The Indifference Curve of an Investor represents different combinations of risk and return that provide the investor with the same level of satisfaction. It illustrates the trade-off between higher returns and increased risk based on an investor’s risk tolerance.
- Upward Sloping: Investors demand higher returns for higher risk.
- Convex Shape: Diminishing marginal utility of risk-taking.
- Higher Curves Indicate Higher Utility: More return for the same risk.
The set of all portfolios with the same utility score plots as a risk-indifference curve. An investor will accept any portfolio with a utility score on her risk-indifference curve as being equally acceptable.
However, there are many possible portfolios on many risk-indifference curves that do not yield the highest return for a given risk. All of these portfolios lie below the efficient frontier. The optimal portfolio is a portfolio on the efficient frontier that would yield the best combination of return and risk for a given investor, which would give that investor the most satisfaction.
These risk-indifference curves, calculated with the utility formula with the risk aversion coefficient = 2, but with higher utility values resulting from setting the risk-free rate to successively higher values. Of course, any investor, regardless of risk aversion, would like to receive a higher return for the same risk. The utility of these risk-indifference curves is that they allow the selection of the optimum portfolio out of all those that are attainable by combining these curves with the efficient frontier. Where 1 of the curves intersects the efficient frontier at a single point is the portfolio that will yield the best risk-return trade-off for the risk that the investor is willing to accept.
In the graph below, risk-indifference curves are plotted along with the investment opportunity set of attainable portfolios. Data points outside of the investment opportunity set designate portfolios that are not attainable, while those portfolios that lie along the northwest boundary of the investment opportunity set is the efficient frontier. All portfolios that lie below the efficient frontier have a risk-return trade-off that is inferior to those that lie on the efficient frontier. If a utility curve intersects the efficient frontier at 2 points, there are a number of portfolios on the same curve that lie below the efficient frontier; hence they are not optimal. Remember that all points on a risk-indifference curve are equally attractive to the investor; therefore, if any points on the indifference curve lie below the efficient frontier, then no point on that curve can be an optimum portfolio for the investor. If a utility curve lies wholly above the efficient frontier, then there is no attainable portfolio on that utility curve.
However, there is a utility curve such that it intersects the efficient frontier at a single point this is the optimum portfolio. The only attainable portfolio is on the efficient frontier, and thus, provides the greatest satisfaction to the investor. The optimum portfolio will yield the highest return for the amount of risk that the investor is willing to take.
Features of Indifference Curve of an Investor:
-
Upward Sloping
The indifference curve is positively sloped, indicating that investors require higher returns to accept higher risk. This reflects the fundamental risk-return trade-off, where rational investors will only take on additional risk if they are compensated with greater expected returns. The more risk an investment carries, the higher the return needed to keep the investor equally satisfied.
-
Convex Shape
The indifference curve is convex to the origin, meaning that as risk increases, investors require disproportionately higher returns. This follows the principle of diminishing marginal utility, where investors demand greater compensation for taking on additional risk beyond a certain point. The curve’s convexity shows that risk tolerance decreases as uncertainty grows.
-
Higher Curves Represent Higher Utility
An investor’s preference improves as the indifference curve shifts upward, meaning they are achieving a higher return for the same level of risk. This is ideal for investors seeking optimal portfolios that align with their risk-return preferences. A higher curve signifies a more desirable investment combination.
-
No Intersecting Curves
Indifference curves never intersect because each represents a different level of utility. If two curves were to cross, it would imply that an investor derives the same satisfaction from different risk-return combinations, which contradicts the rational decision-making process in investing. Each curve uniquely represents a distinct risk preference level.
-
Different Investors Have Different Curves
Each investor has a unique risk tolerance, resulting in different indifference curves. Risk-averse investors have steeper curves, requiring significantly higher returns for taking on additional risk. In contrast, risk-seeking investors have flatter curves, meaning they are willing to accept more risk for relatively lower returns.
-
Downward Movement Shows Lower Satisfaction
If an investor moves to a lower indifference curve, it means they are receiving less return for the same risk, resulting in lower satisfaction. This shift represents a suboptimal portfolio choice or an investment decision that does not align with their preferred risk-return balance.
-
Used in Portfolio Selection
The concept of indifference curves is essential in Modern Portfolio Theory. It helps investors identify optimal portfolios by combining risk-free assets and risky assets. The point where the highest indifference curve touches the efficient frontier represents the ideal portfolio choice for an investor.