Forecasting Risk-Adjusted Performance Metrics Using ARIMA Models: Evidence from Sharpe, Jensen, and Treynor Ratios

Abstract: This study uses ARIMA time series models to examine and predict three important measures of investment performance: the Sharpe Ratio, Jensen Ratio, and Treynor Ratio. Autocorrelation (ACF) and partial autocorrelation (PACF) plots are analyzed for each metric to help select appropriate models. Forecasts are produced starting from the 13th time period, along with 95% confidence intervals. The results show that forecasts for all three ratios remain close to zero and are accompanied by relatively narrow confidence ranges, indicating minimal short-term fluctuation. Among the three measures, the Treynor Ratio displays slightly lower forecast uncertainty, reflected in smaller standard errors. Overall, the findings suggest stable performance expectations, which can aid investment evaluation and risk assessment when market conditions remain steady.

Keywords: ARIMA models, Sharpe ratio, Jensen ratio, Treynor ratio, time series forecasting, autocorrelation (ACF), partial autocorrelation (PACF), financial performance metrics, investment risk analysis, and confidence intervals.