Problem Six $(15$ marks$).$

You work for a small investment management firm. You have been provided with the following historical information for three stocks and the market index. The information is shown in the table below. The amounts are in dollars $($$$).$

$\backslash$table$[[,$AAAInc.,BBB Inc.,CCCIne.,$\backslash$table$[[$Market$],[$Index$]]],[,\backslash$table$[[$Stock$],[$Price$]],$Dividend,$\backslash$table$[[$Stock$],[$Price$]],$Dividend,$\backslash$table$[[$Stock$],[$Price$]],$Dividend$],[2010,15,,53,,95,,15,250],[2011,21,0\mathrm{.}30,32,1\mathrm{.}10,126,2\mathrm{.}50,17,220],[2012,26,0\mathrm{.}30,43,1\mathrm{.}30,151,3\mathrm{.}00,18,340],[2013,29,0\mathrm{.}50,48,1\mathrm{.}50,132,3\mathrm{.}50,20,820],[2014,33,0\mathrm{.}50,32,1\mathrm{.}65,141,3\mathrm{.}60,21,720],[2015,40,0\mathrm{.}75,40,1\mathrm{.}75,146,3\mathrm{.}65,24,325],[2016,30,0\mathrm{.}80,63,1\mathrm{.}75,111,3\mathrm{.}65,19,920],[2017,43,0\mathrm{.}85,73,1\mathrm{.}80,149,3\mathrm{.}75,23,100],[2018,50,0\mathrm{.}90,58,2\mathrm{.}10,168,3\mathrm{.}80,24,500],[2019,63,1\mathrm{.}05,70,3\mathrm{.}00,180,4\mathrm{.}33,28,020],[2020,71,1\mathrm{.}10,103,3\mathrm{.}20,204,4\mathrm{.}85,31,572],[2021,85,1\mathrm{.}25,118,3\mathrm{.}80,211,5\mathrm{.}45,37,445],[2022,70,1\mathrm{.}25,115,4\mathrm{.}00,171,5\mathrm{.}45,33,283],[2023,95,1\mathrm{.}55,130,4\mathrm{.}50,230,6\mathrm{.}25,40,975]]$

Using the data provided, calculate the following for each of the stocks and the market index:

a$)$ What is the average annual retum for the past thirteen years?

b$)$ What is the geometric average annual return for the past thirteen years?

c$)$ What is the population standard deviation and the sample standard deviation?

d$).$ What is the correlation coefficient between Stocks AAA and BBB$?$ Between Stocks AAA and CCC$?$ Between Stocks BBB and CCC$?$

e$)$ What is the sample covariance between Stocks AAA and BBB$,$ between Stocks AAA and CCC and between stocks BBB and CCC$?$

f$)$ What is the coefficient of variation for each of the stocks and the market index? You should use the sample standard deviation.

g$)$ What is the beta of each of the stocks? You can use Excel's "slope" function to estimate this.

h$)$ Assume that the beta of stock AAA is $0\mathrm{.}60,$ the beta of stock BBB is $0\mathrm{.}80$ and the beta of stock CCC is $1\mathrm{.}70.$ What is the beta of a portfolio where the weight in stock AAA is $15\%$ the weight in stock BBB is $35\%$ and the weight in stock CCC is $50\%?$

i$)$ Assuming the risk free rate is $2\mathrm{.}25\%$ and the expected return on the market is $6\mathrm{.}50\%$ what is the expected retum on the portfolio in part $($h$)$ above?