California Public Employees' Retirement System (CalPERS) manages a pension fund for public sector employees in the state of California. CalPERS' assets consist of contributions made by employers and employees. CalPERS invests the contributions in order to generate the funds it needs to pay out retirement benefits in the future. With about 2 million participants in its pension fund, CalPERS manages assets worth over $400 billion and paid out about $24 billion in benefits in 2019. In 2016, CalPERS determined that it would target an expected rate of return from its investments of 7%. Suppose CalPERS believes that the CAPM holds and adopts a simple approach toward constructing its investment portfolio to achieve its expected return target - it will only invest in the S&P 500 index (market portfolio) and 3-month treasury bills (risk-free asset). The 3-month T-bills are expected to yield 2.00% (i.e. the annual risk-free rate is 2.00%) and the S&P 500 index is expected to return 6.00% more than the 3-month T-bill yield (i.e. the expected market risk premium is 6.00%) In light of the new economic conditions, CalPERS revises its investment approach. It will continue to hold the S&P 500 index (market portfolio) but will no longer hold 3-month T-bills (risk-free asset) in its portfolio. In addition to the S&P 500 index, CalPERS will invest in a portfolio of either low-grade/high- yield bonds (junk bonds) or private equity. The S&P 500 index is still expected to have a volatility of 18% and CalPERS has the following information on junk bonds and private equity: Asset Class Volatility Correlation with S&P 500 Return Beta Expected Return 8.00% 9.50% Junk Bonds Private Equity 50% 40% 0.45 0.68 1.25 1.50 6. What would CalPERS' new portfolio allocation (portfolio weights) have to be in order to achieve an expected return of 7% if in addition to the S&P 500 index CalPERS invested in: a. Junk bonds b. Private equity