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045

Case 045Client mandates and IPSHard

A client holds Rs 15 crore of her Rs 18 crore net worth in her employer's shares, a stock with 45% volatility. Compare her portfolio volatility and the chance of a 50% wealth loss before and after diversifying, and lay out a staged three-year selling plan.

1The situation

Farah Contractor, 44, is a senior vice president at Zenvora Labs, a listed diagnostics software company. Over nine years of stock options and share grants she has built up Zenvora shares worth Rs 15 crore, with a tax cost of about Rs 3 crore. Her other investments, Rs 3 crore in balanced funds, take her net worth to Rs 18 crore. Her salary and future grants also come from Zenvora.

For planning, assume Zenvora returns 13% a year with 45% volatility, a diversified portfolio 9% with 12%, and a correlation of 0.4 between them. She is proud of the company and reluctant to sell.

2Your task

How risky is her position today and after diversifying, what is the chance she loses half her wealth, and what selling plan would you put in her investment policy statement? Treat tax as a framework to confirm at current rates.

Quick check

Roughly what is her portfolio volatility today?

Worked solution

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

30-second answerThe answer to give first

Today her wealth swings with about 38% volatility and carries a chance of about 11% of halving within three years; with Rs 2 crore of Zenvora left, volatility falls to about 13% and that chance to well under 1 in 1,000. Sell Rs 13 crore over three years, Rs 6, 4 and 3 crore, front-loaded, inside the company's trading windows or a pre-disclosed trading plan. The tax on the gains is far smaller than one bad year in the stock.

Step 1How much risk does one stock at 83% of net worth carry?

A household that lives on one salary, keeps its savings with that same employer and lives in the company town is not diversified however many accounts it has. Farah's salary, her future grants and 83% of her wealth all depend on Zenvora, so one bad event hits her income and her savings together. On the numbers alone, the portfolio's volatility is about 38.3%, nearly the stock's own 45%, because the Rs 3 crore of balanced funds is too small to offset it.

The relationship
σp=0.8332(0.45)2+0.1672(0.12)2+2(0.833)(0.167)(0.4)(0.45)(0.12)≈38.3%\sigma_p = \sqrt{0.833^2(0.45)^2 + 0.167^2(0.12)^2 + 2(0.833)(0.167)(0.4)(0.45)(0.12)} \approx 38.3\%
0.833Zenvora's share of net worth, 15 / 18
0.45, 0.12volatility of Zenvora and of the diversified funds
0.4correlation between them
What it says in wordsHer wealth today moves with about 38.3% volatility; with Rs 2 crore of Zenvora left the same formula gives about 13.5%.
Step 2How likely is a loss of half her wealth?

Model wealth as lognormal and ask how often it ends below Rs 9 crore after three years. Concentrated, the answer is about 10.8%, roughly one chance in nine; diversified, about 0.003%, effectively nil. The model flatters the concentrated case. A single company can lose most of its value on one event, a failed product, an accounting problem or a regulatory ruling, far more often than a normal curve allows, while a diversified portfolio has no such single point of failure.

Wealth in three years: one stock spreads the outcomes, the loss tail included01020304050half her wealth:Rs 9 crore11% of outcomesbelow Rs 9 croretoday Rs 18 crorediversified: volatility 13%83% in one stock: volatility 38%Wealth in three years, Rs crore (illustrative lognormal model)
With 83% of her wealth in Zenvora, Farah's wealth in three years spreads widely and about 11% of outcomes fall below Rs 9 crore, half of today's Rs 18 crore, while the diversified portfolio is narrow and almost never falls that far.
Step 3Why stage the sale over three years instead of selling tomorrow?

Selling everything at once removes the risk fastest, and that is the benchmark against which any delay must justify itself. Staging is justified by constraints, not by a view on the stock: insider trading windows, tax spread across financial years, and a client who will only follow a plan she accepts. As a senior employee she is likely a designated person who can trade only in open windows with pre-clearance; Indian insider trading rules also allow a trading plan disclosed in advance, so confirm the current conditions with the company's compliance officer. Front-load the plan, because the risk is largest now: Rs 6 crore in year one, Rs 4 crore in year two and Rs 3 crore in year three, each year split into tranches across the open windows.

Sell most in year one, while the risk is largestZenvora sharesdiversified153Today83% in one stockvolatility 38%99End of year 150% in one stockvolatility 26%sell 6513End of year 228% in one stockvolatility 18%sell 4216End of year 311% in one stockvolatility 13%sell 3
Selling Rs 6 crore, Rs 4 crore and Rs 3 crore of Zenvora over three years takes the stock from 83% to 50%, 28% and finally 11% of Farah's Rs 18 crore, and her portfolio volatility from about 38% to about 13%.
Point in planZenvora, Rs croreShare of wealthVolatilityChance of halving in 3 years
Today1583%38.3%10.81%
After year 1950%25.5%1.98%
After year 2528%17.8%0.12%
After year 3211%13.5%0.00%
Each stage of the plan cuts volatility and the three-year chance of halving her wealth, from 10.8% today to 1.98% after the first year's sales, which is why most of the selling sits in year one.
Step 4How do you treat the tax, and what goes in the policy statement?

Frame tax as a cost to compare, not a reason to wait. About 80% of every rupee she sells is gain, so the Rs 13 crore sale realises about Rs 10.4 crore of gains. Every point of tax rate costs about Rs 104.0 lakh; even at an illustrative 20%, chosen to be cautious and not the current rate, the bill is about Rs 2.1 crore, against Rs 6.75 crore lost in one bad year of a 45% volatility stock. Whether gains are long or short term, and the cost basis of shares acquired through options, depend on rules to confirm with her tax adviser at current rates. The policy statement then records the target: Zenvora at no more than about 10% to 15% of net worth by the end of year three, the selling schedule, a rule to sell faster if the stock rises sharply, and a rule that new grants are sold as they vest.

Where candidates lose it

The common loss is treating this as a tax problem. Candidates spend the time on how to minimise the bill and never show that the risk of holding is several times the tax cost of selling.

The second is forgetting that her job is also a Zenvora position. A plan that sells the shares but lets new grants pile up, or that ignores trading windows, will not survive its first quarter.

What the interviewer asks next

  • Zenvora rises 40% in the first six months of the plan. Do you sell faster or slower?
  • Could she protect the position with options instead of selling, and what would that cost her?
  • How would the plan change if she expected to leave Zenvora within a year?
← Case 044The rupee falls 8%. A global allocation fund has Rs 1,000 crore: 25% unhedged US equity, 20% domestic IT exporters whose earnings rise 6% for an 8% fall, 15% oil-importing sectors that fall 5%, and 40% domestic bonds. Estimate the net effect.Case 046 →A small cap fund has Rs 3,000 crore in 60 stocks averaging Rs 6 crore of daily volume. If a quarter of the fund is redeemed in a month and it trades 20% of daily volume, how many days does a pro rata sale take, and who bears the cost if it sells the liquid names first?

Company names and figures are illustrative.

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