Portfolios, EMH, Finance and Markets Case Study

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Investments

Investment returns are the amount that the investment is worth (upon sale), net of taxes, over and above the price paid for the investment. The returns can be expressed either in absolute terms, or in annualized terms. The return on an investment that cost $1,000 and is sold for $1,060 a year later is as follows:

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Return

% Return

This graph shows that the odds of an outcome increase as the expected return approaches 6%. If there were an infinite number of scenarios, the graph would look like this, but the tails on the y axis would by fully extended infinitely as the probability of an outcome approaches zero.

The expected rate of return on the Treasury bonds is the weighted average of the probabilities and returns listed in the table. Thus:

Probability

Return

W.Avg

-14

-1.4

-4

-0.8

Expected Return

The expected return therefore is 6% on the Treasury bond.

d. Stand-alone risk reflects the risk associated with a single asset. In the portfolio, stand-alone risk reflects the undiversified risk of any one individual asset (Investopedia, 2015). The standard deviation of the bond's expected return for the next year is as follows:

Probability

Return

W.Avg

0.1

-14

-1.4

0.2

-4

-0.8

0.4

6

2.4

0.2

16

3.2

0.1

26

2.6

6

2.130728

The standard deviation is 2.13.

e. The standard deviation of Blandy's returns over the past ten years is as follows:

e.

26

15

-14

-15

2

-18

42

30

-32

28

25.193

Standard Deviation

The standard deviation of the returns for Blandy is 25.193.

f. The client should be surprised that I would recommend reducing risk by purchasing a stock with even more risk than Blandy has. The returns of this portfolio over the past ten years would have been as follows:

Year

Blandy

Gourmange

Combined

1

26

47

31.25

2

15

-54

-2.25

3

-14

15

-6.

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75

4

-15

7

-9.5

5

2

-28

-5.5

6

-18

40

-3.5

7

42

17

35.75

8

30

-23

16.75

9

-32

-4

-25

10

28

75

39.75

Avg

6.4

9.2

7.1

Std Dev

25.19

38.58

22.16

The average return of the combined portfolio would have been 7.1%, which is intuitive, but the client will also notice that the standard deviation of the returns of the combined portfolio is lower than the standard deviation of either security individually.

g. Correlation is the degree to which two things are related. In investments, correlation specifically refers to the degree to which two assets move together. The estimated correlation between Blandy and Gourmange is:

g.

Year

Blandy

Gourmange

1

26

47

2

15

-54

3

-14

15

4

-15

7

5

2

-28

6

-18

40

7

42

17

8

30

-23

9

-32

-4

10

28

75

0.1125

Correlation

The correlation between Blandy and Gourmange is 0.1125. This means that the returns of these two securities are very poorly correlated with each other. This is the reason why the standard deviation of the combined portfolio is lower than the standard deviation of either asset individually -- the movements of one are typically offset by the movements of the either. Because the two assets have a low correlation, diversifying with these two will lower the overall standard deviation of the portfolio.

h. As a general rule, each random stock added to the portfolio will reduce its standard deviation. The portfolio's risk will thus decrease with each added stock. . This is because each added stock decreases the amount of firm-specific risk that the portfolio has, until enough stocks have been added than only systemic risk remains. The movements of the individual stocks will offset.....

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