《黄金驱动因素的量化视角解读——“黄金时代”贵金属系列报告（二）》

Quantitative Models and Construction Methods - Model Name: OLS Regression Model Model Construction Idea: Utilize macroeconomic and fundamental factors to predict gold prices, incorporating high-frequency data and shorter lag periods for better recent market fit[4][23][27] Model Construction Process: 1. Select macroeconomic and fundamental factors such as the US Dollar Index, US 10-year Treasury yield, Federal Reserve total assets, global gold reserves, and quantitative price momentum indicators (e.g., 120-day momentum and DT strategy signals)[4][27][51] 2. Perform regression analysis using Ordinary Least Squares (OLS) method 3. Incorporate additional quantitative factors like momentum and DT signals to improve prediction accuracy[27][30][47] Formula: $ Y = -6492.97 - 11.776 X1 + 55.694 X2 + 0.00003005 X3 + 0.2596 X4 + 246800 X5 - 49.237 X6 $ - $ Y $: London gold price - $ X1 $: US Dollar Index - $ X2 $: US 10-year Treasury yield - $ X3 $: Federal Reserve total assets - $ X4 $: Global gold reserves - $ X5 $: 120-day price momentum - $ X6 $: DT strategy timing signal[51] Model Evaluation: Improved prediction accuracy with added quantitative factors, capturing non-macro and non-fundamental drivers[30][50] Quantitative Factors and Construction Methods - Factor Name: Momentum Factor Factor Construction Idea: Analyze price trends by calculating average returns over a specific period, assuming price movements persist[9][13][19] Factor Construction Process: 1. Define daily logarithmic returns: $ r_i = \ln(P_i / P_{i-1}) $ 2. Calculate cumulative or average returns over $ N $ days: $ Momentum_T = \sum_{i=T-N}^{T} r_i $ or $ Momentum_T = \frac{1}{N} \sum_{i=T-N}^{T} r_i $ 3. Use thresholds to determine trading signals: - Open long positions when momentum exceeds a positive threshold - Open short positions when momentum falls below a negative threshold[12][13][19] Factor Evaluation: Effective for capturing long-term trends but less sensitive to short-term fluctuations[39][42] - Factor Name: Dual Thrust (DT) Strategy Signal Factor Construction Idea: A rule-based timing strategy derived from historical price ranges to generate buy/sell signals[3][19][20] Factor Construction Process: 1. Calculate $ HH $, $ LC $, $ HC $, and $ LL $: - $ HH $: Highest high of $ N $ days - $ LC $: Lowest close of $ N $ days - $ HC $: Highest close of $ N $ days - $ LL $: Lowest low of $ N $ days 2. Compute upper and lower bounds: $ Upper = Open + K1 \cdot \max(HH - LC, HC - LL) $ $ Lower = Open - K2 \cdot \max(HH - LC, HC - LL) $ 3. Generate signals: - Open long positions when price exceeds $ Upper $ - Open short positions when price falls below $ Lower $[19][20] Factor Evaluation: Provides predictive timing signals with moderate Sharpe and Calmar ratios[20][22] Model Backtesting Results - OLS Regression Model: - R-squared: 0.950 - Adjusted R-squared: 0.947 - F-statistic: 288.8 - Prob(F-statistic): 5.41e-66[47][50] - Momentum Factor: - R-squared (120-day momentum): 0.909 - Adjusted R-squared: 0.909 - F-statistic: 563.1 - Prob(F-statistic): 5.23e-171[35][39] - DT Strategy Signal: - Sharpe Ratio: 0.61 - Calmar Ratio: 0.26 - Annualized Return: 6% - Total Return: 89.1%[20][22] Factor Backtesting Results - Momentum Factor: - R-squared (250-day momentum): 0.921 - Adjusted R-squared: 0.921 - F-statistic: 563.1 - Prob(F-statistic): 5.23e-171[39][42] - DT Strategy Signal: - Sharpe Ratio: 0.61 - Calmar Ratio: 0.26 - Annualized Return: 6% - Total Return: 89.1%[20][22]