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FRM Exam Part I · Fund Management

Mutual Funds and Open-End vs Closed-End Funds

Updated 11 October 2026 · Fact-checked

A mutual fund pools investor money in a portfolio. An open-end fund issues and redeems shares at NAV, where NAV per share = (assets − liabilities) ÷ shares outstanding. A closed-end fund has a fixed share count traded on an exchange at a price that can differ from NAV. ETFs trade on exchanges but use creation and redemption.

Understand Mutual Funds and Open-End vs Closed-End Funds

A mutual fund (an investment company) pools money from many investors and invests it in a portfolio of securities. Each investor owns shares of the fund and so owns a proportional claim on the portfolio. This gives diversification, professional management and low minimum investment.

The key measure is net asset value (NAV). NAV per share is the market value of the fund's assets, minus its liabilities (accrued fees, borrowings, payables), divided by the number of shares outstanding. Funds compute NAV once a day after markets close, using closing prices.

An open-end fund (the usual mutual fund) sells new shares to investors and redeems shares at NAV (plus or minus any sales load or redemption fee). The share count changes every day. Because trades happen at NAV, the price cannot be at a premium or discount to NAV. The fund may have to sell assets to meet redemptions, which creates liquidity risk and can hurt remaining holders.

A closed-end fund raises capital once in an offering and then has a fixed number of shares. Investors buy and sell these shares on an exchange from other investors, so the market price is set by supply and demand and can trade at a premium or discount to NAV. The manager does not face redemptions, so it can hold less liquid assets and use leverage more easily.

An ETF is usually open-end in legal form but trades on an exchange all day. Only authorized participants create or redeem large blocks (creation units), often in kind, swapping a basket of securities for ETF shares. This arbitrage keeps the ETF price close to NAV. Compared with a mutual fund, ETFs trade intraday and are often more tax-efficient. Investors also pay a bid-ask spread and brokerage.

Key formulas to remember

NAV per share
NAV = (Market value of assets − Liabilities) ÷ Shares outstanding
Use closing market values. Liabilities include accrued management fees and borrowings.
Premium or discount (closed-end fund)
Premium/(Discount) = (Market price − NAV) ÷ NAV
Positive means premium, negative means discount. Applies to closed-end funds and ETFs, not to open-end mutual funds.
Fund return over a period
Return = (NAV_end − NAV_begin + Distributions) ÷ NAV_begin
Distributions are income and capital gains paid per share in the period.
Shares issued or redeemed
Shares = Amount invested ÷ NAV (net of any load)
For a front-end load: shares = amount × (1 − load) ÷ NAV.
Front-end load offer price
Offer price = NAV ÷ (1 − Load %)
The load is a percentage of the offer price, not of NAV.

How to solve Mutual Funds and Open-End vs Closed-End Funds questions

Most questions ask you to compute NAV, a return, or a premium or discount, or to identify which structure a description fits. Work in this order.

  1. 1Identify the fund type from the wording: continuous issue and redemption at NAV means open-end; fixed shares traded on an exchange means closed-end; exchange-traded with creation and redemption means ETF.
  2. 2List total assets at market value, not at cost. Include cash and accrued income.
  3. 3Subtract all liabilities, including accrued fees, borrowings and payables, to get net assets.
  4. 4Divide by shares outstanding at that date. Check whether new shares were issued or redeemed before the NAV date.
  5. 5If asked for return, add distributions to the change in NAV and divide by beginning NAV. Include fees and loads only if the question says so.
  6. 6For a premium or discount, compare market price with NAV using (price − NAV) ÷ NAV.
  7. 7Sanity check the sign and size of the answer, then match it to the one option that fits.

Quickest way: Net assets first, then divide

When to use it: Use for any NAV, return or premium/discount calculation with numbers given.

