ABC Company Hired You To Explain The Assessment Criteria

Abc Company Has Hired You To Explain The Criteria For Assessing The Pe

Abc Company has hired you to explain the criteria for assessing the performance of a security, specifically expected rate of return, standard deviation of rate of return, and coefficient of variation (CV). They also want you to show how, by forming a portfolio, an instrument can be generated that has properties better than each of its constituents in terms of the standard deviation of rate of return and CV. How would you explain and show this information to ABC Company?

Paper For Above instruction

When evaluating the performance of a security, investors and analysts rely on specific criteria that help determine its attractiveness and risk profile. The three primary measures used for such assessment are the expected rate of return, the standard deviation of the rate of return, and the coefficient of variation (CV). Each of these metrics provides insight into different aspects of a security’s performance and risk, facilitating informed investment decisions.

Expected Rate of Return

The expected rate of return is the anticipated average return an investor expects to earn from an investment over a specified period. It is calculated by taking the weighted average of all possible returns, with weights corresponding to the probabilities of each return occurring. Mathematically, it is expressed as:

Expected Return = ∑ (Probability of Outcome × Return in Outcome)

This measure is crucial as it provides an estimate of potential profitability. A higher expected return generally signifies a more lucrative investment; however, it must be considered alongside risk factors to avoid solely chasing high returns without regard to volatility.

Standard Deviation of Rate of Return

The standard deviation measures the dispersion or variability of returns around the expected return, thereby quantifying risk. A larger standard deviation indicates higher volatility and, consequently, greater uncertainty regarding future returns. The calculation involves the square root of the variance, which is the average squared deviations from the expected return:

Standard Deviation = √∑ [Probability × (Return - Expected Return)²]

This metric helps investors understand how much actual returns might fluctuate, thereby informing risk management strategies. Securities with lower standard deviations are often deemed less risky, although this should be balanced with return expectations.

Coefficient of Variation (CV)

The coefficient of variation provides a standardized measure to compare the risk per unit of return, especially useful when assessing securities with different expected returns. It is calculated as:

CV = Standard Deviation / Expected Return

A lower CV indicates a more efficient investment, offering a better trade-off between risk and return. It enables investors to compare securities regardless of their nominal return levels, focusing on risk relative to reward.

Enhancing Performance Through Portfolio Diversification

While individual securities can be evaluated using these criteria, combining assets into a portfolio can optimize risk and return characteristics. Diversification aims to construct portfolios where the overall risk, measured by the standard deviation, is reduced beyond what is achievable by individual securities alone.

The core principle lies in the correlation between asset returns. When assets are not perfectly positively correlated, their price movements tend to offset each other to some extent, reducing overall portfolio volatility. This is expressed mathematically through the portfolio variance, which takes into account the weights of individual securities and their pairwise covariances.

The formula for portfolio variance is:

Variancep = ∑i=1 ∑j=1 wi wj Cov(Ri, Rj)

where wi and wj represent weights assigned to securities i and j, and Cov(Ri, Rj) is the covariance between their returns.

Through optimal portfolio construction—determining the right combination of assets and weights—investors can achieve a portfolio with a lower standard deviation than any individual security. Moreover, the CV of the portfolio can also be improved, offering a more efficient risk-return profile.

For example, suppose Security A has a high expected return but also a high standard deviation, while Security B has a lower expected return but also a lower standard deviation. By blending these securities in the right proportions, the portfolio may exhibit a lower overall standard deviation and CV than Security A alone, while maintaining a respectable expected return.

Practical Implications for ABC Company

To communicate these concepts effectively, ABC Company should understand that evaluating individual securities is essential but insufficient for optimal investment performance. Portfolio diversification exploits the correlation properties among assets to reduce risk. By calculating the expected returns, standard deviations, and CVs of potential assets and then modeling various combinations, investors can identify portfolios that outperform individual securities in terms of risk-adjusted returns.

Additionally, modern portfolio theory (MPT) emphasizes that an efficient portfolio lies on the efficient frontier—offering the highest expected return for a given level of risk. Using software tools and statistical models, ABC Company can simulate different asset mixes to find the optimal portfolio that minimizes the CV and standard deviation, thus achieving superior risk-adjusted performance.

Conclusion

In summary, the assessment of securities through expected rate of return, standard deviation, and coefficient of variation provides foundational insights into their performance and risk profiles. Portfolio theory demonstrates that combining assets intelligently can produce a portfolio with better properties—specifically lower risk and CV—than any individual security. Implementing such strategies enables ABC Company to optimize its investment performance, balancing risk and reward effectively in pursuit of its financial goals.

References

  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
  • Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119–138.
  • Luenberger, D. G. (1997). Investment Science. Oxford University Press.
  • Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2009). Modern Portfolio Theory and Investment Analysis (8th ed.). Wiley.
  • Fabozzi, F. J., & Markowitz, H. M. (2011). The Theory and Practice of Investment Management. Wiley.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
  • Ross, S., Westerfield, R., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.
  • Levy, H. (2017). Securities Analysis and Portfolio Management. McGraw-Hill Education.
  • Fan, J., & Li, Q. (2012). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348–1360.
  • Gurobi Optimization, Inc. (2021). Mathematical Optimization Guide. Retrieved from https://www.gurobi.com/

Related Assignments