Annie Williams is considering a retirement portfolio and wonders if she should move some of her money into an international investment. She has been working for a short time period $($she graduated University just four years ago, she has put her retirement savings into a mutual fund whose strategy mimicked the return of the S&P $500$ stock index$/$ large company stock$),$ this fund has historically earned a return averaging $12\%$ over the last $80$ years, but recently the returns were somewhat depressing, as the economy is going through a mild recession because of this Annie is considering an international mutual fund that diversifies its holdings around the industrialized economies of the world and average $14\%$ annual rate of return. The international funds higher average return is offset by the fact that the standard deviation in its return is $30\%$ compared to only $20\%$ for the domestic index fund. Reviewing more closely, she learned that the domestic and international fund tend to earn high returns and low return at about the same time in the business cycle such that the correlation co$-$efficient is $0\mathrm{.}75.$

If Annie decides to move half her money into the international fund and leave the remaining in the domestic fund, what would be her expected portfolio return and standard deviation in the portfolio return and standard deviation in the portfolio return be for the combined portfolio$/$

$1.$ Display this information in a tabulated format showing the important information needed.

$2.$ The challenge the Annie is facing is the estimate the portfolio$$s expected return and standard deviation if she places half her money in each of the two mutual funds.

$3.$Calculate the expected return for the portfolio and the standard deviation for the portfolio.