Investor’s Optimal Portfolio: Understanding Risk Aversion and Indifference Curves | CFA Level I Portfolio Management

In this lesson, we’ll dive into determining an investor’s optimal portfolio by exploring risk aversion, indifference curves, and capital allocation lines.

Risk Aversion: The Different Types of Investors

Before we go any further, let’s clarify what risk aversion is. There are three main types of investors: risk-averse, risk-neutral, and risk-seeking. Given two assets with the same expected return, one less risky and the other more risky:

• A risk-neutral investor is indifferent between the two.
• A risk-seeking investor prefers the risky asset, hoping for a higher return.
• A risk-averse investor goes for the risk-free asset, avoiding additional risk.

To convince a risk-averse investor to take more risk, the asset should have a higher expected return to compensate for the additional risk. This leads us to the concept of an investor’s indifference curve.

Indifference Curves: Risk Aversion Spectrum

Risk aversion varies among investors, resulting in different indifference curves. These curves represent the levels of utility or satisfaction an investor derives from an investment. Key points:

• Same level of satisfaction for investments on the same curve
• Higher satisfaction for investments on a higher curve

Efficient Frontier and Risk-Free Assets

When considering all investable risky assets, we can construct an opportunity set and an efficient frontier of risky assets. The efficient frontier represents the set of most optimal portfolios for each level of return. The introduction of a risk-free asset allows investors to invest in portfolios matching their risk-aversion levels.

Capital Allocation Line and Optimal Risky Portfolio

By combining a risk-free asset with a risky portfolio, we create the capital allocation line (CAL). The CAL is steepest when it is tangential to the efficient frontier, indicating the optimal risky portfolio.

Finding the Optimal Risky Portfolio for an Investor

By bringing back the investor’s indifference curves, we can identify the optimal portfolio for a particular investor. This point is where the CAL intersects the investor’s highest achievable utility indifference curve.

Expected Return and Standard Deviation

The expected return of the portfolio is the weighted average of the risk-free rate and the risky rate of return. The standard deviation of returns is the weight of the risky portfolio multiplied by its standard deviation.

Different Investors, Different Optimal Portfolios

As we mentioned earlier, investors have varying levels of risk aversion, leading to different optimal portfolios. Highly risk-averse investors tend to invest a larger proportion in risk-free assets, resulting in lower risk and return. In contrast, less risk-averse investors may have a higher proportion of risky portfolios, even leveraging to increase risk and return.