Understand mutual funds and NAV — Stock-Market notes

WHAT is a mutual fund?

WHY does NAV exist? Because the basket's value changes every day as market prices move. You cannot trade "1/500,000th of a basket" without agreeing on what one slice is worth today. NAV is that agreed slice price.

HOW NAV is derived — from first principles

We want a fair price for one unit such that no existing investor is diluted when a new person joins.

Step 1 — Value what the fund owns (Assets). Add up the market value of every holding at today's closing prices: $A = \sum_{i} p_i \, q_i$ where $p_i$ = current price of security $i$ , $q_i$ = quantity held. Add any uninvested cash. Why this step? Because ownership must reflect current market reality, not what was paid.

Step 2 — Subtract what the fund owes (Liabilities). $L = \text{management fees payable} + \text{expenses} + \text{other dues}$ Why this step? Investors only own what's left after the fund settles its bills — the net worth.

Step 3 — Divide by the number of slices (units). $\text{NAV} = \frac{A - L}{N}$ Why this step? Every unit is identical, so the net worth is shared equally per unit.

Why buying at NAV is fair (the dilution argument)

Suppose net assets $= V$ , units $= N$ , so $\text{NAV} = V/N$ . A new investor pays $\Delta$ and gets $\Delta/\text{NAV}$ new units.

New net assets $= V + \Delta$ . New units $= N + \dfrac{\Delta}{\text{NAV}}$ .

New NAV: $\frac{V+\Delta}{N + \frac{\Delta}{\text{NAV}}} = \frac{V+\Delta}{N + \frac{\Delta N}{V}} = \frac{V+\Delta}{\frac{N(V+\Delta)}{V}} = \frac{V}{N} = \text{NAV}$

The NAV is unchanged. This proves that transacting at NAV protects all investors — new money neither dilutes nor enriches existing holders. That's the whole point.

Figure — Understand mutual funds and NAV

Worked Examples

Common Mistakes (Steel-manned)

Active Recall

Recall Quick self-test (hide and answer)

Write the NAV formula from scratch. Why subtract liabilities?
If you invest ₹5,000 at NAV ₹25, how many units? (Ans: 200)
Does a big new investor dilute existing holders? Why not?
What is the ONLY thing that moves NAV day to day?
Is a ₹10 NAV fund cheaper than a ₹100 NAV fund?

Recall Feynman: explain to a 12-year-old

Imagine a giant fruit basket that lots of kids chipped in to buy. Instead of owning "the whole basket," each kid owns a number of stickers, and each sticker is worth an equal slice of the basket. Every evening we check the price of all the fruit, subtract the money we owe the shopkeeper, and split what's left across all the stickers — that per-sticker price is the NAV. If a new kid joins and pays the sticker price, everyone still owns the same value as before — that's why it's fair. The sticker price only goes up or down because the fruit got pricier or cheaper, not because more kids joined.

Connections

Exchange-Traded Funds (ETFs) — trade intraday at market price near NAV (iNAV), unlike mutual funds.
Expense Ratio — the fees that show up as liabilities and quietly reduce NAV.
Open-ended vs Closed-ended Funds — units created/redeemed at NAV vs fixed units traded on exchange.
SIP (Systematic Investment Plan) — rupee-cost averaging buys varying units as NAV moves.
Portfolio Diversification — the WHY behind pooling into a basket.
Total Return vs Price Return — why NAV growth alone understates returns when dividends are paid out.

Flashcards

What is a mutual fund?

A pooled vehicle collecting money from many investors, invested by a manager in a portfolio; investors hold units proportional to their contribution.

Define NAV.

Net Asset Value = (Total Assets − Total Liabilities) ÷ Units Outstanding; the per-unit value of the fund.

Why subtract liabilities in NAV?

Investors only own what remains after the fund pays its fees and dues — the net worth.

How often is open-ended mutual fund NAV calculated?

Once per day, after market close (end-of-day pricing).

Does new investor money change NAV?

No — money adds to both assets and units proportionally, leaving NAV unchanged (dilution-neutral).

What is the only thing that moves NAV day to day?

Changes in the market value of the fund's underlying holdings (and accrued fees).

Is a low-NAV fund cheaper/better than a high-NAV fund?

No — NAV is an accounting artifact of unit count; returns depend on portfolio performance, not the NAV number.

Units received when investing amount M at NAV P?

Units = M ÷ P.

Formula for a fund's total assets?

A = Σ(price_i × quantity_i) + cash.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Socho ek badi si tokri (basket) hai jisme bahut saare log paisa daalte hain. Ek fund manager us pooled paise se stocks aur bonds kharidta hai. Har investor ko units milti hain — jitna paisa daala, utni units. Yeh hi mutual fund hai: ek shared portfolio jise professional manage karta hai, aur aap uska ek chhota hissa (units) own karte ho.

Ab NAV kya hai? Simple — ek unit ki price. Formula: NAV = (Total Assets − Liabilities) ÷ Total Units. Pehle fund ke saare holdings ki aaj ki market value nikaalo (assets), phir fund jo fees/kharche owe karta hai woh minus karo (net worth mila), aur usse total units se divide kar do. Bas — ek unit ki fair keemat mil gayi.

Sabse important baat jo log galat samajhte hain: kam NAV wala fund sasta ya behtar nahi hota. ₹10 NAV aur ₹100 NAV — dono me ₹10,000 lagane pe aapko same portfolio ka same slice milta hai. Return portfolio ke performance pe depend karta hai, NAV number pe nahi. Aur jab naya investor aata hai, NAV nahi badalta, kyunki paisa assets aur units dono me proportionally add hota hai — yeh maine derivation me prove bhi kiya. NAV sirf tab hilta hai jab underlying holdings ki value upar-neeche hoti hai. Yeh baat yaad rakhoge toh aadha fund investing clear ho jayega — 80/20 rule!

Test yourself — Funds, ETFs & Pooled Vehicles

Connections