# CML Derivation

How the CML is derived?

The line of possible portfolio risk and return combinations given the risk-free rate, risk and return of a portfolio of risky assets is referred to as the capital allocation line (CAL).

A simplifying assumption underlying modern portfolio theory is that investors have homogeneous expectations, i.e., they all have the same estimates of risk, return, and correlations with other risky assets for all risky assets. Under this assumption, all investors face the same efficient frontier of risky portfolios and will all have the same optimal risky portfolio and CAL.

Under the assumption of homogeneous expectations, this optimal CAL for all investors is termed the capital market line (CML).

A line used in the capital asset pricing model to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio.

The CAPM is a model for pricing an individual security or a portfolio

expected return = risk-free rate + portfolio beta* (the difference between the expected return on the market as a whole and the risk-free rate).

Efficient frontier:

Efficient frontier is the set of portfolios among all the possible portfolios of combinations of individual risky assets that offers the highest expected return for each level of risk (standard deviation

The concept of an efficient frontier can be used to illustrate the benefits of diversification. An undiversified portfolio can be moved closer to the efficient frontier by diversifying it. Diversification can, therefore, increase returns without increasing risk, or reduce risk without reducing expected returns.

The assumptions:

The assumptions of Capital Market theory are primarily eightfold and I will attempt to explain them below. 1. Everyone is an Efficient Investor – It goes without saying that everyone wants to be a efficient investor. No investor wants economic loss and all