Case 079Portfolio constructionCore

Dhruvika's Rs 1,000 crore portfolio is 60% equity and 40% bonds. Equities rise 30% and bonds are flat. How far has it drifted, what trade restores it and what does that cost at 10 bps, and should the fund rebalance on a calendar or a threshold?

The situation

Dhruvika Asset Managers runs a Rs 1,000 crore balanced fund with a policy mix of 60% equity and 40% bonds. Over the past year equities rose 30% while bonds returned nothing. Trading costs are 10 basis points on each rupee traded, in either asset.

For the risk figures, use volatilities of 18% for equities and 6% for bonds and a correlation of 0.2 between them. The fund currently rebalances once a quarter, whatever has happened; the investment committee asks whether a threshold rule, trading only when the equity weight leaves a band of 55% to 65%, would be better.

Your task

Compute the drift, the rebalancing trade and its cost, what the drift did to the fund's risk, and compare calendar and threshold rebalancing.

Quick check

After a 30% equity rally with bonds flat, what is the equity weight?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The fund drifts to 66.1% equity; restoring 60/40 means selling Rs 72 crore of equity into bonds, at a cost of about Rs 14.4 lakh. The drift raised volatility from 11.5% to 12.5%, with equities now 94% of the risk. A 55% to 65% threshold rule would also trade here, but only because drift passed the band edge, which needs a 24% rally, not because a quarter ended.

Step 1How far has the portfolio drifted?

Think of a thali where the rice is meant to be 60% of the plate: if someone doubles the dal without touching the rice, the rice share falls even though you added nothing to it. Weights drift because each asset's share is measured against a total that moves with every price. Equity grows from Rs 600 crore to Rs 780 crore and the fund from Rs 1,000 crore to Rs 1,180 crore, so equity is 66.1%. To restore 60%, equity should be 60% of 1,180, which is Rs 708 crore, so sell Rs 72 crore of equity and buy the same amount of bonds.

A 30% equity rally turns 60/40 into 66/34StartEquity 600Bonds 40060.0% equityAfter the rallyEquity 780Bonds 40066.1% equityRebalancedEquity 708Bonds 47260.0% equitysell Rs 72 crore of equity, buy bondscost at 10 bps a leg: Rs 14.4 lakh
Dhruvika's Rs 1,000 crore at 60/40 becomes Rs 1,180 crore at 66.1% equity after a 30% equity rally; selling Rs 72 crore of equity into bonds restores 60/40 at a cost of about Rs 14.4 lakh.
Step 2Why does a six point drift matter?

Because equities carry most of the risk, and the drift gives them more. At 60/40, volatility is about 11.5% and equities supply 92% of it; at 66.1/33.9, volatility is 12.5% and equities supply 94%. Clients chose a balanced fund, and the fund is quietly turning into an equity bet after every rally, which is exactly when equities are more expensive. Rebalancing is a discipline that sells what has risen, not a forecast.

The relationship
σp=w2σe2+(1−w)2σb2+2w(1−w)ρ σeσbσp(0.60)=11.5%,  σp(0.661)=12.5%\sigma_p = \sqrt{w^2\sigma_e^2 + (1-w)^2\sigma_b^2 + 2w(1-w)\rho\,\sigma_e\sigma_b} \qquad \sigma_p(0.60) = 11.5\%, \; \sigma_p(0.661) = 12.5\%
wequity weight
sigma e, sigma bvolatility of equities 18% and bonds 6%
rhocorrelation between them, 0.2
What it says in wordsPortfolio volatility depends on the weights, each asset's volatility and how the two move together; more equity weight raises it quickly because equity volatility is three times the bonds'.
Step 3Calendar or threshold: which rule is better?

A calendar rule trades every quarter whatever the drift, so it pays costs for tiny corrections in quiet markets and can sit on a large drift for weeks in a fast one. A threshold rule trades only when drift is large enough to be worth the cost. With a 55% to 65% band and bonds flat, equities must rally about 23.8% before the rule fires, so small wobbles cost nothing. When it does fire, the fund can trade back to the target, Rs 72 crore and Rs 14.4 lakh here, or only to the band edge, Rs 13 crore and Rs 2.6 lakh, accepting a little more drift for a much smaller trade.

A threshold rule trades only once drift leaves the band60%65%70%55%band: 55% to 65%, no trading insideedge hit at +23.8%+30%: 66.1%+0%+10%+20%+30%+40%Equity return since the last rebalance, bonds flat
With bonds flat, Dhruvika's equity weight reaches the 65% edge of the threshold band only after a 23.8% equity rally, and a 30% rally takes it to 66.1%, so a threshold rule stays idle through small moves and trades only past the edge.

Close with the limit. The best band width is a trade-off between tracking the policy mix and paying costs, and it depends on volatility: wider bands for assets that move a lot, narrower when trading is cheap. Many funds combine the two rules, checking monthly and trading only if a band is breached. Taxes on realised gains, where they apply, argue for rebalancing with new inflows first, before selling anything.

Where candidates lose it

The arithmetic trap is saying equity is now 78% by dividing 780 by the old total of 1,000. Every weight must be recomputed on the new total.

The judgement trap is treating rebalancing as pure cost. The drift has raised the fund's volatility by about a percentage point and made it a different product from the one clients chose; the cost of Rs 14.4 lakh on Rs 1,180 crore is about one basis point, small against that change.

What the interviewer asks next

  • Bonds fall 10% at the same time as equities rise 30%. What is the trade now?
  • How would you size the band if equity volatility doubled?
  • The fund receives Rs 50 crore of new money. How do you use it before selling anything?
  • Why might rebalancing add return in a mean-reverting market and cost return in a trending one?

Company names and figures are illustrative.