Author: Sohum Muley
This quantitative research report is based on Joseph Attia's paper "The Applications of Graph Theory to Investing," adapted for the Indian market using Nifty 50 as the stock universe.
The study focuses on constructing portfolios based on stock correlations using graph theory. Two types of portfolios are explored: higher correlation and lower correlation portfolios. The portfolios are created using a 4-year back window and held for 4 years before rebalancing.
Graphs are constructed with stocks as nodes and correlations as edges. For the higher correlation portfolio, nodes with correlations below a threshold (0.46) are connected, and for the lower correlation portfolio, nodes with correlations below a threshold (0.33) are connected.
| Portfolio | CAGR | Absolute Returns | Max Drawdown | Calmar Ratio | Sharpe Ratio |
|---|---|---|---|---|---|
| Market | 19.71% | 245% | -38.45% | 1.66 | 0.7 |
| Higher correlation | 21.6% | 261% | -35.2% | 1.9 | 0.72 |
| Lower correlation | 23.9% | 285% | -37.87% | 2.49 | 0.69 |
| Portfolio | CAGR | Absolute Returns | Max Drawdown | Calmar Ratio | Sharpe Ratio |
|---|---|---|---|---|---|
| Market | 12.64% | 126% | -14.47% | 5.64 | 0.82 |
| Higher correlation | 13.07% | 127% | -14.62% | 5.12 | 0.84 |
| Lower correlation | 18.02% | 139% | -14.23% | 6.04 | 0.77 |
Portfolios with threshold values of 0.2 and 0.3 exhibit exceptional performance.
| Portfolio | CAGR | Absolute Returns | Max Drawdown | Calmar Ratio | Sharpe Ratio |
|---|---|---|---|---|---|
| 0.2 Portfolio | 26.6% | 325% | -14.6% | 4.64 | 0.63 |
| 0.3 Portfolio | 19% | 275% | -14.23% | 2.59 | 0.72 |
Threshold values of 0.2 and 0.3 consistently outperform the market across indices (Nifty 100 and Nifty 200).
Highly correlated portfolios can yield surprising results, with the threshold of 0.8 showing strong performance.
| Portfolio | CAGR | Absolute Returns | Max Drawdown | Calmar Ratio | Sharpe Ratio |
|---|---|---|---|---|---|
| 0.6 Portfolio | 9.6% | 172% | -71.63% | 0.23 | 0.49 |
| 0.7 Portfolio | 9.09% | 167% | -69.05% | 0.24 | 0.71 |
| 0.8 Portfolio | 20.5% | 300% | -46.44% | 1.57 | 0.58 |
Graph theory offers promising avenues for investment analysis in the Indian market. It enables the creation of portfolios with diverse correlations, potentially outperforming the market. Balancing factors such as historical data and stock selection can enhance these models further, making them robust for various market conditions. Mixing stocks with varying correlation strengths can enhance reliability.
Note: This is a condensed summary of the research report based on the original paper by Joseph Attia, adapted for the Indian market using Nifty 50 as the stock universe.