This study explores modern portfolio theory by integrating the Black-Litterman portfolio with time-series clustering, specificially emphasizing K-shape clustering methodology. K-shape clustering enables grouping time-series data effectively, enhancing the ability to plan and manage investments in stock markets when combined with the Black-Litterman portfolio. Based on the patterns of stock markets, the objective is to understand the relationship between past market data and planning future investment strategies through backtesting. Additionally, by examining diverse learning and investment periods, it is identified optimal strategies to boost portfolio returns while efficiently managing associated risks. For comparative analysis, traditional Markowitz portfolio is also assessed in conjunction with clustering techniques utilizing K-Means and K-Means with Dynamic Time Warping. It is suggested that the combination of K-shape and the Black-Litterman model significantly enhances portfolio optimization in the stock market, providing valuable insights for making stable portfolio investment decisions. The achieved sharpe ratio of 0.722 indicates a significantly higher performance when compared to other benchmarks, underlining the effectiveness of the K-shape and Black-Litterman integration in portfolio optimization.

Pair trading is a statistical arbitrage investment strategy. Traditionally, cointegration has been utilized in the pair exploring step to discover a pair with a similar price movement. Recently, the clustering analysis has attracted many researchers' attention, replacing the cointegration method. This study tests a clustering-driven pair trading investment strategy in the Korean stock market. If a pair detected through clustering has a large spread during the spread exploring period, the pair is included in the portfolio for backtesting. The profitability of the clustering-driven pair trading strategies is investigated based on various profitability measures such as the distribution of returns, cumulative returns, profitability by period, and sensitivity analysis on different parameters. The backtesting results show that the pair trading investment strategy is valid in the Korean stock market. More interestingly, the clustering-driven portfolio investments show higher performance compared to benchmarks. Note that the hierarchical clustering shows the best portfolio performance.