  1. Write net assets = assets − liabilities in one line.
  2. Divide by shares to get NAV. On a calculator, enter the net assets and divide before rounding.
  3. For premium or discount, compute price ÷ NAV − 1 directly.
  4. For load questions, divide by (1 − load) to get the offer price.
  5. Eliminate options that treat an open-end fund as trading at a discount.

Common mistakes in Mutual Funds and Open-End vs Closed-End Funds

  • Forgetting to subtract liabilities such as accrued fees from assets.

    Students focus on the portfolio value and treat it as NAV.

    Fix: Always write assets − liabilities first and check the question for any payables or borrowings.

  • Saying an open-end fund can trade at a premium or discount to NAV.

    Students mix up open-end funds with closed-end funds and ETFs.

    Fix: Remember that open-end shares are bought and sold with the fund at NAV, so no premium or discount arises.

  • Calculating the front-end load as a percentage of NAV.

    It seems natural to add 5% to NAV.

    Fix: A load is a percentage of the offer price, so offer price = NAV ÷ (1 − load).

  • Assuming ETF shares are always bought and sold at exactly NAV.

    Arbitrage keeps prices close, so students treat them as identical.

    Fix: ETFs trade at market prices that can deviate slightly from NAV. Only authorized participants transact at NAV.

  • Using the wrong share count after new purchases or redemptions.

    Questions give share counts before and after flows.

    Fix: Use the share count that matches the NAV date you are calculating.

Worked examples

Example 1

A fund holds securities worth ₹250 crore and cash of ₹10 crore. It has accrued management fees of ₹2 crore and other payables of ₹3 crore. There are 5 crore shares outstanding. What is the NAV per share?

Show the solution
  1. Total assets = 250 + 10 = ₹260 crore.
  2. Liabilities = 2 + 3 = ₹5 crore.
  3. Net assets = 260 − 5 = ₹255 crore.
  4. NAV = 255 ÷ 5 = ₹51 per share.

Answer: NAV per share = ₹51.

Example 2

A closed-end fund has net assets of $180 million and 12 million shares outstanding. Its shares trade at $13.50. Compute the premium or discount, and the shares an investor receives for $13,500 invested in an open-end fund with the same NAV and no load.

Show the solution
  1. NAV = 180 ÷ 12 = $15.00.
  2. Premium/(discount) = (13.50 − 15.00) ÷ 15.00 = −1.50 ÷ 15 = −10%.
  3. So the closed-end fund trades at a 10% discount.
  4. In the open-end fund, shares = 13,500 ÷ 15.00 = 900.

Answer: The closed-end fund trades at a 10% discount to NAV; the investor receives 900 open-end shares.

Exam tips

  • Questions often test structure: know who sets the price (NAV for open-end, the market for closed-end, arbitrage for ETFs).
  • In NAV questions, scan for hidden liabilities such as accrued fees or borrowings before dividing.
  • Expect conceptual items on liquidity risk: open-end funds face redemption pressure, closed-end funds do not.
  • Check whether a load is front-end or back-end and whether it is applied to NAV or offer price.
  • Watch the sign: a discount is negative and is measured relative to NAV, not market price.

Practice questions from Fund Management

Mutual Funds and Open-End vs Closed-End Funds: frequently asked questions

What is the main difference between open-end and closed-end funds?

An open-end fund continuously issues and redeems shares at NAV, so its share count changes. A closed-end fund issues a fixed number of shares that trade on an exchange, often at a premium or discount to NAV.

How do you calculate the NAV of a mutual fund?

Take the market value of all assets, subtract liabilities such as accrued fees and payables, and divide by shares outstanding. Funds do this daily using closing prices.

How is an ETF different from a mutual fund?

An ETF trades on an exchange throughout the day at market prices, while a mutual fund transacts once a day at NAV. ETFs use authorized participants and creation and redemption to keep price near NAV.

Why can closed-end funds trade at a discount?

Their price is set by supply and demand, not by redemption at NAV. Investors may demand a discount for fees, illiquid holdings, or weak sentiment.