Question

1.

The following spreadsheet contains monthly returns for Cola Co. and Gas Co. for 2013. Using these​ data, estimate the average monthly return and the volatility for each stock.

Cola Co.    Gas Co.
January -0.0990   0.0440
February -0.0160   0.0560
March 0.0420   -0.0130
April -0.0260   -0.0200
May -0.0910   -0.0160
June -0.0820   -0.0380
July 0.1200   0.0470
August -0.0070   0.0040
September -0.0700   -0.0090
October 0.0120    0.0040
November 0.0920   0.1020
December -0.0110   0.0550

The average monthly return for Cola Co. is ___​%.

​(Round to two decimal​ places.)

2. Given $100,000 to​ invest, construct a​ value-weighted portfolio of the four stocks listed below.

Stock    Price/Share ($) Number of shares outstanding (millions)
Golden Seas 15 1
Jacobs and Jacobs 21 1.59
MAG 42 27.92
PDJB 8 13.29

Enter the portfolio weight​ below:  ​(Round to two decimal​ places.)

Stock	​% of Total Value ​(portfolio weight)
Golden Seas		_______​%

3. Stocks A and B have the following​ returns:

   Stock A   Stock B
1   0.11   0.05
2   0.07   0.02
3   0.13   0.04
4   -0.03   0.01
5   0.09   -0.04

What are the standard deviations of the returns of the two​ stocks?

If their correlation is 0.45​, what is the expected return and standard deviation of a portfolio of 55​% stock A and 45​% stock​ B?

Answer 1

2)

First we will calculate the value of each stock by multiplying price per share by the number of shares outstanding as per below:

Golden seas : $15 * 1  = $15

Jacobs & Jacobs:$21 * 1.59 = $33.39

MAG: $42 * 27.92 = $1172.64

PDJB: $8 * 13.29 = $106.32

Total value of portfolio = $15 + $33.39 + $1172.64 + $106.32 = $1327.35

Next, we will calculate the weights or percentage of each stock in the portfolio by dividing the value of the stock by the total value in the portfolio as per below:

Golden seas : $15 / $1327.35 * 100= 1.13%

Jacobs & Jacobs: $33.39 / $1327.35 * 100 = 2.51%

MAG: $1172.64/ $1327.35 * 100 = 88.34%

PDJB: $106.32/ $1327.35 * 100 = 8.009%

Now, the portfolio of $100000 will include the following amounts of each stock:

Golden seas: $100000 * 1.13% = $1130

Jacobs & Jacobs : $100000 * 2.51% = $2510

MAG: $100000 * 88.34% = $88340

PDJB: $100000 * 8.009% = $8009

3)

Year	Return of Stock A	Deviation from Mean of Stock A [ Return - E (R) ]	Square of Deviation of Stock A	Return of Stock B	Deviation from Mean of Stock B [ Return - E(R) ]	Square of Deviation of Stock B
1	0.11	0.11 - 0.074 = 0.036	0.001296	0.05	0.05 - 0.016 = 0.034	0.001156
2	0.07	0.07 - 0.074 = (-0.004)	0.000016	0.02	0.02 - 0.016 = 0.004	0.000016
3	0.13	0.13 - 0.074 = 0.056	0.003136	0.04	0.04 - 0.016 = 0.024	0.000576
4	-0.03	- 0.03 - 0.074 = (-0.104)	0.010816	0.01	0.01 - 0.016 = (-0.006)	0.000036
5	0.09	0.09 - 0.074 = 0.016	0.000256	-0.04	-0.04 - 0.016 = (- 0.056)	0.003136
Sum	0.37		0.01552	0.08		0.00492

Expected Return= Sum of All returns / No. of years

Expected Return of Stock A = 0.37 / 5
= 0.074

Variance of Stock A = 0.01552 / (5-1)
= 0.00388

Standard Deviation of Stock A=

= 0.0622

Expected Return= Sum of All returns / No. of years

Expected Return of Stock B = 0.08/ 5
= 0.016

Variance of Stock B = 0.00492/ (5-1)
= 0.00123

Standard Deviation of Stock B=

= 0.03507

Asset Weights of Stock A = 0.55

Asset Weights of Stock B = 0.45

correlation is 0.45

Expected Return of Portfolio= R_A * WA +  R_B *  W_B   

= 0.074 * 0.55 + 0.016 * 0.45

= 0.0407 + 0.0072

= 0.0479 or 4.79%

Standard deviation of a portfolio =  
= 0.0435