Question

- Troy wants to form a portfolio of four different stocks. Summary data on the four stocks appears below. The average standard deviation (found simply by summing the standard deviations and dividing by 4 which is the same as the weighted average in this example) across the four stocks is 17.25%. If Troy forms a portfolio by investing 25% of his money in each of the stocks in the table, it is very likely that the standard deviation of this portfolio’s return will be (more than, less than, equal to) 17.25%. Choose one of the options (more than, less than, equal to) and explain WHY? (You are not asked to calculate portfolio standard deviation or correlation. You do not need to do any math at all to answer this.)

Stock Return Standard deviation

#1 12% 20%

#2 -5% 29%

#3 7% 13%

#4 2% 7%

Answer #1

Troy forms a portfolio by investing 25% of his money in each of
the stocks, it is very likely that the standard deviation of this
portfolio’s return will be **less than 17.25%.**

It is because of the reason that when you choose different stocks for investments rather than investing in only one stock, diversification benefit occurs. It means, if you invest in different stocks, your return get averaged but your risk get reduced. Risk is reduced because stocks may have positive, less positive or negative correlation with one another. Due to correlation between them, diversification benefit occurs and due to diversification benefit portfolio risk is reduced.

So it is very likely that actual standard deviation of portfolio of this portfolio's return will be less than weighted average of standard deviation of stocks i.e. less than 17.25%.

An investor currently holds the following portfolio of 4 stocks,
each having equal weight:
Stock Expected Return (rs) Beta
A 13.2% 1.70
B 12.00% 1.5
C 6.0% 0.5
D 7.8% 0.8
a. What is the portfolio’s expected return?
b. What is the portfolio’s beta risk? Is it more or less risky
than the market?
c. Is the portfolio more or less risky than the market? How do
you know?
The investor is not comfortable with holding a portfolio that
has...

A portfolio consists of Stock A and Stock B The summary
statistics for these 2 stocks are as follow. Assume we place equal
90% weight in stock A. Calculate the portfolio risk? (10) b) Now
replace stock B with a T–bill and calculate the portfolio risk
again. A B Return (%) 12 20 Standard Deviation (%) 15.8 25.5
Covariance -120%

. Portfolio risk and return
Emma holds a $5,000 portfolio that consists of four stocks. Her
investment in each stock, as well as each stock’s beta, is listed
in the following table:
Stock
Investment
Beta
Standard Deviation
Andalusian Limited (AL)
$1,750
0.90
12.00%
Tobotics Inc. (TI)
$1,000
1.30
12.00%
Water and Power Co. (WPC)
$750
1.20
18.00%
Makissi Corp. (MC)
$1,500
0.40
19.50%
Suppose all stocks in Emma’s portfolio were equally weighted.
Which of these stocks would contribute the least...

Jennifer creates a portfolio of stocks by investing in ABC, Inc.
and XYZ, Inc an equal proportion of money. The portfolio has a mean
rate of return of 1% per week and a standard deviation of 2.50% per
week. How much is the probability that the portfolio’s return can
be -2% in one week? How much is the probability that the stock’s
return can go up to 3% in one week? Assume normal distribution of
portfolio returns. What happens if...

7. Portfolio risk and return
Ariel holds a $7,500 portfolio that consists of four stocks. Her
investment in each stock, as well as each stock’s beta, is listed
in the following table:
Stock
Investment
Beta
Standard Deviation
Perpetualcold Refrigeration Co. (PRC)
$2,625
0.90
18.00%
Zaxatti Enterprises (ZE)
$1,500
1.70
11.00%
Western Gas & Electric Co. (WGC)
$1,125
1.10
18.00%
Flitcom Corp. (FC)
$2,250
0.60
25.50%
Suppose all stocks in Ariel’s portfolio were equally weighted.
Which of these stocks would contribute...

8. Portfolio risk and return
Elle holds a $10,000 portfolio that consists of four stocks. Her
investment in each stock, as well as each stock’s beta, is listed
in the following table:
Stock
Investment
Beta
Standard Deviation
Perpetualcold Refrigeration Co. (PRC)
$3,500
0.90
15.00%
Kulatsu Motors Co. (KMC)
$2,000
1.50
12.00%
Water and Power Co. (WPC)
$1,500
1.20
18.00%
Makissi Corp. (MC)
$3,000
0.50
22.50%
Suppose all stocks in Elle’s portfolio were equally weighted.
Which of these stocks would contribute...

2: Consider the following 6 months of return for 2 stocks and a
portfolio of those 2 stocks
Jan
Feb
Mar
Apr
May
Jun
Stock
A
2%
5%
-6%
3%
-2%
4%
Stock
B
0%
-3%
8%
-1%
4%
-2%
Portfolio
1%
1%
1%
1%
1%
1%
A: What is the average monthly return and standard deviation of
returns for each of the two stocks?
B: what is the average monthly return and standard deviation of
returns for the...

8. Portfolio risk and return
Elle holds a $7,500 portfolio that consists of four stocks. Her
investment in each stock, as well as each stock’s beta, is listed
in the following table:
Stock
Investment
Beta
Standard Deviation
Omni Consumer Products Co. (OCP)
$2,625
0.80
9.00%
Tobotics Inc. (TI)
$1,500
1.50
11.00%
Water and Power Co. (WPC)
$1,125
1.10
16.00%
Mainway Toys Co. (MTC)
$2,250
0.30
22.50%
Suppose all stocks in Elle’s portfolio were equally weighted.
Which of these stocks would...

3. Portfolio risk and return
Ariel holds a $10,000 portfolio that consists of four stocks.
Her investment in each stock, as well as each stock’s beta, is
listed in the following table:
Stock
Investment
Beta
Standard Deviation
Omni Consumer Products Co. (OCP)
$3,500
1.00
9.00%
Zaxatti Enterprises (ZE)
$2,000
1.50
12.00%
Water and Power Co. (WPC)
$1,500
1.20
20.00%
Makissi Corp. (MC)
$3,000
0.30
22.50%
Suppose all stocks in Ariel’s portfolio were equally weighted.
Which of these stocks would contribute...

Elle holds a $10,000 portfolio that consists of four stocks. Her
investment in each stock, as well as each stock’s beta, is listed
in the following table:
Stock
Investment
Beta
Standard Deviation
Omni Consumer Products Co. (OCP)
$3,500
1.00
12.00%
Zaxatti Enterprises (ZE)
$2,000
1.30
11.00%
Water and Power Co. (WPC)
$1,500
1.10
20.00%
Flitcom Corp. (FC)
$3,000
0.40
19.50%
Suppose all stocks in Elle’s portfolio were equally weighted.
Which of these stocks would contribute the least market risk to...

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