assume you have all your wealth (a million dollars) invested in the Vanguard 500 index fund and that you expect to earn an annual return of 12%, with a standard deviation in returns of 25%. You have become more risk averse, and so you decide to shift $200,00 form Vanguard 500 index fund to treasury bills. The treasury bill rate is 5%.

If you wish to invest in a portfolio generating an expected return of 10%, how much should you invest in treasury bills? Estimate the standard deviation of your portfolio.