0.4 The instrument map · M00 On-ramp

Motivation

The products on a broker's app range from a government bond to a weekly index option. They differ in what you own, what it costs, how it can hurt you and how it is taxed. This section is a map; the module named in each entry is the territory.

0.4.1The instruments#

Equity shares Part-ownership of a listed company: a claim on its future profits, with votes. Suits: investors willing to analyse businesses and hold for years, and swing traders. Costs: delivery round trip about 24 bp at current rates (0.2.7), DP charge per sale, tax (0.7). Risks: a single company can fall 50% or more and never recover; liquidity is poor in small companies. Course: M06, M06A (investing), M04, M04A (trading).

Exchange-traded funds (ETFs) A fund whose units trade on the exchange like a share, holding an index (Nifty 50, Nifty Next 50, Sensex), gold, silver, or government securities. Suits: investors who want index exposure through a demat account. Costs: the fund's expense ratio (deducted daily from its assets), brokerage, the bid–ask spread and any gap between the market price and the fund's indicative NAV (iNAV): thinly traded ETFs can trade at a premium or discount to the value of their holdings. Risks: those of the index, plus liquidity. Gold ETFs hold physical gold of standard purity; gains on units held more than 12 months are long-term and taxed at 12.5% (Finance (No. 2) Act 2024; verify). Course: M06 · 6.11, M10 for gold; M06B · 6B.8–6B.9 for how ETFs track, trade and stray from iNAV. See it live: listed ETFs grouped as gold, silver, equity and debt at https://oicharts.com/etfs (e.g. https://oicharts.com/etfs/gold); compare two ETFs on the same index and you will see that price levels differ while daily percentage moves are close.

Mutual funds (MFs) A pooled fund run by an asset management company (AMC); you buy and redeem units from the AMC at the NAV (net asset value per unit), computed once a day after the close. The NAV you get depends on the cut-off time and on when the AMC receives your money.

Index funds replicate an index; active funds try to beat one. The SPIVA India scorecards report that most active large-cap funds trailed their benchmark over 5 and 10 years (S&P Dow Jones Indices, SPIVA India Scorecard, mid-year 2025: about 73% over 10 years, as reported; verify against the scorecard; M06 · 6.11 discusses the benchmark controversy).
Direct versus regular plans. Every scheme has a direct plan (bought from the AMC or a platform without a distributor commission) and a regular plan (sold through a distributor, whose commission is paid from the scheme's expenses). Same portfolio, lower expense ratio in the direct plan. Direct plans have existed since 1 Jan 2013 (SEBI circular of September 2012; verify).
Expense ratio. The annual fee, deducted daily from the fund's assets, so the NAV is already net of it. Since 1 Apr 2026 the SEBI (Mutual Funds) Regulations, 2026 replaced the 1996 Regulations and introduced a base expense ratio, with statutory levies (GST, STT, stamp duty) charged at actuals on top, and lowered most caps (SEBI (Mutual Funds) Regulations, 2026, notified January 2026; the cap for index funds and ETFs is reported as 0.90%; verify). Small differences compound: at 12% versus 11% a year for 20 years, ₹10 lakh grows to ₹96.5 lakh versus ₹80.6 lakh, 16.4% less.
Exit load. A redemption charge some schemes levy on units sold within a stated period (for example a percentage on units redeemed within a year); the scheme information document states it.
Categories. SEBI fixes scheme categories so that names mean something (large-cap, mid-cap, flexi-cap, liquid, gilt, and so on). A recategorisation circular of 26 Feb 2026 regrouped them into equity, debt, hybrid, life-cycle and other schemes (SEBI circular of 26 Feb 2026; verify; the exact number of categories was not checked).
Tax. Equity-oriented funds are taxed like listed shares (0.7). Funds with more than 65% in debt ("specified mutual funds") bought on or after 1 Apr 2023 are taxed at slab rates whatever the holding period (definition as amended by the Finance Act 2025 from 1 Apr 2025; verify).
Course: M06 · 6.11 (the index baseline), M14 (portfolio construction); M06B covers funds in full: structure, NAV, the 2026 expense rules (verified there), AMC economics, SIPs, tax and building a fund portfolio.

SIPs A systematic investment plan is not an instrument but a standing instruction: a fixed amount is debited each month (or week) and invested in a chosen fund at that day's NAV. Its value is discipline and automation. Its arithmetic is in 0.4.2.

Government securities and bonds A bond pays fixed coupons and returns its face value at maturity. G-secs (dated central government bonds), T-bills (short-term, issued at a discount) and SDLs (state government bonds) carry no credit risk in rupees. Individuals can bid in RBI auctions and trade in the secondary market through RBI Retail Direct (https://rbiretaildirect.org.in, launched 12 Nov 2021; no fee to open or maintain the Retail Direct Gilt account; verify on the RBI site). Corporate bonds are available through exchange-traded issues and SEBI-registered online bond platforms; they add credit risk. Risks: interest-rate risk if sold before maturity (a 10-year bond loses roughly 7% of its value when yields rise one percentage point; M11 · 11.2 derives duration), inflation, and for corporates, default. Interest is taxed at slab rates. Course: M11 · 11.1–11.5.

