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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.

Managerial Accounting
Managerial Accounting
15th Edition
ISBN:9781337912020
Author:Carl Warren, Ph.d. Cma William B. Tayler
Publisher:Carl Warren, Ph.d. Cma William B. Tayler
Chapter16: Financial Statement Analysis
Section: Chapter Questions
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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: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.
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 Done
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 Done
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