Guide · Portfolio construction · Updated 2026-09-23

A 50:50 split of Indian equity and government bonds carried 93 per cent of its risk in equity, and levering the equal-risk version back up paid only at the overnight rate

Every figure below is computed at build time from published NSE index data, with the rules stated so the work can be redone, and the page ends on the question the formula leaves open: how to get a useful return out of a book made mostly of government bonds.

Equal capital is not equal risk

A two-asset book has one variance with four terms inside it. With w_E of the money in equity and w_B in bonds, volatilities σ_E and σ_B and correlation ρ, the variance is w_E²σ_E² + w_B²σ_B² + 2w_Ew_Bρσ_Eσ_B. Each asset owns its own squared term and one of the two cross terms. That split is not a convention. An asset's risk contribution is its weight times the rate at which the book's volatility rises with that weight, and the two contributions add up exactly to the book's volatility; the build checks the identity to twelve decimal places before it writes anything.

Put the measured inputs in. With half the money in each, equity's own term is 0.5² × 16.07² = 64.6 in squared per cent a year, the bonds' own term is 3.4, and each cross term is 0.5 × 0.5 × 0.11 × 16.07 × 3.68 = 1.6. Equity's row totals 66.2 out of 71.2: 93.0 per cent of the risk from 50 per cent of the money. A book described as balanced was an equity position with a bond cushion.

The correlation moves that split less than the ratio of the volatilities does, and not in the direction most people expect. Holding both volatilities at their measured values, a correlation of +0.5 would have left equity with 87.0 per cent of a 50:50 book's risk and a correlation of zero 95.0 per cent. A correlation of −0.5 would have given equity 107.5 per cent: the bond leg's contribution turns negative, because it then subtracts risk instead of adding it, and equity carries more than the whole book's risk. What makes a 50:50 split an equity bet is that equity moved about 4.4 times as much as the bond index. The correlation only decides whether the bond leg cushions that bet or hedges it.

The equal-risk weights need two volatilities, and the correlation cancels

Risk parity sets the two contributions equal. Write equity's row equal to the bonds' row: w_E²σ_E² + w_Ew_Bρσ_Eσ_B = w_B²σ_B² + w_Ew_Bρσ_Eσ_B. The cross term appears once on each side, identically, and drops out. What is left is w_Eσ_E = w_Bσ_B: each weight times its own volatility must match. With the weights summing to one, w_E = σ_B / (σ_E + σ_B).

On the measured inputs that is 3.68 / (16.07 + 3.68) = 18.6 per cent in equity and 81.4 per cent in bonds, or 4.4 rupees of bonds for every rupee of equity. Each asset then carries exactly half the risk. The build confirms the result two ways before publishing it: the closed form gives equal contributions at every correlation tested from −0.9 to +0.95, and a numerical search for equal contributions that never uses the formula lands on the same weight to nine decimal places.

This corrects a common statement of the method, that the equal-risk weights take the correlation as an input. For two assets they do not. The answer is inverse volatility weighting, exactly, and it stops being so only at three or more assets, where each position's cross terms differ and the correlation structure does move the weights. That case is worked through on nine sector indices in correlation-adjusted position sizing, where the adjustment changed the weights by up to a fifth.

The correlation has not vanished. It has moved from the weights to the size of the book. At risk parity weights the book's volatility is w_Eσ_E × √(2(1 + ρ)), so with the measured volatilities the same weights give a book of 3.54 per cent a year at a correlation of −0.3, 4.23 at zero, 4.46 at the sample's 0.11, 5.06 at the latest one-year reading of +0.43 and 5.52 at +0.7. The weights are identical in all five. Anything scaled to a risk target, including a levered version of the book, inherits the correlation through that size.

The weights move because the volatilities move

The formula is exact and its inputs are not fixed. Recomputed every session from the 250 sessions before it, the risk parity weight in equity ran from 12.2 per cent on 1 February 2021 to 33.6 per cent on 2 February 2018. Over the same stretch the equity share of a 50:50 book's risk never fell below 79.7 per cent and reached 98.6.

Two things in that table carry the mechanism. Bond volatility is not a fixed property of government bonds: it ran from 2.16 per cent in 2024 to 4.65 per cent in 2018, more than two to one, and a weight built on it moves with it. And the weight answers a storm after it arrives. Equity volatility reached 31.3 per cent over 2020, and the trailing weight in equity reached its low in February 2021, when the worst of that volatility was already in the window rather than ahead of it. A weight estimated from the past describes the past, which is the same lag that decides what volatility targeting can and cannot do.

