Question

Given decreasing marginal utility, it is possible to prove that in a meanvariance framework no individual will hold 100% of his or her wealth in the risk-free asset. Why? (Hint: The answer requires using the shape of investors’ indifference curves as well as the Capital Market Line.)

Answer 1

Solution:

The capital market line (CML) represents portfolios that optimally combine risk and return. Capital asset pricing model (CAPM), depicts the trade-off between risk and return for efficient portfolios. It is a theoretical concept that represents all the portfolios that optimally combine the risk-free rate of return and the market portfolio of risky assets. Under CAPM, all investors will choose a position on the capital market line, in equilibrium, by borrowing or lending at the risk-free rate, since this maximizes return for a given level of risk.

1) The capital market line (CML) represents portfolios that optimally combine risk and return.

2)The intercept point of CML and efficient frontier would result in the most efficient portfolio called the tangency portfolio.

3)As a generalization, buy assets if sharpe ratio is above CML and sell if sharpe ratio is below CML.

Formula : ​Rp​=rf​+​(RT​−rf​)*​σp​ / σt

Where:

Rp​=portfolio return.

rf​=risk free rate

RT​=market return

σp = Standard deviation of Market return.

σt = Standard deviation of Portfolio return.