Ratanlal Mahanta

Computational Finance | AI-Driven Quantitative Research

Alpha-Generating Strategy — Mathematical Model

Designed and tested alpha-generating trading strategies combining time-series momentum, machine-learning classification signals, statistical and arbitrage based capital allocation. Deployed backtesting platform with walk-forward validation and multi-asset optimization.

1) Time-Series Momentum

Directional momentum signal over lookback L (price or log-return form):

$$ m_t = \operatorname{sign}\big(R_{t,L}\big),\quad R_{t,L} = \sum_{j=1}^{L} r_{t-j} \quad \text{or} \quad m_t = P_t - P_{t-L} $$

Scaled position with risk targeting (volatility $ \hat{\sigma}_t $):

$$ x_t^{\text{mom}} = \tau\,\dfrac{R_{t,L}}{\hat{\sigma}_t} $$

2) ML Classification Signal

Classifier outputs up-move probability $ p_t = \Pr(r_{t+1} > 0\mid \mathbf{x}_t) $. Signed score and position:

$$ s_t^{\text{ml}} = 2p_t - 1 \in [-1,1], \qquad x_t^{\text{ml}} = \tau\,\dfrac{s_t^{\text{ml}}}{\hat{\sigma}_t} $$

3) Statistical Arbitrage Spread

Cointegrated spread $ X_t $ as OU process and half-life:

$$ \mathrm{d}X_t = \kappa(\mu - X_t)\,\mathrm{d}t + \sigma\,\mathrm{d}W_t, \qquad t_{1/2} = \dfrac{\ln 2}{\kappa} $$

Z-score and mean-reversion position:

$$ z_t = \dfrac{X_t - \hat{\mu}}{\hat{\sigma}}, \qquad x_t^{\text{stat}} = -\eta\,z_t $$

4) Signal Combination & Vol Targeting

Blend signals with weights $ w_1,w_2,w_3 $ ($\sum w_i = 1$) and target portfolio risk $ \sigma^* $:

$$ x_t^{\text{raw}} = w_1 x_t^{\text{mom}} + w_2 x_t^{\text{ml}} + w_3 x_t^{\text{stat}}, \qquad x_t = x_t^{\text{raw}} \cdot \frac{\sigma^*}{\hat{\sigma}_p(t)} $$

5) Walk-Forward Validation

Rolling train/validation/test; for window $k$:

$$ \theta_k = \arg\min_\theta\, \mathcal{L}(\theta; \mathcal{D}^{\text{train}}_k), \quad \text{evaluate on } \mathcal{D}^{\text{test}}_k $$

6) Multi-Asset Optimization with Costs

Mean–variance with transaction costs and turnover cap:

$$\begin{aligned} \max_{\mathbf{w}}\; & \mathbf{w}^T\boldsymbol{\mu} - \tfrac{\lambda}{2}\,\mathbf{w}^T\Sigma\,\mathbf{w} - \left\lVert \Gamma(\mathbf{w}-\mathbf{w}_{t-1}) \right\rVert_1 \\ \text{s.t.}\; & \mathbf{1}^T\mathbf{w}=1,\quad \left\lVert \mathbf{w}-\mathbf{w}_{t-1} \right\rVert_1 \le \Lambda,\quad w_i\in[w_i^{\min}, w_i^{\max}] \end{aligned}$$

7) Performance & Risk

Information ratio and drawdown:

$$ \mathrm{IR} = \dfrac{\mathbb{E}[R_p - R_b]}{\sqrt{\operatorname{Var}(R_p - R_b)}} ,\qquad \mathrm{DD}_t = \dfrac{\max_{\tau\le t} (\mathrm{NAV}_\tau - \mathrm{NAV}_t)}{\max_{\tau\le t} \mathrm{NAV}_\tau} $$

Applications