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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.

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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

jeff jeffy answered 1 year ago
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