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Based on the most helpful WSO content, first-year salaries in the finance sector, especially for those transitioning from banking or PE backgrounds with 3-4 years of experience, can vary widely depending on the role, firm size, location, and specific sector within financials. However, a $400K annualized package for someone moving into a public sector role from private equity or investment banking, with that level of experience, seems to be on the higher end of the spectrum, particularly for a first-year position.

In the context of investment banking and private equity, first-year analysts in investment banking can expect salaries including bonuses in the range of $160K to $170K, based on the highest ranked content on WSO. For private equity, the compensation can be significantly higher, with first-year associates potentially earning total compensation in the range of $275K to $350K, as indicated by previous WSO threads.

Your package of $400K, while substantial, reflects the premium for your experience and the transition to a role that values your unique mix of banking and PE experience. It's also important to consider the long-term career trajectory and the potential for salary growth, bonuses, and other forms of compensation beyond the base salary in your new role.

Remember, compensation in finance, especially at the intersection of public sector roles and private equity/banking backgrounds, is influenced by many factors including performance, firm profitability, and market conditions. It's beneficial to also weigh the non-monetary aspects of your new role, such as work-life balance, the opportunity for impact, and career development opportunities, when evaluating your overall compensation package.

Sources: Leaving a single manager to start a book at a platform, From "how do I break in" to "how do I escape", Ask CompBanker, How much do you learn as a 3rd year IB Analyst vs 3rd year PE Associate? (How common is a 3rd year in PE?), Q&A: London BB IBD to top 3 PE