We are doing a risk management project. We aim to examine whether an actively managed portfolio can outperform the Hang Seng Index(HSI) in the Hong Kong stock market. We have collected the stock price data of four representative companies: Tencent Holdings, China Resources Medical, HSBC Holdings and CK Hutchison Holdings and HSI data(daily rate of return HSI) from 2022 to 2024, using 2022-2023 for model construction and 2024 for testing. We use Excel for data analysis and optimization, and use the Solver to assign different weights to the four stocks to construct an investment portfolio to maximize three matrics: Sharpe Ratio, Treynor Ratio, Jensen Alpha.

But we observed that the Solver results for all three indices (Sharpe ratio, Treynor ratio, Jensen's alpha) recommend concentrating investments in just a few stocks (e.g., CR and HSBC) rather than diversifying the portfolio(please refer to the attachments below).

Q1. Why does this violate the principle of diversification?

Sharpe ratio suggests buying only CR(0.02) and HSBC(0.98), 0 in other 2 stocks. Sum of weights is 1.

Treynor ratio and Jensen's alpha recommend 100% HSBC, 0 in other 3 stocks.

Q2. Why do the recommended stocks differ across the three indices?

For example, Sharpe includes CR, while Treynor/Jensen focus solely on HSBC.

Potential factors I've considered:

Solver constraints: No lower and upper limit on individual stock weights.

Stock-specific metrics: Differences in Beta, Alpha, average daily return, and daily return standard deviation.

Could you explain the specific reasons behind this? What else could be driving these results?

Your explanations would be highly appreciated!!!

Model Training 5. For Sharpe ratio (result) : Weight_CKH O Weight_CR 0.024418401 Weight_HSBC 0.975581599 Weight Tencent O Sum Average daily return 0.000959639 Annualized Rate of Return 0.232131015 of the portfolio Standard Deviation 0.016155843 Annualized standard deviation 0.256466054 Risk-free rate 2022 3.06% Risk-free rate 2023 3.91% Risk-free rate 2022/2023 0.034828834 Sharp Rate 0.769311096Model Training 6. For Treynor ratio (result) : Weight_CKH Weight_CR Weight_HSBC HOHOO Weight Tencent |Sum Average daily return 0.000972272 Annualized Rate of Return 0.234823 of the portfolio Standard Deviation 0.016397661 Risk-free rate 2022 3.06% Risk-free rate 2023 3.91% Risk-free rate 2022/2023 0.034828834 Treynor Rate 0.406897188 Beta 0.491510976Model Training 7. For Jensen alpha (result): Weight_CKH Weight_CR Weight_HSBC HOHOO Weight Tencent Sum Average daily return 0.000972272 Annualized Rate of Return 0.234823269 of the portfolio Standard Deviation 0.016397661 Risk-free rate 2022 3.06% Risk-free rate 2023 3.91% Risk-free rate 2022/2023 0.034828834 Jensen Alpha 0.290117068 Beta 0.491510976 Average daily return -0.000482839 Annualized Rate of Return mkt -0.1485295 of the mkt