The bond index you choose sets the weight

Government bonds are not one asset for this purpose. Duration sets a bond index's volatility, and the volatility sets its risk parity weight. The maturity bucket indices in the same files, measured over the common window from 9 November 2015, show it directly.

Moving from the 4 to 8 year bucket to the 15 year and above bucket lifts the bond volatility from 2.89 to 5.39 per cent, lifts the equity weight from 15.2 to 25.1 per cent and cuts the leverage needed to reach a 50:50 book's risk from 2.27 to 1.47 times. That is the quiet alternative to borrowing: take the extra risk through duration instead of through a loan. It is not free. The long bucket's extra risk is interest rate risk, concentrated in exactly the sessions when rates reprice, which is the risk the 2021 to 2022 and 2026 episodes below delivered.

The last row is the error to avoid. The clean price version of the 10 year benchmark index leaves out coupons and accrued interest, and over the same window it returned −0.75 per cent a year against +6.19 for the total return version of the same index. The coupons were more than the whole of the return: the price component lost money. Run risk parity on a clean price series and the bond leg looks like a decade of losses; run it on the equity price index and it drops the dividends, the gap measured in total return against price return. Both legs have to be total return.

Three portfolios, one rebalance rule, measured

The comparison runs from the close of 28 October 2016, the first month end with a full 250-session window behind it, to 18 September 2026: 9.9 years and 119 monthly rebalances. The equity leg is the broad index's published total return index; the bond leg is the Composite G-sec Index, which the index provider computes on a total return basis from the ten most traded government bonds with more than a year to run. Every book is rebalanced at the close of the last session of each month. The 50:50 book resets to half and half. The risk parity book resets to σ_B / (σ_E + σ_B), with both volatilities estimated from the 250 sessions ending the session before the rebalance, so no weight uses the day it is traded on. Equity alone is simply held. Nothing is charged for trading, tax or tracking.

Read the volatility and drawdown columns together. Risk parity ran at 4.52 per cent volatility against 16.22 for equity, and its worst fall, 9.0 per cent, was under a quarter of equity's 38.3. All three worst falls were the same event, the slide to 23 March 2020, and the recoveries were ordered by depth: 58 sessions for risk parity to regain its previous high, about 3 months, 79 sessions for 50:50 and 157 sessions, about 7 months, for equity.

The longest time under water tells a different story from the worst drawdown. None of the longest spells was 2020. Equity's two longest were 265 sessions each, from October 2021 to November 2022 and from September 2024 to October 2025. The 50:50 book's longest, 223 sessions, and risk parity's, 171, both fell in the stretch from late 2021 into 2022 when the bond index fell as well. On 18 September 2026 equity stood 10.5 per cent below its high of 2 January 2026, the 50:50 book 4.2 per cent below its own and risk parity 2.1.

The return column is the price of the other columns: 11.92, 9.57 and 7.53 per cent a year for equity, 50:50 and risk parity. Equal risk bought the smoother path by holding far more of the lower-returning asset, which is what the formula does by construction: it reads volatility and never return. A worst drawdown is one draw from a distribution of paths, and a different ordering of the same decade would have produced a different number, which is the subject of maximum drawdown as a sample statistic.

The correlation assumption, and the falls that tested it

A mixed book is usually described as working because bonds rise when equity falls. The sample lets that be tested rather than assumed. The table lists every fall of ten per cent or more in the equity total return index since October 2015, what the bond index did over the same window, the daily correlation inside the fall and what each book lost.

Across the 8 falls the bond index rose in 5 and fell in 3: the 2015 to 2016 decline, the fall from October 2021 to June 2022, which spanned the Reserve Bank's off-cycle 40 basis point repo rate increase of 4 May 2022, and the 2026 fall. The daily correlation inside the fall was positive in 6 of the 8. On the ten worst single sessions for equity in the sample the bond index fell on 6, and across all ten it moved −0.15 per cent on average, against +0.03 per cent on an average session. On the worst of them, 23 March 2020, when the equity index lost 12.9 per cent, the bond index lost 0.88 per cent.

