Fight Finance

(a) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2##

(b) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12##

(c) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12^2##

(d) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times \sqrt{12}##

(e) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times {12}^{1/3}##

(a) ##\sigma_\text{annual} = 0.09 \times 5 + 0.14 \times 7##

(b) ##\sigma_\text{annual} = (0.09 \times 5 + 0.14 \times 7)^{1/2}##

(c) ##\sigma_\text{annual} = (0.09^2 \times 5 + 0.14^2 \times 7)^{1/2}##

(d) ##\sigma_\text{annual} = (1+0.09)^5\times (1+0.14)^7 - 1##

(e) ##\sigma_\text{annual} = \left( \dfrac{0.09^2 \times 5 + 0.14^2 \times 7}{12} \right)^{1/2}##

(a) The arithmetic average of variable X is represented by ##\bar{X}##.

(b) The standard deviation of variable X is represented by ##\sigma_X##.

(c) The variance of variable X is represented by ##\sigma_X^2##.

(d) The covariance between variables X and Y is represented by ##\sigma_{X,Y}^2##.

(e) The correlation between variables X and Y is represented by ##\rho_{X,Y}##.

(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.

(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.

(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(e) Percent per annum ##(\% pa)## and percent per annum ##(\% pa)##.

(a) Adjusted closing prices add back dividends and reverse the effect of stock splits.

(b) Apple's effective annual total return between the market close on 2 January 2008 and 2 January 2009 was -0.534269 (=(24.22-11.28)/24.22).

(c) Sample variance of the S&P500's effective annual total returns over the 3 year period was 0.084452.

(d) Sample covariance of effective total annual returns between Apple and the S&P500 index over the 3 year period was 0.041131.

(e) Apple's equity beta of annual total returns over the 3 year period was 3.530767.

(a)

(b)

(c)

(d)

(e)