The following three defense stocks are to be combined into a stock index in January $2010($perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance$)$: Assume the index is scaled by a factor of $10$ million; that is$,$ if the average firm$$s market value is $$5$ billion, the index would be quoted as $500.$

Price

Shares

$($millions$)1/1/101/1/111/1/12$

Douglas McDonnell $210$ $ $94$ $ $97$ $ $111$

Dynamics General $450363145$

International Rockwell $350655468$

a$.$ Calculate the initial value of the index if a value$-$weighting scheme is used.

Index value

b$.$

What is the rate of return on this index for the year ending December $31,2010?$ For the year ending December $31,2011?($Negative amounts should be indicated by a minus sign. Round your answer to $2$ decimal places. Omit the $"\%"$ sign in your response. $)$

$2010$ return

$\%$

$2011$ return

$\%$