Fund Net Asset Value and Personal Investment Returns

Divide a fund's net assets by its number of shares, and you get the net asset value, or NAV, of a single share. Three things move it: gains and losses in the holdings, expenses already accrued inside the fund, and cash distributions.

When no dividends are paid and the share basis is consistent, the return over a stretch is simply ending NAV divided by starting NAV, minus 1. Dividends complicate that. A total-return figure has to fold the payout in, along with the reinvestment assumption used for it, because once cash leaves the fund it has moved into holders' pockets and the raw NAV alone understates what the money earned.

For your own books, that means tracking two kinds of records at once: the shares you hold and the NAV at which they're valued, plus all cash you've actually contributed or withdrawn. Converting between funds inside one account doesn't count as money flowing in or out; only cash that crosses the account's boundary does.

Here's a teaching example, with all amounts in Chinese yuan. A fund rises 20% in the first year and falls 10% in the second. No dividends, no extra charges on buying and selling. Starting NAV of 1 ends up at 1 × 1.2 × 0.9 = 1.08, so the fund's own two-year record shows an 8% gain.

Now an investor buys 10,000 at the start of year one, then adds 90,000 at the start of year two, right before the drop:

The investor put in 100,000 and holds 91,800, a shortfall of 8,200 against contributions. The fund gained 8%; the investor lost money. The small stake rode the rally, and the large stake rode the slide. That timing is the whole story.

The time-weighted rate of return strips out external cash flows and multiplies each period's growth factor together. It answers the question "how did this asset behave?" and is the right tool for comparing products or evaluating managers. On this example: 1.2 × 0.9 − 1 = 8%, which annualizes to about 3.92%.

The money-weighted rate of return accounts for the amount and timing of each external cash flow. A common calculation is the internal rate of return. In this example, with only contributions and an ending position, it is the compound rate that makes the contributions, grown for their respective holding periods, sum to the final value.

Both years here are the same length, so with r as the annual money-weighted rate:

10,000 × (1 + r)² + 90,000 × (1 + r) = 91,800.

Solving gives r of about −7.51%. Notice that −8,200 ÷ 100,000 = −8.2% is a different, simpler number: it's just the loss as a share of everything contributed, with no regard for the fact that the 90,000 was held one year while the 10,000 was held two.

When dates are unevenly spaced, you hand the full history to a date-aware IRR calculator: every contribution and withdrawal with its date, plus the ending position value. From the investor's perspective, contributions are recorded as negatives, withdrawals as positives, and the ending value as a positive on the final day.

Before comparing any two returns, agree on the period, the scope of holdings, dividend treatment, and the fee basis. A price index tracks only price movement. A total-return index reinvests dividends according to the index rules. When fund returns include dividends, use the corresponding total-return benchmark so both sides include the same types of income.

An index and an index fund aren't the same object. The index describes a rules-based basket of securities; the fund chases it with real holdings, carries expenses, keeps some cash on hand, and drifts slightly in weighting and trading. These factors can create differences between fund and index returns. When judging a fund, first check what it invests in and which benchmark it names, then compare its fee-adjusted results over the same span.

For your own account, assemble the records in this order: contributions by date and amount, then withdrawals and dividends, then the ending position value, then a note on which fees are already embedded versus paid separately. From there you can compute three different things: the simple gain or loss on your money, your personal money-weighted return, and the product's own total return over the same period.

• How assets generate returns: stock returns and purchase prices. For exchange-traded fund prices, see index rules and fund trading prices.
• Adding money regularly: regular contributions and purchase costs. Taking money out for living expenses: retirement spending and asset withdrawals.
• Calculating purchasing power: compounding, fees, and purchasing power.

Full reading route: how investment returns become personal gains.