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In: Accounting

The following table contains monthly returns for Cola Co. and Gas Co. for 2010 ​(the returns...

The following table contains monthly returns for Cola Co. and Gas Co. for

2010

​(the returns are shown in decimal​ form, i.e., 0.035 is​ 3.5%). Using this table and the fact that Cola Co. and Gas Co. have a correlation of

−0.0969​,

calculate the volatility​ (standard deviation) of a portfolio that is

65%

invested in Cola Co. stock and

35%

invested in Gas Co. stock.

Month   Cola Co   Gas Co
Jan   -0.0210   0.0280
Feb   0.0000   -0.0050
Mar   -0.0200   -0.0180
Apr   0.0090   0.0280
May   -0.0310   0.0840
Jun   -0.0840   -0.0460
Jul   -0.1190   0.0820
Aug   -0.0160   0.0460
Sep   0.0550   0.0300
Oct   -0.0110   0.0140
Nov   -0.0380   0.0290
Dec   -0.0220   0.0740

​(Click the icon to view the monthly​ returns.)

Calculate the volatility​ by:

a.

Using the​ formula:

Var left parenthesis Upper R Subscript p right parenthesis equals w Subscript 1 Superscript 2 Baseline SD left parenthesis Upper R 1 right parenthesis squared plus w Subscript 2 Superscript 2 Baseline SD left parenthesis Upper R 2 right parenthesis plus 2 w 1 w 2 Corr left parenthesis Upper R 1 comma Upper R 2 right parenthesis SD left parenthesis Upper R 1 right parenthesis SD left parenthesis Upper R 2 right parenthesisVarRp=w21SDR12+w22SDR2+2w1w2CorrR1,R2SDR1SDR2.

b.

Calculating the monthly returns of the portfolio and computing its volatility directly.

c.

How do your results​ compare?

a.

Use the formula

Var left parenthesis Upper R Subscript p right parenthesis equals w Subscript 1 Superscript 2 Baseline SD left parenthesis Upper R 1 right parenthesis squared plus w Subscript 2 Superscript 2 Baseline SD left parenthesis Upper R 2 right parenthesis plus 2 w 1 w 2 Corr left parenthesis Upper R 1 comma Upper R 2 right parenthesis SD left parenthesis Upper R 1 right parenthesis SD left parenthesis Upper R 2 right parenthesisVarRp=w21SDR12+w22SDR2+2w1w2CorrR1,R2SDR1SDR2.

The volatility​ (standard deviation) of the portfolio is

nothing​%.

​(Round to two decimal​ places.)

Solutions

Expert Solution

How do your results​ compare?

1 . Results under both scenario will be same

ekkarill92 answered 1 year ago
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