Here are some historical data on the risk characteristics of Ford and Harley Davidson.

Ford Harley Davidson

Yearly standard deviation of return $(\%)30\mathrm{.}717\mathrm{.}0$

Assume the standard deviation of the return on the market was $19\mathrm{.}0\%.$

a$.$ The correlation coefficient of Ford$$s return versus Harley Davidson is $0\mathrm{.}44.$ What is the standard deviation of a portfolio invested half in each share?

b$.$ What is the standard deviation of a portfolio invested one$-$third in Ford, one$-$third in Harley Davidson, and one$-$third in risk$-$free Treasury bills?

c$.$ What is the standard deviation if the portfolio is split evenly between Ford and Harley Davidson and is financed at $50\%$ margin, that is$,$ the investor puts up only $50\%$ of the total amount and borrows the balance from the broker?

d$-1.$ What is the approximate standard deviation of a portfolio composed of $100$ stocks with betas of $1\mathrm{.}68$ like Ford?

d$-2.$ What is the approximate standard deviation of a portfolio composed of $100$ stocks with betas of $0\mathrm{.}73$ like Harley Davidson?

Note: For all requirements, use decimals, not percent, in your calculations. Do not round intermediate calculations. Enter your answers as a percent rounded to $2$ decimal places.