ECONOMETRIC AND PROBABILITY OF RETURN ANALYSIS: STATISTICAL DIAGNOSIS OF PRICE BEHAVIOR IN NUBANK (NU)

 

The price chart shows robust growth from an initial value of 14,000 to a closing price of 65,160, representing a total return of 365.43%.

This analysis includes three trend lines: one linear and two polynomial lines, one of order 6 and the other of order 3. The polynomial line of order 6 has the highest coefficient of determination (R² = 92.70%), indicating that it accurately captures the cyclical fluctuations and volatility of the asset.

The linear model suggests continued growth toward 85,657 over a 360-day horizon. However, the polynomial nature of the trend line indicates that the current price is in an acceleration phase. Historically, these spikes often precede technical corrections that seek the mean.

The relationship between the mean (40,302), median (43,340), and mode (18,460) is fundamental to understanding the risk.

The value of -0.017 indicates a nearly imperceptible negative skewness (quasi-symmetric distribution), but the fact that the median is greater than the mean suggests that most price closes are above the historical average, which is positive for a "growth" thesis.

The kurtosis value of -1.34 (Platykurtic) is vital. A platykurtic distribution has thinner tails than a normal distribution. In finance, this indicates that extreme events (black swans or catastrophic crashes) have been less frequent during this period than in a standard normal distribution. There is greater dispersion, but less "tail risk."

The histogram reveals a bimodal or multi-peaked distribution. It does not follow a perfect Gaussian (normal) bell curve, which is typical for high-growth assets that rapidly change their trading "floor."

The 42,950 - 52,949 range has the highest frequency (215 days), establishing a zone of strong psychological and operational support.

With a Z-score of 1.61 and a cumulative probability (p) of 94.62%, the current price (X = 65,160) is at the upper end of the historical distribution. This means that only 5.38% (q) of the time has the price been or would be above this level under current conditions.

From a statistical and econometric perspective, my diagnosis is Operational Caution (Hold/Wait for a Pullback) for the following reasons:

The current price is at the 95th percentile (94.62% probability). Buying here would place you in the "right tail" of the distribution, where statistically the probability of a mean reversion (40,302) is higher than that of an immediate continuation at the same rate.

Although the average monthly return is attractive (1.25%), the asset has recently risen parabolically.

While the 360-day target is higher (85,657), entering at the highest point of the current study reduces the margin of safety.

A massive entry ("all-in") at this 65,160 level is not recommended. Ideally, one should wait for a correction towards the higher-frequency zone identified in the histogram (42,950 - 52,949) or make discrete purchases (DCA) to average down the cost, given that the series' long-term bias remains bullish.

Studying Value at Risk (VaR) is the logical next step to quantify the risk identified in the tables in monetary terms.

VaR answers the key question: "What is the maximum I can expect to lose in a day (or period) with a given level of certainty?"

Based on this analysis using the standard deviation data (15,445) and the current price (65,160), the parametric (or analytical) VaR can be calculated.

Individual VaR Calculation

For financial assets, we typically use a confidence level of 95% or 99%. For 95% confidence, the critical Z-value is 1.645. For 99% confidence, the critical Z-value is 2.326.

Using the parametric VaR formula:

 

Where sigma is the standard deviation of your data:

Where the VaR (95%) is 25,407.96 and the (99%) is 35,926.39.

If you decide to invest in Nubank at the current price of 65,160:

There is a 95% probability that, under normal market conditions, your loss will not exceed 25,407.96 monetary units over the study's time horizon. In other words, there is only a 5% chance that you will suffer a loss greater than that amount.

In the table, the kurtosis is -1.34 (Platykurtic). This is excellent news for calculating VaR:

Because it is negative, the distribution has "thin tails." This means that the calculated VaR is more reliable, as there is less probability of "extreme events" outside the range predicted by the standard deviation. In distributions with positive kurtosis (leptokurtic), the VaR tends to underestimate the true risk.

The asset has exceptional growth, but the VaR indicates high volatility (a deviation of more than 15,000 from a price of 65,000).

Given that the current price is in the "probability reached" zone of 94.62%, the risk of a correction reaching the VaR level (a drop of approximately 25,000) is statistically possible if the market decides to adjust towards the average of 40,302.

While the previous statistical analysis showed an asset with impeccable historical growth (high R² and a return of 365%), the current technical analysis is bearish or corrective in nature.

The fact that 10 of the 12 moving averages are indicating a "Sell" signal is a critical warning sign. The current price is crossing below its short- and medium-term averages (MA5 to MA100), confirming that the immediate trend has broken to the downside. Only the MA200 (Simple and Exponential) maintains a buy signal, validating that the long-term trend remains intact, but the current price is corrective.

The RSI (38.28) is approaching the oversold zone (30), but still has room to fall further. The Stochastic Oscillator (93.77) indicates extreme overbought conditions, suggesting that any recent rebound was weak and the price is exhausted. The ATR (1680) shows increased volatility, indicating that price movements will be more abrupt, increasing execution risk.

The cumulative probability is 94.62% in the long term and 5.38% in the short term.

Statistically, the asset has reached levels that only occur 5% of the time in its history. In investment terms, this is known as a stretched asset. The probability of the price continuing to rise without a prior correction is only 5.38%.

The market is attempting to return to the area of ​​greatest density on the histogram we saw earlier (the equilibrium zone). Investing.com's data provides context on the company's health: The P/E ratio (32.2x) is a high valuation for the traditional financial sector, but reasonable for a high-growth fintech. However, the Price-to-Book ratio (7.6x) suggests that the market is paying 7.6 times Nubank's book value, a considerable risk premium.

The return on equity (ROE) of 27.8% is extraordinary. It indicates very efficient capital management, which explains why the long-term trend has been so bullish.

Based on Camarilla and Fibonacci levels, the central pivot point is at 65,653.

Since the last close is below this point, the bias is bearish towards the support levels S1 (64,306) and S2 (63,453).

If the price breaks S3 (62,106), we would enter a phase of technical capitulation where the polynomial regression statistical model would begin to target the 40,000 moving average.

Confirming the assessment of uncertainty, the final technical-econometric recommendation is: Do not buy at this time. The technical analysis (10 sells vs. 2 buys) invalidates an immediate entry despite the optimism of the 360-day linear forecast. The risk of "catching a falling knife" is high.

The Highs/Lows indicator (-3020) and the Bull/Bear Power (-4168) show that sellers have complete control of the current order flow.

Wait for the oscillators (RSI and Stochastic) to reach extreme oversold levels and for the price to test the Fibonacci support (63,453). Only If the price stabilizes at these levels, the long-term probability of 94.62% would again favor the investor. The company is fundamentally sound (ROE 27.8%), but the price is undergoing a severe technical correction after reaching extreme probability levels. Moderation is, indeed, the wisest course of action at this time.