
5666.44		Simple Return
9918.8		Walt Disney	$                             498.64		Walt Disney	1935.48
864.3		Ulta Beauty Inc	$                                84.20		Ulta Beauty Inc
3948		Twitter Inc.	$                                  1.65		Twitter Inc.
1608		Apple Inc	$                             488.89		Apple Inc
22005.54		Starbucks	$                                40.12		Starbucks
		Total	$                          1,113.50		Total	1935.48

Answer 1

Portfolio return can be calculated in absolute terms and in annualized percentage terms. Following formula are used for both the terms of portfolio return:

Portfolio Return (simple) = (Capital gain from stock + Income from stock)

Where-

Capital gain from stock = [(Value of stock at the end of the period - Value of stock in the beginning of the period) / Value of stock in the beginning of the period[

Income from stock = Dividend per share * Number of shares

Portfolio Return (annualized) = Portfolio return (simple) / Total Investment in all stocks in the beginning of the period

Now let us calculate the above two using given data of name of company, number of shares, beginning of year price, end of year price and dividend per share

Statement showing Individual Return

Company	Shares (A)	Beginning of Year Price (B)	Dividend per share (C )	End of Year Price   (D)	Beginning Value    E = (B * A)	Capital Gain F = [(D-B) * A]	Income     G = (C * A)	Total Return   (F + G)
Walt Disney Co.	52	108.97	-	146.21	5,666.44	1,936.48	-	1,936.48
Ulta Beauty Inc	40	247.97	2.00	252.64	9,918.80	186.80	80.00	266.80
Twitter Inc	30	28.81	-	30.21	864.30	42.00	-	42.00
Apple Inc	25	157.92	3.04	266.92	3,948.00	2,725.00	76.00	2,801.00
Starbucks	25	64.32	1.49	86.28	1,608.00	549.00	37.25	586.25
Total					22,005.54	5,439.28	193.25	5,632.53

Portfolio Return (simple) = (Capital gain from stock + Income from stock)

Portfolio Return (simple) = $5,632.53

Portfolio Return (annualized) = Portfolio return (simple) / Total Investment in all stocks in the beginning of the period

Portfolio Return (annualized) = $5,632.53 / $22,005.54

= 0.256 or 25.6%

Now, let us calculate the portfolio beta using the below mentioned formula:

Portfolio Beta = ( Security Beta * Security Weights )

Statement showing Portfolio Beta

Company	Shares (A)	Beginning of Year Price (B)	Beginning Value     C = (B * A)	Weights D = (C / Total of C)	Beta    (E )	Portfolio Beta (E * D)
Walt Disney Co.	52	108.97	5,666.44	0.258	1.02	0.263
Ulta Beauty Inc	40	247.97	9,918.80	0.451	1.12	0.505
Twitter Inc	30	28.81	864.30	0.039	0.56	0.022
Apple Inc	25	157.92	3,948.00	0.179	1.23	0.221
Starbucks	25	64.32	1,608.00	0.073	0.52	0.038
Total			22,005.54			1.048

Portfolio Beta = ( Security Beta * Security Weights )

Portfolio Beta = 1.048

Hence the portfolio beta matches with the actual results given in the question.

The required rate of return can be calculated using Capital Asset Pricing Model which can be calculated as follows:

Required Return = Risk free rate + (Market rate - Risk free rate)

Where:

= 1.048 (portfolio beta)

Risk free rate is not given, then let us assume that Risk free rate is 0

Market rate is also not given, then let us assume that Market represents the bunch of shares given in the question and hence the market rate can be assumed as portfolio return i.e. 25.6%

On putting these figures in the above formula, we get -

Required Return = Risk free rate + (Market rate - Risk free rate)

Required Return = 0 + 1.048 (25.6 - 0)

Required Return = 26.83%

Hence the portfolio is not earning its required rate of return.