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061A company grew EPS 40% last year while its sector grew 10%. Assume that 30% of any company's growth above the sector average persists into the following year, a persistence coefficient of 0.3. What EPS growth should you forecast for next year?Sell-side equity researchBuy-side equity research
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What growth do you forecast for next year?
Show the worked solution
About 19%. Start from the sector's 10%, the base rate, and keep only the part of the outperformance that tends to persist. The excess was 40% - 10% = 30 points, and a coefficient of 0.3 keeps 9 of them, so the forecast is 10% + 0.3 x 30 = 19%. Extreme results are partly luck, and luck does not repeat, so the forecast sits much nearer the average than last year's number.
Why not forecast 40% again?
A student who scores 95 in one mock exam, when the class averages 60, is probably both able and lucky that day. On the next mock she is likely to beat the class again, but by less, because the luck part does not come back. An extreme result is part skill and part luck, and only the skill carries forward, so the best forecast pulls the result back towards the average. The persistence coefficient says how much pulling to do: 0.3 means 30% of the gap survives and 70% fades.
At 40% growth last year, extrapolating gives 40% and assuming nothing persists gives the sector's 10%, while keeping 30% of the 30 point excess gives a forecast of 19%, much nearer the average than the outlier. The relationship\hat g next year's forecast growth \bar g the sector average, the base rate g the company's growth last year \beta the persistence coefficient, the share of the excess that carries over What it says in wordsThe forecast is the average plus the share of last year's excess that tends to persist.Where does the 0.3 come from, and what if you are not given it?
It is an empirical fact about a set of companies, not a law. You would estimate it by comparing one year's growth with the next across many companies in your universe over several years. Without data, the question to ask is how much of last year's jump came from something that recurs, such as a new plant or share won from rivals, and how much from something that does not, such as a one-off order, a weak base year or a tax credit. A jump built on recurring drivers deserves a higher coefficient.
How does this show up on a research desk?
Forecasts for last year's winners are often extrapolations with a haircut too small. A stock priced as if 40% growth continues is exposed when growth drifts back towards the sector, even if the company stays better than average. Say that link after the number: it shows you understand why the interviewer framed the question around a forecast rather than a fact.
Where candidates lose it
Candidates either extrapolate 40% or, overcorrecting, snap all the way back to the sector's 10%. Both ignore the coefficient they were handed, which is the entire point of the question.
The quieter slip is multiplying the whole 40% by 0.3 and saying 12%. The shrinkage applies to the excess over the average, not to growth itself. Anchor on 10%, then add back 30% of the 30 point gap.
What the interviewer asks next
- What would a coefficient of 1, or of 0, say about the business?
- Why might growth that came from winning market share persist more than growth from a one-off order?
- How would you estimate the coefficient from ten years of data?
086Ten analysts each forecast a company's EPS. Every forecast is unbiased, the errors are independent and all the same size. You pick the highest of the ten. On average, how far above the true EPS is it?Sell-side equity researchHedge fund long/short
Try it first
Each forecast is unbiased. Is the highest of the ten biased?
Show the worked solution
About 1.54 standard deviations too high. Each forecast is right on average, but choosing the highest selects for the biggest positive error. The expected maximum of ten independent draws from a normal distribution is 1.54 standard deviations above the mean. If each analyst's error has a spread of Rs 2 around a true EPS of Rs 50, the top forecast averages Rs 53.08.
Why does choosing the highest create bias when nobody is biased?
Weigh yourself on ten bathroom scales, each accurate on average but each a little off, and write down only the heaviest reading. You will always look heavier than you are. The bias is not in any one estimate; it comes from the choosing, because the maximum picks whichever estimate had the largest positive error. Auction theory calls the same effect the winner's curseThe tendency for the winning bid in an auction to overestimate the value of the prize, because the highest estimate of many noisy ones is usually too high.: the bidder with the highest estimate wins, and usually overpaid.
Ten unbiased estimates spread around a true EPS of Rs 50 average out to Rs 50, but the highest of them sits 1.54 standard deviations above it, about Rs 53.08, so choosing the top number builds in optimism. How do you get to 1.5 without tables?
Ask where the maximum has an even chance of landing. All ten estimates must fall below a level for the maximum to fall below it, so you need the level where the chance for one estimate, raised to the tenth power, is one half. That single-estimate chance is 0.5 to the power one tenth, about 0.933, which a normal table puts at 1.50 standard deviations. The mean of the maximum is a touch higher, 1.54, because the distribution of the maximum has a longer right tail. Either number is a fine answer in the room if you show the route.
The relationshipPhi(x) the chance one estimate lands below x standard deviations 10 the number of independent estimates sigma the standard deviation of each analyst's error What it says in wordsThe maximum of ten is below a level only if all ten are, which puts its middle near 1.5 standard deviations and its average near 1.54.Where does this bite an analyst?
Anywhere the top of a list is chosen after the fact. The most bullish forecast in the consensus, the best of ten back-tested strategies and the top-ranked fund of the year all carry a selection premium that will not repeat. The effect grows with the list: the highest of five is 1.16 standard deviations high, of twenty about 1.87. The fix is to shrink the chosen number back towards the average in proportion to how noisy the estimates are. The limit of this answer is the independence assumption: analysts who talk to the same management team share errors, and correlated errors shrink the gap.
Where candidates lose it
Most candidates say zero, reasoning that averaging unbiased numbers gives an unbiased number. That is true of the average and false of the maximum. The question is built to see whether you notice the selection.
The second loss is saying biased upwards without a size. Reaching 1.5 standard deviations through the one-half route turns a hunch into a number the interviewer can check.
What the interviewer asks next
- How would the answer change with twenty analysts instead of ten?
- If the analysts' errors are correlated, does the bias grow or shrink?
- How would you adjust the best back-tested strategy's return before trusting it?