What protected the mixed books was not bonds moving the other way. It was bonds moving very little. A leg with a volatility near 3.7 per cent a year does not need a negative correlation to cushion a fall; it needs only to be large and quiet, and a risk parity weight makes it both. The protection scales with how much of the book sits in the quiet asset, not with any hedge. Risk parity went into the 2020 fall with 23.2 per cent of its money in equity against 50 for the 50:50 book, and lost 7.3 per cent against 18.9. The smaller equity weight accounts for about 10.3 of those 11.6 points; the bond index's 2.5 per cent gain over the same weeks, earned on the larger bond weight, for about 0.7.

The correlation is the least stable input on the page. The one-year reading was positive 79 per cent of the time and ran from −0.11 in November 2017 to +0.43 on 18 September 2026, the highest reading of the sample and the latest. The three-month reading ran from −0.35 to +0.70. Two cautions apply to any correlation measured inside a fall. The window was chosen because it was a fall, and selecting on large moves inflates a measured correlation even when the relationship underneath has not changed, one of the reasons a correlation is an estimate over a window you chose. And a positive reading means the same sessions moved both indices the same way, which is exactly when a mixed book's cushion is thinnest.

Equal risk buys a smaller return, and the gap is filled with leverage

Risk parity's measured 7.53 per cent a year sits well below the 50:50 book's 9.57. Institutions that run it close the gap by borrowing: scale the whole book up until its risk matches a target, and finance the difference. Both versions were run on the same data. One levers the risk parity book each month to the 50:50 book's estimated volatility; the other to equity's. The borrowed amount accrues at the Nifty 1D Rate Index, which compounds the overnight rate on the Clearing Corporation of India's tri-party repo market, plus a stated spread. The index compounded at 5.40 per cent a year over the period. For scale, the Monetary Policy Committee held the repo rate at 5.25 per cent at its meeting of 3 to 5 August 2026, with the standing deposit facility at 5.00 per cent and the marginal standing facility at 5.50.

At the overnight rate itself, the first version measured 9.68 per cent a year against 9.57 for the 50:50 book it was built to match, a lead of about a tenth of a point a year that is gone at a spread of 0.12 points. The second version measured 12.87 per cent against equity's 11.92, a lead of 0.95 points gone at a spread of 0.32 points. Each point of spread cost roughly the borrowed share of the book: about 1.0 points of annual return for the first version and 2.7 for the second.

The mechanism is arithmetic. A constant multiple of leverage scales a book's excess return over the financing rate and its volatility by the same factor, so it cannot raise the ratio between them. Measured over the period, equity earned 0.46 of excess return over the overnight rate per unit of volatility and the bond index 0.30. Risk parity puts four fifths of the money in the asset with the weaker ratio, and its own ratio came out at 0.475, below the 50:50 book's 0.516. Held at one constant multiple of 1.85, chosen with hindsight to bring its volatility to about the 50:50 book's, risk parity measured 9.19 per cent a year against 9.57. The monthly version did slightly better, a ratio of 0.523, only because its leverage moved with the estimated volatilities, which is volatility timing of the kind volatility targeting measures, not a property of risk parity. Levered risk parity pays when the two assets earn similar excess returns per unit of risk and the borrowing is close to the overnight rate. Over this decade in India the first condition did not hold, and the second is not available to an individual: the overnight rate is set in an institutional market whose eligible participants, as the Clearing Corporation lists them, are banks, financial institutions, primary dealers, mutual funds, insurers, finance companies, corporates and provident and pension funds.

Leverage also moves the worst period. Unlevered, all three books had their worst fall in March 2020. Levered, the worst fall became the decline from late 2021 to June 2022, when bonds and equity fell together: 15.3 per cent for the first version, not regained until 4 May 2023, and 29.9 per cent for the second, not regained until 14 December 2023. Inside the equity fall of that period the first version lost 13.8 per cent where the plain 50:50 book lost 9.6. It went into the fall at its rebalance of 30 September 2021 holding 2.28 times its capital in the bond index against 0.5 for the 50:50 book, and paying the overnight rate on the borrowed 1.65. The leverage was that high because the bond index had just spent a year barely moving, at 2.48 per cent volatility over the trailing window: a book scaled to a volatility target borrows most when its quiet asset has been quiet longest, which is when a rate shock does the most damage. On 18 September 2026 the same book was in a spell under water that began on 26 May 2025, 327 sessions long and still open.

Put plainly: for an individual, unlevered risk parity is a way to hold much less risk than equity and accept a lower return. Levered risk parity is a different product, a bet that you can borrow close to an institutional overnight rate and that bonds will not fall when equity does. On this sample the first was not available to an individual borrower and the second failed in the 2021 to 2022 fall and again in 2026. A retail investor usually should not use leverage to run it, and the measured figures above are the reason, not a matter of temperament.

