Title LM02 Portfolio Risk and Return Part II IFT Notes.pdf ✅

LM02 Portfolio Risk and Return: Part II 2025 Level I Notes © IFT. All rights reserved 3 1. Introduction In this reading, we will discuss:  The capital market line (CML).  The two components of total risk: systematic and nonsystematic risk.  The capital asset pricing model (CAPM) and the security market line (SML). The primary objective of this reading is to identify the optimal risky portfolio using CAPM. 2. Capital Market Theory: Risk-Free and Risky Assets Portfolio of Risk-Free and Risky Assets This is a repetition of what we have seen in the previous reading. When a risk-free asset is combined with a risky asset, it results in higher risk-adjusted returns because the risk-free asset has zero correlation with the risky asset. This leads to the capital allocation line. Investors have different views of the market (and different levels of risk aversion) which means the individual risky assets (e.g. securities) they choose to form their portfolio are different. Combining the capital allocation line with an investor’s indifference curve leads to different optimal risky portfolios, as illustrated in the exhibit below. We now explore whether a unique optimal risky portfolio exists for all investors. The answer is yes, if there is homogeneity of expectations. What is homogeneity of expectations?  It means that all investors have the same economic expectations for an asset.  For example, assume there are two securities. With homogeneity of expectations, all
LM02 Portfolio Risk and Return: Part II 2025 Level I Notes © IFT. All rights reserved 4 investors have the same views on risk, return, price, cash flows, and the correlation between the two assets. This means the calculation to arrive at optimal risky portfolio for all investors would be the same. 3. Capital Market Theory: The Capital Market Line Since all investors have the same expectations, they will construct only one efficient frontier. If there is one efficient frontier, there will be only one capital allocation line. The point where this capital allocation line is tangential to the efficient frontier is called the market portfolio. This is the optimal risky portfolio when all investors have the same expectations. The CML is a special case of the CAL where the efficient portfolio is the market portfolio. Now, let us derive the equation for CML. We will use a basic equation of the form: Y = C + mX where: Y= Rp (portfolio return) C = Rf (risk-free rate) m = slope = (Rm - Rf) / σm X = portfolio standard deviation = σp The equation for CML can be written as Rp = Rf + (Rm − Rf σm ) ∗ σp Any point along the CML is a combination of the risk-free asset and the market portfolio. At the point where the CML intersects y-axis, 100% is invested in the risk-free asset and its weight decreases as we go up along the CML. What is the market? Theoretically, the market includes all risky assets or anything that has value. Examples