Sovereign Gold Bonds (SGBs) Government bonds denominated in grams of gold, paying 2.5% a year on the issue value. No new tranche has been issued since SGB 2023-24 Series IV (February 2024); asked on 1 Feb 2025 whether the scheme was being discontinued, the Finance Minister said "yes, in a way", citing its cost to the government (post-Budget press conference, 1 Feb 2025, as reported; RBI's SGB issue notices end with Series IV of 2023-24; verify). Existing bonds run to maturity (8 years), can be redeemed early after 5 years on interest dates, and trade thinly on exchanges. Check the current tax treatment of redemptions before buying in the secondary market. Course: M10 · 10.6 (what drives gold).

REITs and InvITs Listed trusts that own rent-producing real estate (real estate investment trusts: offices, malls) or infrastructure (infrastructure investment trusts: roads, power transmission, telecom towers) and pass most of their cash flow to unitholders. Units trade on the exchange. Distributions are a mix of interest, dividend and repayment of capital, each taxed differently; the trust's distribution notice states the split. Risks: interest rates (they behave partly like long bonds, M11 · 11.4), occupancy and tariff risk, sponsor leverage, thin trading. Course: M11 for rate sensitivity; M06 for valuation.

Futures and options (F&O) Exchange-traded derivatives on indices (Nifty 50, Bank Nifty, Sensex and others) and a list of large, liquid stocks set by the exchanges. A future is an obligation to buy or sell at a fixed price on expiry, margined and marked to market daily. An option is a right, bought for a premium. Index contracts have a minimum value of about ₹15 lakh (the Nifty lot is 65 units from the January 2026 contracts; M09A · 9A.15 and M07 · 7.4 have the current specifications). Suits: hedgers and traders with a tested process and a risk budget. Risks: leverage; losses on futures and short options can exceed the margin; most individual option buyers lose money (SEBI's FY26 study: about 97% of individual F&O traders were option buyers, and about 88% of individual options traders lost money; 0.6). SEBI's studies (0.6) show that close to nine in ten individual F&O traders lose money each year. Course: M07, M08, M09, M09A, M15. Do not trade F&O before finishing at least M07 and M08.

Commodity derivatives (MCX) Futures and options on gold, silver, crude oil, natural gas and base metals, traded on MCX until late evening. Suits: hedgers and traders who follow global markets. Risks: overnight moves in global prices, leverage, contract specifications that differ by commodity (lot, tick, delivery). Course: M10 · 10.10.

Currency derivatives Rupee futures and options (USD-INR and others) on NSE and BSE. Under RBI's directions in force since 3 May 2024, a user must have an underlying foreign-exchange exposure; positions up to USD 100 million across exchanges need no documentary proof, but the exposure itself must exist (RBI press release, https://www.rbi.org.in/Scripts/BS_PressReleaseDisplay.aspx?prid=57628). For an individual without foreign-currency income, expenses or assets, these contracts are not a speculative product. Course: M11 · 11.8–11.11.

Instrument	Typical holding period	Leverage	Main risk for a beginner	Module
Index fund / index ETF	Years	None	Selling in a crash	M06 · 6.11, M14
Active MF	Years	None	Paying for underperformance	M06 · 6.11
Shares (delivery)	Months to years	None (MTF: some)	Concentration	M06, M06A, M04
Shares (intraday)	Minutes to hours	Up to ~5×	Costs and overtrading	M05
G-secs, T-bills	To maturity	None	Rate risk if sold early	M11
REITs, InvITs	Years	None	Rates, liquidity	M11
Futures	Days to weeks	High: margin is a fraction of contract value	Gap losses beyond margin	M07
Options (buy)	Hours to weeks	Implicit	Time decay, lottery behaviour	M08, M09, M09A
Options (sell)	Days to weeks	High	Unbounded tail losses	M09 · 9.9
MCX futures	Days to weeks	High, as for futures	Overnight global moves	M10

0.4.2SIP arithmetic#

Setup

You invest $P$ at the start of each month for $n$ months. The fund earns a constant monthly return $i$ (an idealisation; real returns vary, see the remark below). An annual rate $r$ must be converted to a monthly rate; two conventions are in use:

i_{\text{eff}} = (1+r)^{1/12} - 1, \qquad i_{\text{nom}} = r/12. \tag{0.1}

With $i_{\text{eff}}$ , twelve months compound to exactly $r$ ; with $i_{\text{nom}}$ they compound to $(1 + r/12)^{12} - 1 > r$ . Fund returns are quoted as annual compound rates, so use $i_{\text{eff}}$ .

Proposition 0.1future value of a SIP

The value immediately after the end of month $n$ is

FV = P\,(1+i)\,\frac{(1+i)^n - 1}{i} \qquad (i \neq 0), \tag{0.2}

and $FV = nP$ when $i = 0$ . If instead the instalments are invested at the end of each month (an ordinary annuity), drop the factor $(1+i)$ .

