Question

Please consider all that we have learned thus far regarding the impact of diversification, risk-free securities, and market premiums. With that in mind, Please describe how adding a risk-free security to modern portfolio theory allows investors to do better than the efficient frontier. Additionally, explain how might the magnitude of the market risk premium impact people's desire to buy stocks?

Answer 1

what do the risk-free rate and the optimal risky portfolio(efficient Frontier) create?

They create a portfolio with the maximum utility.

1. Modern portfolio theory assumes that investors are rational.
2. They want to maximize the utility of their portfolio.
3. According to modern portfolio theory utility is a positive function of return and negative function of risk.
4. To calculate portfolio with maximum utility, we calculate the coefficient of variation.
5. Coefficient of variation is standard deviation divided by the return of the portfolio.
6. Lower the coefficient of variation, the better, the lower the unit of risk per unit of return.
7. The portfolio with a lower coefficient of variation in the pool of portfolio- lies on efficient Frontier.
8. So a portfolio on efficient Frontier gives the lowest amount of risk per unit of return.
9. That's why we invest in the portfolio on efficient Frontier rather than portfolio below the Efficient Frontier (inefficient portfolio/all other possible portfolios).
10. By adding a risk-free asset to the optimal risk portfolio - the overall return increase keeping the Sharpe ratio intact.

How?
11. This is done by shorting the risk-free asset and investing the proceeds in the optimal portfolio. As the portfolio has a higher return then compared to the risk-free asset.
Thus increasing the overall return.

Thus investing in such a way by improving utility maximization.

Market risk premium decides the overall return on the equity.

As per the Capital Asset pricing model:

As per CAPM model:
Re= Rf+(Rm-Rf)B

Re= required rate of return/return on equity.
Rf= Risk-free rate.
Rm =Market Risk Premium.
B = Beta, systematic risk.

So from the equations, it becomes clear that as market risk premium increases/decreases so does the return on equity.

As the return on equity increase/decreases so does the willing to buy stock increases/decreases.