BUSFIN4221 – Investments (Module 2 – Portfolio Theory)

Module 2: Portfolio Theory

(BUSFIN 4221 – Investments)

Instructor:	Andrei S. Gonçalves
E-mail:	Andrei_Goncalves@kenan-flagler.unc.edu
Website:	andreigoncalves.com/BUSFIN4221

Welcome to Module 2!

Download the class slides here and the “to print” version here.

Suppose an investor has a good sense of the risks and rewards associated with different financial securities in capital markets. How should he/she build a portfolio? In Module 2 we will answer this question.

We start by defining “risk” and “reward” as the volatility, $\sigma[r]$ , and expected return, $\mathbb{E}\left[r\right]$ , of an investment. Then, we demonstrate how portfolios can be formed to achieve the best possible risk-return combination. The key concept here is diversification (decreasing risk by combining different financial securities).

The process of forming a portfolio can be separated into two steps:

Step 1: Find the Optimal Risky Portfolio

Investors should start by finding the portfolios with the best risk-reward combinations (the efficient frontier). Each investor will hold a risky portfolio in the efficient frontier:

If investors have access to unlimited borrowing and lending at the risk-free rate, they all hold the same risky portfolio, which is called the “tangent portfolio” (or “optimal risky portfolio”). The reason is that the tangent portfolio is the best portfolio to be combined with a position in the risk-free asset:

Step 2: Combine the Optimal Risky Portfolio (or Tangent Portfolio) with a position on the Risk-Free Asset

Once the optimal risky portfolio is selected, each investor needs to combine it with a position on the risk-free asset (i.e., form his/her “complete portfolio”). Different weights simply allocate investors to different points in the Capital Allocation Line (CAL). Even though the optimal risky portfolio is the same for all investors, the complete portfolio is not and it will depend on the risk aversion of each investor (more risk averse investors will tend to select complete portfolios that are closer to the risk-free asset in the risk-reward space):