The following table contains monthly returns for Cola Co. and Gas Co. for 2010 E (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 55% invested in Cola Co. stock and 45% invested in Gas Co. stock. Calculate the volatility by: a. Using the formula: Var (R,) = w sD(R,)² + w² sD (R2) + 2w, w2Corr(R,.R2) SD (R,) SD (R2) b. Calculating the monthly returns of the portfolio and computing its volatility directly. c. How do your results compare? a. Using the formula: Var (R,) = w} sD(R, )² + wž SD (R2) + 2w, wz Corr(R1.R2) SD (R,) SD (R2) The volatility (standard deviation) of the portfolio is 11 %. (Round to two decimal places.) b. Calculating the monthly returns of the portfolio and computing its volatility directly. The volatiltiy (standard deviation) of the portfolio is 1%. (Round to two decimal places.) c. How do your results compare? (Select the best choice below.) O A. The portfolio volatility calculated using the Var(Rp) formula in part (a) is much smaller than the portfolio volatility calculated used the monthly portfolio returns. O B. The portfolio volatility calculated using the Var (Rp) formula in part (a) is much larger than the portfolio volatility calculated used the monthly portfolio returns. OC. The two portfolio volatilities, calculated using the Var (Rp) formula in part (a) and using the monthly portfolio returns, are the same or almost the same. O D. This cannot be determined from the information given.
The following table contains monthly returns for Cola Co. and Gas Co. for 2010 E (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 55% invested in Cola Co. stock and 45% invested in Gas Co. stock. Calculate the volatility by: a. Using the formula: Var (R,) = w sD(R,)² + w² sD (R2) + 2w, w2Corr(R,.R2) SD (R,) SD (R2) b. Calculating the monthly returns of the portfolio and computing its volatility directly. c. How do your results compare? a. Using the formula: Var (R,) = w} sD(R, )² + wž SD (R2) + 2w, wz Corr(R1.R2) SD (R,) SD (R2) The volatility (standard deviation) of the portfolio is 11 %. (Round to two decimal places.) b. Calculating the monthly returns of the portfolio and computing its volatility directly. The volatiltiy (standard deviation) of the portfolio is 1%. (Round to two decimal places.) c. How do your results compare? (Select the best choice below.) O A. The portfolio volatility calculated using the Var(Rp) formula in part (a) is much smaller than the portfolio volatility calculated used the monthly portfolio returns. O B. The portfolio volatility calculated using the Var (Rp) formula in part (a) is much larger than the portfolio volatility calculated used the monthly portfolio returns. OC. The two portfolio volatilities, calculated using the Var (Rp) formula in part (a) and using the monthly portfolio returns, are the same or almost the same. O D. This cannot be determined from the information given.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text: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 55% invested in Cola Co. stock and 45% invested in Gas Co. stock. Calculate the volatility by:
a. Using the formula:
Var (R,) = w SD (R,)² + w% SD (R2) + 2w, w,Corr (R, R2) SD (R,) SD (R2)
1.
b. Calculating the monthly returns of the portfolio and computing its volatility directly.
c. How do your results compare?
a. Using the formula:
Var(Rp) = w; SD(R,)² + w½ SD (R2) + 2w, w2Corr (R,.R2) SD (R,) SD (R2)
1:
The volatility (standard deviation) of the portfolio is 11 %. (Round to two decimal places.)
b. Calculating the monthly returns of the portfolio and computing its volatility directly.
The volatiltiy (standard deviation) of the portfolio is 1%. (Round to two decimal places.)
c. How do your results compare? (Select the best choice below.)
A. The portfolio volatility calculated using the Var (Rp) formula in part (a) is much smaller than the portfolio volatility calculated used the monthly portfolio returns.
B. The portfolio volatility calculated using the Var (Rp) formula in part (a) is much larger than the portfolio volatility calculated used the monthly portfolio returns.
C. The two portfolio volatilities, calculated using the Var (Rp) formula in part (a) and using the monthly portfolio returns, are the same or almost the same.
D. This cannot be determined from the information given.
Transcribed Image Text:Data Table
Month
Cola Co.
Gas Co.
January
- 0.0210
0.0280
February
0.0000
- 0.0050
March
- 0.0200
- 0.0180
Аpril
0.0090
0.0280
May
- 0.0310
0.0840
June
- 0.0840
- 0.0460
July
- 0.1190
0.0820
August
- 0.0160
0.0460
September
0.0550
0.0300
October
- 0.0110
0.0140
November
- 0.0380
0.0290
December
- 0.0220
0.0740
Print
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