15.3 Relationship Between Risk And Return In Portfolio

15.3 Relationship Between Risk And Return In Portfolio

Calculate and Interpret the Expected Return of a Portfolio of Securities

The relationship between risk and return is a foundational concept in investment theory and practice. When considering a portfolio, you need to understand both how to calculate the expected return and interpret its implications. Here’s how to do that:

Calculating Expected Return

The expected return of a portfolio is the weighted average of the expected returns of the individual securities in the portfolio. This can be calculated using the formula:

• \(E(R_p)\) is the expected return of the portfolio
• \(w_i\) is the weight of security i in the portfolio
• \(E(R_i)\) is the expected return of security i

Example

If you have a portfolio with three securities with the following expected returns and weights:

• Security A: Expected return = 10%, weight = 50%
• Security B: Expected return = 8%, weight = 30%
• Security C: Expected return = 6%, weight = 20%

Then the expected return of the portfolio would be calculated as:

Thus, the portfolio’s expected return is 8.6%.

Benefits and Challenges of Combining Securities in a Portfolio

Benefits of Combining Securities (Diversification)

1. Risk Reduction:

   • By investing in a variety of securities, specific risk (also known as unsystematic risk) can be reduced.
   • Diversification diminishes the impact of any one security’s performance on the overall portfolio.

2. Potential for Higher Returns:

   • Diversification provides access to different securities with varying performance, some of which may yield higher returns.

3. Smoothing Out Volatility:

   • Grouping a mix of securities helps stabilize returns, as not all investments will react to market changes in the same way or at the same magnitude.

Challenges of Diversification

1. Diminishing Returns:

   • After a certain point, adding more securities provides fewer benefits in risk reduction and may not significantly affect returns.

2. Higher Transaction Costs:

   • More securities mean more transactions, which leads to increased transaction costs and management fees.

3. Complexity:

   • Managing a diversified portfolio can be complex and might require time, resources, and expertise beyond the average investor.

Key Takeaways

• Expected Return Calculation: The expected return of a portfolio is a weighted sum of the expected returns of individual assets.
• Risk and Return Trade-Off: Proper diversification can help reduce risk without dramatically impacting potential returns.
• Diversification Benefits and Challenges: While reducing specific risk, diversification comes with certain logistical and cost challenges.

Frequently Asked Questions (FAQs)

What is the significance of the expected return in portfolio management?

The expected return provides an estimate of the potential gain from the portfolio over a certain period, helping investors compare different portfolios and set realistic financial goals.

How does diversification reduce risk?

Diversification reduces risk by spreading investments across diverse assets, which generally lowers unsystematic risk as the poor performance of one security can be offset by better performance of others in the portfolio.

Is there a limit to the benefits of diversification?

Yes, after a certain level, additional securities bring diminishing benefits in risk reduction. This phenomenon is due to various securities’ inherent correlation, where most non-systematic risks get diversified away with a sufficiently large and varied portfolio.

Glossary

• Expected Return: The average return an investor anticipates receiving from an investment or a portfolio.
• Portfolio: A group of financial securities that an investor holds.
• Diversification: The strategy of reducing risk by investing in a variety of assets.
• Unsystematic Risk: Risk that is unique to a specific company or industry.

Visualizations

Diversification Effect on Risk

    pie
	    title Diversification's Impact on Risk Level
	    "Unsystematic Risk Reduced" : 70
	    "Remaining Risk" : 30

Conclusion

Understanding the relationship between risk and return is crucial in creating a well-balanced investment portfolio. Calculating and interpreting the expected return, while appreciating the pros and cons of diversification, can significantly assist investors in achieving their financial goals.

In this section

• 15.3.1 Calculating Rate Of Return In Portfolio
  A comprehensive guide on calculating the rate of return for a portfolio including mathematical formulas, examples, FAQs, and key takeaways.
• 15.3.2 Measuring Risk In Portfolio
  An in-depth guide on how to measure risk in a portfolio, balancing diversification, and strategies to limit losses using derivatives.
• 15.3.3 Combining Securities In Portfolio
  Learn the principles and methodologies of combining securities in a portfolio to optimize risk and return in the Canadian Securities Course.