Click to copy table.
The following table contains monthly returns for Cola Corporation and Gas Corporation for 2012: (The returns are shown in decimal form, i.e., 0.035 is 3.5%.) Using this table and the fact that Cola Corporation and Gas Corporation have a
correlation of -0.0969, calculate the volatility (standard deviation) of a portfolio that is 50% invested in Cola Corporation shares and 50% invested in Gas Corporation shares. Calculate the volatility by
a. using the following formula, $Var(R_p) = w_1^2 SD(R_1)^2 + w_2^2 SD(R_2)^2 + 2w_1w_2 Corr(R_1, R_2) SD(R_1) SD(R_2)$, and
b. calculating the monthly returns of the portfolio and computing its volatility directly.
c. How do your results compare?
a. Using the following formula, $Var(R_p) = w_1^2 SD(R_1)^2 + w_2^2 SD(R_2)^2 + 2w_1w_2 Corr(R_1, R_2) SD(R_1) SD(R_2)$, the volatility (standard deviation) of the portfolio is 2.81%. (Round to two decimal places.)
b. Calculating the monthly returns of the portfolio and computing its volatility directly, the volatility (standard deviation) is %. (Round to two decimal places.)
Data table
X
Month Cola Corp. Gas Corp.
January -0.0210 0.0280
February 0.0000 -0.0050
March -0.0200 -0.0180
April 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
Clear all Check answer