Fig 5 Portfolio Choice with a Risk Free Security
Portfolio of the risk-free and the risky investments, represented by point P, will yield an
expected return of 22.8% (being 0.4 X 12 + 0.6 X 30) and have a s of 12% (being 0.6 X
20).
The portfolios representing all possible combinations of F and V would lie on the straight
line joining F and V (Fig 5). What is the impact of introducing the risk-free security on
the efficient set? Which risky portfolio from the efficient set of risky portfolios would
investors choose to combine with the risk-free security? The line representing a portfolio
of F and a risky security from the efficient set of risky portfolio would be pushed as far
up as possible. Till it is tangential to the erstwhile efficient set at point M. In their
attempt to maximize the expected return for a given level of risk, all investors would
choose a portfolio lying on this line. Therefore this would become the new efficient set.