The standard deviation of the BP $($British Petroleum$)$ stock has been about $25$ percent over

the last few years. BP$$s beta has been about $2\mathrm{.}8,$ measured against FTSE stock market

index in London. The corresponding risk measures for BA $($British Airways$)$ were $57$ percent, and $2\mathrm{.}17.$A diversified investor is optimistic about BA$$s prospects. He has cash to add to his portfolio

and intends to keep his overall portfolio beta at its current value of $1\mathrm{.}0.$ Hence, he invests

in a combination of BA shares and secure Treasury bills. How much should he invest in BA

shares?