The 2026 rules made the borrowing easier, not cheaper

Two rule changes this year alter who can lever a book like this and how, and pages written before them cite limits and regulation numbers that no longer apply.

The first is the Reserve Bank of India's rewrite of bank lending against securities. It was announced in the Governor's statement of 1 October 2025, which proposed raising the ceiling on bank loans against shares from ₹20 lakh to ₹1 crore and removing the regulatory ceiling on lending against listed debt securities. It was issued as the Credit Facilities Amendment Directions, 2026 for commercial banks on 13 February 2026, and on 30 March 2026 the Reserve Bank deferred its start from 1 April to 1 July 2026. For loans to individuals it now reads as follows.

Read it for what it does to a levered book. Pledging the bond leg now carries no regulatory amount ceiling; for listed debt securities that ceiling was removed by these directions. A bank loan taken to buy securities, which is what leverage is, is capped at ₹25 lakh per individual; margin funding from a stockbroker and loans from finance companies sit under separate rules not covered here. At the 3.61 times average the equity-risk version needed, that finances the book for about ₹9.6 lakh of the investor's own capital, and at the 1.90 times of the 50:50-risk version about ₹27.7 lakh (illustrative arithmetic). And a breach must be cured within seven working days. At the peak leverage of 5.41 times, a book financed against its own holdings starts at a loan to value of 81.5 per cent, so a fall of 4.1 per cent in the whole book takes it through an 85 per cent ceiling, the highest in the table (illustrative). The 2021 to 2022 decline alone took the equity-risk version down 29.9 per cent.

The second is the replacement of the 1996 mutual fund regulations by the SEBI (Mutual Funds) Regulations, 2026, in force from 1 April 2026. Regulation 42 still lets a scheme borrow only to meet temporary liquidity needs such as redemptions and payouts, within twenty per cent of net assets, and the Master Circular for Mutual Funds of 20 March 2026 caps a scheme's cumulative gross exposure across equity, debt and derivatives at 100 per cent of net assets (clause 13.18.1). An Indian mutual fund therefore cannot run levered risk parity. If leverage exists, it sits on the individual's own balance sheet, at the individual's borrowing rate and with the individual's margin calls.

None of this changes the arithmetic of the previous section. The rules decide whether the loan is available. The break-even spread decides whether it pays, and on this data it was a fraction of a point above a rate that individuals cannot borrow at.

Where the method breaks

Volatility is the only risk it sees. The weights treat a unit of bond volatility and a unit of equity volatility as the same risk. Bond losses cluster in rate shocks and equity losses arrive in fat tails, and a standard deviation understates both, the problem set out in why standard deviation understates tail risk.

The estimates are the past. A trailing window reacts after volatility changes. In 2020 the weight cut equity after the fall rather than before it, and it will do the same in the next one.

The bond regime is a policy regime. The composite index's yearly volatility of 2.16 to 4.65 per cent reflects this decade's rate cycles. A period with larger rate moves changes the weight, the leverage and the drawdown together.

Costs, taxes and tracking are left out. Both mixed books turned over about 10 per cent of their value a year one way, and each rebalance that sells a gain is a taxable event for an individual. A fund that tracks either index charges an expense ratio and tracks imperfectly. The levered versions also ignore any charge a lender adds beyond the interest rate.

A decade is one sample. One pandemic crash, one fall in 2021 and 2022 in which both assets dropped, and another in 2026. A different ordering of the same returns would change every drawdown figure, which is how sequence of returns risk works on any balanced book.

What risk parity is actually for

Stripped of leverage, risk parity is a disciplined answer to one question: how much of each asset makes the risk, rather than the money, balanced. For Indian equity and government bonds the answer was about one rupee in five in equity, and it moved between one in eight and one in three as the volatilities moved. That is useful even to someone who never holds the portfolio, because it shows that a split described in rupees says almost nothing about where the risk sits, and that the correlation matters most in the sessions when both assets reprice at once.

It is not a return engine. Its measured return was the lowest of the three books, and the leverage that would lift it depended on a borrowing rate no individual gets and on a correlation that reached its sample high in 2026. The habit this page practises, measuring where the risk sits before naming a portfolio and running a rule on real data before trusting its label, is the one the Bharath Shiksha curriculum is built around.