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Deep Value, Inc.’s annual stock returns for the last ten years are: –5%, 15%, 11%, 18%,...

Deep Value, Inc.’s annual stock returns for the last ten years are: –5%, 15%, 11%, 18%, –8%, 9%, 16%, –3%, 3%, and 35%. The Market Index’s annual returns for the same ten years are: 10%, 22%, 9%, 13%, –7%, 8%, 15%, –13%, –12%, and 18%. What is Deep Value’s beta coefficient? Enter your answer rounded to two decimal places. For example, if your answer is 12.345 then enter as 12.35 in the answer box.

Solutions

Expert Solution

Computation of Mean for Deep Value returns and Market Index returns

Year

Deep Value return

Market Index returns

1

-5.000%

10.000%

2

15.000%

22.000%

3

11.000%

9.000%

4

18.000%

13.000%

5

-8.000%

-7.000%

6

9.000%

8.000%

7

16.000%

15.000%

8

-3.000%

-13.000%

9

3.000%

-12.000%

10

35.000%

18.000%

Total return for 10years

91.000%

63.000%

Mean = Total returns / no. of years

9.100%

6.300%

Standard Deviation from Market Index returns

Year

Market Index return

Mean

Deviation from Mean (Return - Mean)

Squared deviation

1

10.00%

6.300%

3.700%

0.137%

2

22.00%

6.300%

15.700%

2.465%

3

9.00%

6.300%

2.700%

0.073%

4

13.00%

6.300%

6.700%

0.449%

5

-7.00%

6.300%

-13.300%

1.769%

6

8.00%

6.300%

1.700%

0.029%

7

15.00%

6.300%

8.700%

0.757%

8

-13.00%

6.300%

-19.300%

3.725%

9

-12.00%

6.300%

-18.300%

3.349%

10

18.00%

6.300%

11.700%

1.369%

Sum of squared deviation

14.121%

Sum of squared deviation / no. of years

1.412%

Standard Deviation = Square root of (Sum of squared deviation / no. of years)

11.88%

Variance = Standard Deviation^2

1.412%

Computation of Covariance between Deep Value returns and Markets Index returns

Year

Market Index return

Market Index Mean

Deviation from Mean - Market Index (Return - Mean)

Deep Value return

Deep Value Mean

Deviation from Mean - Deep Value Inc (Return - Mean)

Deviation from mean (Market Index) x Deviation from mean (Deep Value Inc)

1

10.00%

6.300%

3.700%

-5.000%

9.100%

-14.100%

-0.522%

2

22.00%

6.300%

15.700%

15.000%

9.100%

5.900%

0.926%

3

9.00%

6.300%

2.700%

11.000%

9.100%

1.900%

0.051%

4

13.00%

6.300%

6.700%

18.000%

9.100%

8.900%

0.596%

5

-7.00%

6.300%

-13.300%

-8.000%

9.100%

-17.100%

2.274%

6

8.00%

6.300%

1.700%

9.000%

9.100%

-0.100%

-0.002%

7

15.00%

6.300%

8.700%

16.000%

9.100%

6.900%

0.600%

8

-13.00%

6.300%

-19.300%

-3.000%

9.100%

-12.100%

2.335%

9

-12.00%

6.300%

-18.300%

3.000%

9.100%

-6.100%

1.116%

10

18.00%

6.300%

11.700%

35.000%

9.100%

25.900%

3.030%

Step 1 : Sum of [Deviation from mean (market index) x Deviation from mean (Deep Value)]

10.407%

Step 2 : NO. of years - 1

9

Step 3 : Covariance between Deep Value and Market Index --->Step 1/Step 2

1.156%

Computation of Beta

A

Covariance between Deep Value returns and Markets Index returns

1.156%

B

Variance of Market returns

1.412%

Beta of Deep Value returns = A/B

                        0.82


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