Case 040Forecasting and modellingCore

Use app and social media data to forecast Sanvora Beauty's quarterly sales. Downloads are up 25% and brand mentions up 40%; your estimate is Rs 410 crore against a street estimate of Rs 450 crore. How confident are you?

Two SigmaNew York · 2024

The situation

Sanvora Beauty sells cosmetics and skincare through its own app, its website and 60 stores. You have eight quarters of app download data from a data vendor alongside reported sales. Downloads rose from 55 lakh to 84 lakh a quarter over that period while sales moved between Rs 365 crore and Rs 409 crore.

This quarter, downloads are 90 lakh, up 25% on the same quarter last year, and brand mentions on social media are up 40%. Historically about 6% of downloads turn into buyers within the quarter. Brand mentions have tracked sales poorly in the past. Your fitted model gives Rs 410 crore of sales; the consensus of analysts is Rs 450 crore.

Your task

How much weight does the estimate deserve, how would you express the view, and what could make the data mislead you?

Quick check

The street is at Rs 450 crore. What decides whether your Rs 410 crore is worth acting on?

Worked solution

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

30-second answerThe answer to give first

Fairly confident the street's Rs 450 crore is too high, and much less confident that sales will be exactly Rs 410 crore. Downloads explained about 63% of the swing in sales over eight quarters, with a typical error of about Rs 13 crore this quarter, so the 95% band runs from about Rs 378 to 442 crore. The street sits above it. Brand mentions get no weight because they never tracked sales.

Step 1Why is a 25% rise in downloads not yet a forecast?

A shopkeeper who counts people walking past his window knows footfall is up, but until he has checked how often passers-by became buyers in past months, he does not know what it means for the till. Alternative data is useful only once you know how well it tracked the thing you care about before, and how far off it has been. The job is to fit the signal against reported sales for past quarters, measure the error, and only then read this quarter.

Does the app signal track sales? Eight quarters, fit and 95% band360400440Street estimate Rs 450 croreThis quarter:Rs 410 croreband 378 to 442Past quarters (open circles)5060708090App downloads in the quarter, lakh
Over eight quarters Sanvora's sales rose with app downloads, and the fitted line gives Rs 410 crore at this quarter's 90 lakh downloads with a 95% band of about Rs 378 to 442 crore; the street's Rs 450 crore sits above that band.
Step 2How confident can you be?

The fitted line says each extra lakh of downloads has come with about Rs 1.2 crore of extra sales, which fits the 6% conversion rate: 6,000 new buyers spending about Rs 2,000 each in their first quarter. The residual error is about Rs 10 crore, and it widens to about Rs 13 crore this quarter because 90 lakh is beyond anything seen before. Rs 450 crore would need about 123 lakh downloads on the historical relationship, far above the 90 lakh observed, so the data argues clearly against the street even though it cannot pin down the number.

The relationship
S^=302+1.20×90≈410band=S^±2.45×13.0≈378 to 442\hat S = 302 + 1.20 \times 90 \approx 410 \qquad \text{band} = \hat S \pm 2.45 \times 13.0 \approx 378 \text{ to } 442
S hatestimated sales this quarter, Rs crore
1.20Rs crore of sales per lakh of downloads, from eight quarters
13.0standard error of a new quarter's estimate, Rs crore
2.45multiplier for a 95% band with only six degrees of freedom
What it says in wordsThe estimate is the fitted line at this quarter's downloads, and the band widens with the model's past error and with how unusual this quarter's reading is.
Step 3What could make the data mislead you?

Three things, each checkable. The app is only part of sales; if stores or marketplaces grew faster this quarter, downloads understate demand. Downloads bought through paid campaigns convert worse than organic ones, so a promotion could inflate the signal. And eight quarters is a short history, so one unusual quarter moves the fit. Brand mentions get zero weight despite rising 40%, because a signal that has not tracked sales before is noise with a big number attached. Express the view as below consensus rather than as Rs 410 crore, and size it to the band, not to the point.

Where candidates lose it

The common loss is quoting the point estimate as if it were a fact, Rs 410 crore against Rs 450 crore, with no sense of the error. With eight data points the honest statement is a range, and the interviewer wants to hear it.

The second is stacking signals because they all point up: downloads plus 25%, mentions plus 40%. Adding a signal with no track record does not raise confidence; it only adds noise you cannot measure.

What the interviewer asks next

  • How would you test whether the data vendor's download counts are consistent over time?
  • Sanvora starts selling on a marketplace. How does that change the model?
  • How many more quarters would you want before trusting the fit, and why?
  • Which other data would you combine with downloads to reduce the error?

Asked at Two Sigma, Generalist, New York, 2024 (Wall Street Oasis): How would you make money with social media data?

Company names and figures are illustrative.