Agric. Econ. - Czech, X:X | DOI: 10.17221/377/2025-AGRICECON

Optimising the Stutzer ratio in multivariate agricultural portfoliosOriginal Paper

Dejan Živkov1, Boris Kuzman1, Jonel Subić1
1 Institute of Agricultural Economics, Belgrade, Serbia

This paper evaluates the risk-adjusted performance of multivariate agricultural portfolios using the Stutzer ratio, an advanced measure that accounts for non-normal return distributions and downside risk. Three four-asset portfolios – grains, softs, and meats – are analysed in this study. The Stutzer ratio incorporates a risk-aversion parameter (θ) that penalises tail risk, providing a more accurate assessment of skewed and fat-tailed returns. Results show that Stutzer-optimised portfolios outperform naïve equal-weight portfolios in risk-adjusted terms, as optimisation effectively balances expected returns and downside exposure. Among the three portfolio categories, the softs portfolio exhibits the highest Stutzer ratio, with the meats portfolio following closely behind. Both portfolios have a relatively high tail-adjustment parameter (theta), indicating a reduced exposure to downside risk and a lower likelihood of extreme negative returns. Consequently, their risk-adjusted performance suggests greater return stability, making them particularly attractive to long-term investors.

Keywords: downside risk; exponential decay factor; risk-adjusted metric

Received: September 12, 2025; Revised: March 1, 2026; Accepted: March 10, 2026; Prepublished online: August 10, 2026 

Download citation

References

  1. Ahmadian-Yazdi F., Roudari S., Omidi V., Mensi W., Al-Yahyaee K.H. (2024): Contagion effect between fuel fossil energies and agricultural commodity markets and portfolio management implications. International Review of Economics & Finance, 95: 103492. Go to original source...
  2. Alekneviciene V., Stareviciute B., Alekneviciute E. (2018): Evaluation of the efficiency of European Union farms: A risk-adjusted return approach. Agricultural Economics - Czech, 64: 241-255. Go to original source...
  3. Benson K., Gray P., Kalotay E., Qiu J. (2008): Portfolio construction and performance measurement when returns are non-normal. Australian Journal of Management, 32: 445-462. Go to original source...
  4. Bessler W., Taushanov G., Wolff D. (2021): Optimal asset allocation strategies for international equity portfolios: A comparison of country versus industry optimization. Journal of International Financial Markets, Institutions and Money, 72: 101343. Go to original source...
  5. Bondarenko O. (2014): Variance trading and market price of variance risk. Journal of Econometrics, 180: 81-97. Go to original source...
  6. Furuoka F., Yaya O.S., Ling P.K., Al-Faryan M.A.S., Islam M.N. (2023): Transmission of risks between energy and agricultural commodities: Frequency time-varying VAR, asymmetry and portfolio management. Resources Policy, 81: 103339. Go to original source...
  7. Gorton G.B., Hayashi F., Rouwenhorst K.G. (2013): The fundamentals of commodity futures returns. Review of Finance, 17: 35-105. Go to original source...
  8. Haley M.R. (2008): A simple nonparametric approach to low-dimension, shortfall-based portfolio selection. Finance Research Letters, 5: 183-190. Go to original source...
  9. Haley M.R., McGee M.K. (2011): 'KLICing' there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance. Journal of Empirical Finance, 18: 341-352. Go to original source...
  10. Hanif W., Mensi W., Vo X.V., BenSaïda A., Hernandez J.A., Kang S.H. (2023): Dependence and risk management of portfolios of metals and agricultural commodity futures. Resources Policy, 82: 103567. Go to original source...
  11. Hernandez J.A., Kang S.H., Yoon S.M. (2020): Spillovers and portfolio optimization of agricultural commodity and global equity markets. Applied Economics, 53: 1326-1341. Go to original source...
  12. Investing.com (2025): Commodities. [Dataset]. Available at https://www.investing.com/commodities/ (accessed Aug 15, 2025).
  13. Khalfaoui R., Shahzad U., Asl M.G., Jabeur S.B. (2023): Investigating the spillovers between energy, food, and agricultural commodity markets: New insights from the quantile coherency approach. The Quarterly Review of Economics and Finance, 88: 63-80. Go to original source...
  14. Liu Y., Yao Z. (2025): Soft commodity volatility prediction: A perspective of climate risk concerns. Finance Research Letters, 85: 108049. Go to original source...
  15. Nguyen D.B.B., Prokopczuk M. (2019): Jumps in commodity markets. Journal of Commodity Markets, 13: 55-70 Go to original source...
  16. Stutzer M. (2000): A portfolio performance index. Financial Analysts Journal, 56: 52-61. Go to original source...
  17. Voicilas D.M. (2020): Reflections on the evolution of the cereals' market in Romania. Western Balkan Journal of Agricultural Economics and Rural Development, 2: 31-43. Go to original source...
  18. Zakamouline V., Koekebakker S. (2009): Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance. Journal of Banking & Finance, 33: 1242-1254. Go to original source...
  19. Zhang J., Yu J., Ma S., Li J., Zhu Z. (2025): Green finance and agricultural climate resilience: Evidence from China. Research in International Business and Finance, 78: 102995. Go to original source...
  20. Zhao Y., Ju R. (2025): Biofuel, grain and vegetable oil markets: Dynamic connectedness and the optimal portfolio. Agribusiness. Go to original source...
  21. Živkov D., Kuzman B., Subić J. (2022): Measuring the risk-adjusted performance of selected soft agricultural commodities. Agricultural Economics - Czech, 68: 87-96. Go to original source...

This is an open access article distributed under the terms of the Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.