Proof

The instalment invested at the start of month $k$ ( $k = 1, \dots, n$ ) grows for $n - k + 1$ months, to $P(1+i)^{n-k+1}$ . Summing and substituting $j = n - k + 1$ ,

FV = P\sum_{j=1}^{n}(1+i)^j = P(1+i)\sum_{j=0}^{n-1}(1+i)^j = P(1+i)\frac{(1+i)^n - 1}{i},

by the geometric series.∎

Inverting (0.2), the instalment that reaches a target $T$ is $P = T\,i / \big[(1+i)\big((1+i)^n - 1\big)\big]$ .

Worked example 0.1

₹10,000 a month for 10 years ( $n = 120$ ) at $r = 12\%$ :

$i_{\text{eff}} = 1.12^{1/12} - 1 = 0.9489\%$ ; $FV = \text{₹}22{,}40{,}359$ on ₹12,00,000 invested.
At $i_{\text{nom}} = 1\%$ a month, $FV = \text{₹}23{,}23{,}391$ , 3.7% more. A projection that says "12%" without saying how it compounds can overstate the result by this much.
Invested at month ends instead: ₹22,19,300.
Over 20 years, ₹10,000 a month at 12% gives ₹91,98,574; at 11% it gives ₹81,56,072. One percentage point of annual cost (for example the gap between a high-expense regular plan and a cheap index fund) costs ₹10.4 lakh, 11.3% of the final value.
To reach ₹1 crore in 20 years at 10% needs ₹13,812 a month.

Remark (sequence risk). Returns are not constant. Because a SIP has invested the most money near the end of its life, a fall in the last years hurts it more than the same fall in the first years. Formula (0.2) is a planning device; M02 · 2.2 shows why the realised compound rate is below the average return.

0.4.3XIRR: the return on irregular cash flows#

A SIP's money was invested at different dates, so neither the absolute return (gain over total invested) nor a compound annual growth rate (CAGR) from the first date measures it. The right measure is the internal rate of return of the dated cash flows.

Definition 0.1XIRR

Let cash flows $c_0, \dots, c_m$ occur on dates $d_0 \le \dots \le d_m$ (outflows negative, inflows positive, the current value counted as a final inflow), and let $t_k = (d_k - d_0)/365$ in days over 365. The XIRR is the rate $x > -1$ solving

f(x) = \sum_{k=0}^{m} c_k\,(1+x)^{-t_k} = 0. \tag{0.3}

This is the convention of spreadsheet XIRR functions and of mutual fund statements.

Proposition 0.2uniqueness

If every outflow occurs on or before a date $s$ and every inflow strictly after it, with at least one of each, then (0.3) has at most one root in $(-1, \infty)$ , and it has one if $\sum_k c_k (1+x)^{-t_k}$ changes sign on that interval (in particular, when the sum of inflows exceeds the sum of outflows, the root is positive).

Proof

Let $\tau = (s - d_0)/365$ and $g(x) = (1+x)^{\tau} f(x) = \sum_k c_k (1+x)^{\tau - t_k}$ ; $g$ and $f$ have the same roots on $(-1,\infty)$ . For an outflow, $c_k < 0$ and $\tau - t_k \ge 0$ , so $c_k(1+x)^{\tau - t_k}$ is non-increasing in $x$ . For an inflow, $c_k > 0$ and $\tau - t_k < 0$ , so $c_k(1+x)^{\tau - t_k}$ is strictly decreasing. Hence $g$ is strictly decreasing and has at most one root. At $x = 0$ , $g(0) = \sum_k c_k$ ; as $x \to \infty$ the inflow terms vanish and $g < 0$ . So if $\sum_k c_k > 0$ , by continuity the root lies in $(0, \infty)$ .∎

A SIP followed by a single valuation satisfies the hypothesis. With interleaved inflows and outflows (partial withdrawals between purchases), (0.3) can have several roots, and the XIRR should be reported with care.

Computing it $f$ is smooth, and for these cash flows monotone after the transformation above, so Brent's method on a bracket $[-0.9999, \text{hi}]$ (doubling hi until $f$ changes sign) is robust; Newton's method from $x = 0.1$ is faster but can overshoot below $-1$ . Exercise m00_sip_xirr implements both pieces and tests against the standard spreadsheet example ( $-10{,}000$ on 1 Jan 2008 followed by four inflows, XIRR $= 37.336\%$ ).

Worked example 0.2

₹10,000 invested on the 5th of each month from January to December 2025 (₹1,20,000 in total); the holding is worth ₹1,28,000 on 5 Jan 2026.

Absolute return: $8{,}000/1{,}20{,}000 = 6.67\%$ .
XIRR: solving (0.3) gives 12.48% a year.
Sanity check: the average rupee was invested for 0.544 years, and $6.67\%/0.544 \approx 12.3\%$ , close to the XIRR.
Had the holding been worth ₹1,15,000, the XIRR would be −7.57%.

Exercisem00_sip_xirr.pyOpen in editor →