$($ST$-1)$ Stocks A and B have the following historical returns:

a$.$ Calculate the average rate of return for each stock during the $5-$year period. Assume

that someone held a portfolio consisting of $50\%$ of Stock A and $50\%$ of Stock B$.$ What

would have been the realized rate of return on the portfolio in each year? What would

have been the average return on the portfolio for the $5-$year period?

b$.$ Now calculate the standard deviation of returns for each stock and for the portfolio.

Use Equation $6-5.$

c$.$ Looking at the annual returns data on the two stocks, would you guess that the

correlation coefficient between returns on the two stocks is closer to $0\mathrm{.}8$ or to $-0\mathrm{.}8?$

d$.$ If you added more stocks at random to the portfolio, which of the following is the

most accurate statement of what would happen to ${}_p?$

$(1){}_p$ would remain constant.

$(2){}_p$ would decline to somewhere in the vicinity of $20\%.$

$(3){}_p$ would decline to zero if enough stocks were included.