The Office of the New York City Comptroller serves as investment adviser and custodian for five pension systems with holdings valued at $170 billion, with a majority invested in passive instruments and index strategies. That doesn’t keep it from being one of the most active asset owners in the U.S., according to Michael Garland, assistant comptroller for corporate governance and responsible investing. In fact, he said the only way to protect the portfolio’s value is to engage with companies for improved governance. Mr. Garland talked about the value of proxy access, the lessons of Wells Fargo & Co.’s mishaps and the limits of private ordering.

The comptroller has been at the forefront of the push for proxy access in the U.S., as regulators have failed to establish shareholder rights to nominate directors on a company’s proxy ballot. Are there limits to shareholders’ ability to shape corporations through proposals, the tactic known as private ordering?

Mr. Garland: We didn’t want to do a lot of shareholder proposals because private ordering is not the way to enact change in the markets…but it was clear there wasn’t political appetite for a proxy access rule. We saw an opportunity to leverage a particular capacity we had to file a lot of shareholder proposals.

We didn’t think it would be as successful so quickly…in a way, private ordering did work. We are up to 450 companies with proxy access today, from seven companies three years ago. But I worry that all of these bylaws that are 10 pages long and have all sorts of clauses included means that companies can easily change [the rules of proxy access].

Why does proxy access matter?

Mr. Garland: It is a fundamental right that investors around the world have, and it’s provided through regulation. It is also a very powerful right that would be rarely used, but it would make boards more responsive, which is why investors want it. There is an abundance of research that links good governance and sustainable practices to higher stock-market values, and the CFA Institute published a study that shows proxy access would increase investor wealth between 0.02% and 1.1%.

Because we launched the board accountability campaign publicly, we created an event, and a statistics group within the Securities and Exchange Commission did a study that found that the campaign had an abnormal positive impact on the market of 53 basis points. The fact that proxy access is linked to value creation sends a message to the market.

The New York comptroller’s campaign has entered a new phase, with board composition as its main focus for 2018. What are you trying to achieve?

Mr. Garland: We remain focused on board quality and composition. Over the past decade we concentrated on board independence and accountability, but the conversation is evolving. A key part of achieving the right balance on the board is diversity. We are now pushing companies to improve disclosure of gender and racial diversity so we can assess not only the board’s skills and experience, but also its diversity.

How do you balance greater requests for transparency with its attached costs? Is there a risk of asking too much?

Mr. Garland: One investor might ask for things other investors don’t care about and you don’t want the board to spend time on things that aren’t significant. But if investors believe certain disclosures are important and material, then boards should be managing them. If in fact boards are managing these issues, then information exists and should be disclosed to investors.

We often ask companies to tell their story and to link it to the strategy, and to put a little more of the information they may be already disclosing in [annual reports] in the proxy. I don’t think it’s too much disclosure—we want good disclosure that isn’t boilerplate and tells the company’s story.

How do you look at corporate culture?

Mr. Garland: We think about it in two pieces, and let me take the problems at Wells Fargo as an example. One is tone at the top, and how to try and encourage that. The intention of our clawback inititative was to set a tone at the top for ethical conduct and compliance, although that isn’t something you necessarily incentivize people to do because the expectation is that is the baseline. As investors, we want to put a mechanism in place where individuals are held accountable for misconduct. The big clawback may have sent a message to others.

The other nexus of culture and another hot topic is human capital. Wells Fargo was a failure of human capital management as much as a compliance failure. One of the lessons is that boards need to think about how to have oversight of human capital management. It doesn’t mean boards should be setting pay structures for lower-level employees, but it’s unclear whether boards are getting information about employee satisfaction, turnover, whistleblower’s mechanisms.

Write to Mara Lemos Stein at mara.lemos-stein@wsj.com.