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Describe how an open-end mutual fund's share price is linked to its net asset value (NAV).

FRM® Part I · Financial Markets and Products · Fund Management · FRM1.FM.3.c

The idea

An open-end fund does not trade at a market price. Purchases and redemptions are with the fund, generally at its net asset value, subject to loads and fund-specific mechanisms. NAV per share comes from the fund's balance sheet: NAV = (value of assets − liabilities) ÷ shares outstanding. Assets are marked to market at the close, and liabilities include accrued fees and payables for securities bought but not yet settled. Orders placed during the day get the next NAV struck after the close (forward pricing), so the investor does not know the price when ordering. A front-end load is deducted from the cash paid in, so the amount invested at NAV is lower than the cash paid, and a redemption fee or back-end load is deducted from what is paid out. A distribution lowers NAV by the amount paid per share, leaving the investor's wealth unchanged before tax. Because redeemers are paid at NAV, the trading costs of raising cash fall on the holders who stay. The exam point is that the price is the next NAV, adjusted for loads and such mechanisms, with no closed-end premium or discount.

Formulas

NAV per share of an open-end fund

NAV = (A − L) ÷ N

A
the value of the fund's assets, marked to market at the close
L
liabilities, including accrued fees and payables for unsettled purchases
N
shares outstanding

Remember the liabilities. Purchases and redemptions take place at the next NAV struck, adjusted for loads.

Shares received with a front-end load

Shares = C × (1 − f) ÷ NAV

C
the cash paid in
f
the front-end load as a fraction of the amount paid
NAV
net asset value per share

The load is deducted before investing at NAV. Dividing the full cash by NAV overstates the shares.

A practice question

From the question bank, with the reason each wrong option is wrong.

An investor places an order to buy an open-end fund at 2 pm. Which price does the order receive?

  1. The NAV calculated at the previous closeWhy not: Stale: forward pricing uses the next NAV struck after the order, which would otherwise enable late trading.
  2. The NAV calculated after the close the same day (plus any load) - correct
  3. The market price at 2 pm, which may be above or below NAVWhy not: Open-end shares have no intraday market price; that applies to closed-end funds and ETFs.
  4. The average of the day's high and low net asset valuesWhy not: The fund calculates one NAV per day, after the close, not an intraday range.

Open-end funds use forward pricing: the order is filled at the next NAV struck after the cut-off, so the investor does not know the price when ordering.

A harder one

An open-end fund reports the following at the close, in USD millions: securities at market value 480, cash 12, dividends receivable 3, accrued management fees 2 and payables for securities purchased 7. There are 20 million shares outstanding. What is the NAV per share, closest to?

  1. USD 24.75Why not: Ignores the liabilities of 9 million.
  2. USD 23.55Why not: Leaves out cash and receivables (480 - 9 = 471) before dividing by shares.
  3. USD 24.30 - correct
  4. USD 24.15Why not: Leaves out the 3 million of dividends receivable (483) although it is an asset.

Assets = 480 + 12 + 3 = 495. Liabilities = 2 + 7 = 9. Net assets = 486. NAV = 486 / 20 = 24.30.

The hardest tier

An investor owns 1,000 shares of an open-end fund with a NAV of 30.00. The fund pays a distribution of 1.20 per share, so the ex-distribution NAV is 28.80. The investor reinvests the distribution in new shares at the ex-distribution NAV. What is the value of the holding after reinvestment?

  1. USD 31,200Why not: Adds the distribution to an unchanged NAV, ignoring that the NAV fell by the amount paid.
  2. USD 30,000 - correct
  3. USD 28,800Why not: Values 1,000 shares at the new NAV and ignores the reinvested distribution.
  4. USD 29,952Why not: Reinvests at the pre-distribution NAV of 30.00 (1,040 shares) instead of 28.80.

Distribution = 1,200, reinvested at 28.80 buys 41.67 shares. Total shares 1,041.67 x 28.80 = 30,000. A distribution moves value from NAV to the investor and creates no gain, which follows from price being equal to NAV.

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