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%)

1. What would CalPERS portfolio allocation have to be (portfolio weights) i.e. what fraction of its portfolio would it need to invest in the S&P 500 index and what fraction would it need to invest in 3-month T-bills in order for it to meet its expected return target of 7%?