Efficient Frontier With One Risk-free Asset (A risk-free security)
Is one that has zero variance and, hence, standard deviation (square root of variance). James Tobin has pointed out that (a) Portfolio made up of risky asset and one risk·free asset generate investment opportunities (portfolio opportunity set) with linear relationship between expected return and risk; (b) One such
portfolio opportunity set will dominate and/or portfolios of securities/other asset. To facilitate further discussion, let us denote a unroll by portfolio by M, and a complete portfolio formed by combining them as the fraction of the overall portfolio invested in M, and the remaining (= 1 - 11) in 1, the expected return of the complain portfolio may be calculated by using Equation 3,1
Shows three capital allocation lines originating from point F and passing through A, M and Z Point F represents a pure portfolio (100 per cent holding) of risk-free assets, with expected rate return E(r) and zero standard deviation of expected returns, Point A is the lower end of the minimum variance frontier of risky assets. Point Z is the top end of the minimum variance frontier assets, It is obvious from the figure that the supported by the efficient frontier risky assets is tangential at point M. In other words, combinations of portfolio M with risk- free offer the, best risk-return trade-off. Point M represents the pure portfolio (100 per cent holding) of a risky asset, with expected return E(r,) and standard deviation 0. The Investor can obtain any combination of risk and mum on line segment- FM by combinations the risk-free asset F
with a portfolio of risky assets, namely, M. Thus, portfolio M is the best risky portfolio to be combined with a risk-free asset. Portfolios represented by line segment FM are known as lending portfolios.