We actively follow over 350 Taiwan companies across a variety of sectors, focusing on companies in physical asset and distribution supply chains. Over the past four years, our Taiwan models have forecast upside and downside revenue surprises with ~91.8% directional accuracy. As Figure 1 depicts below, we have generated nearly 5,000 forecasts over the past 16 quarters, broken down into three categories: Beat, No Call, and Miss. We exclude companies with less than two publishing analysts.

**Figure 1: Historical Taiwan Revenue Forecasts vs. Actuals**

Calls (Beat, Miss) are made when Street expectations are +/- 1s from the mean of our forecast probability distribution. For any particular period, aggregate distributions tend to be non-normal and thus the probability "cutoff" that defines a call varies from quarter to quarter; this is why, as Figure 1 shows above, forecast "Beats" (green) and "Misses" (red) overlap with the "No Calls" set (grey). For any individual period, there is no overlap on a probability basis: Beats plus Misses plus No Call sum to one.

First, we address historical performance and statistics. As shown in Figure 1, there is a clear relationship between forecast probability and actual results vs. Street expectations. As the probability of a forecast Beat or Miss increases, so does the actual results vs. Street expectations in terms of directional magnitude. The sigmoid function of the aggregated forecast group is analogous to a cumulative distribution function (CDF) used to measure the probability of a single event. As with a CDF, probability (in this case Beat as opposed to Miss) is on the y-axis, with values (actual results vs. Street expectations on a percentage basis) on the x-axis.

Figure 2 below shows the forecast count by top-level GICS sector, as well as forecast type (Miss, No Call, Beat). Info Tech broadly speaking accounts for the majority of forecasts, but there are significant numbers of Consumer Discretionary, Industrials, and Materials as well. Forecast beats and misses appear generally symmetrically dispersed.

**Figure 2: Historical Forecast Count by Sector and Type**

*Source: RAD Advisors, Bloomberg*

Figures 3, 4, and 5 below show the distributions of the Beat, No Call, and Miss sets, respectively, over the four-year forecast history, as measured by actual results vs. Street expectations. Understanding these distributions can help us predict the likelihood of any individual forward-looking forecast. Based on fit as measured by AIC, the Beat and Miss sets most closely resemble a Generalized Logistic distribution, whereas the No Call set most closely resembles a Hyperbolic Secant distribution (which is similar to a Normal distribution, but with higher kurtosis).

**Figure 3: Distribution of "Beat" Forecasts, Q1:2013-Q4:2016**

*Source: RAD Advisors*

As we summarized in Figure 1, the "Beat" set is comprised of 1,118 forecasts over 16 quarters; 985 (88.1%) were correct (i.e., actual results beat Street expectations). These results are shown in Figure 3, which approximates a Generalized Logistic distribution (m = 0.082, s = 0.092) skewed right. As we would expect (or hope), most of the values (88.1%, to be exact) for the "Beat" set are above zero.

**Figure 4: Distribution of "Miss" Forecasts, Q1:2013-Q4:2016**

*Source: RAD Advisors*

The "Miss" set is comprised of 1,234 forecasts over 16 quarters; 1,175 (95.2%) were correct (i.e., actual results missed Street expectations). This is reflected in the distribution depicted in Figure 4, which like Figure 3 approximates a Generalized Logistic distribution (m = -0.110, s = 0.097), in this case (appropriately) skewed left; it is essentially a mirror image of the "Beat" set.

**Figure 5: Distribution of "No Call" Forecasts Q1:2013-Q4:2016**

*Source: RAD Advisors*

The "No Call" set is comprised of 2,627 forecasts over the same 16-quarter, four-year period. As shown in Figure 5 above, it is best fit by a Hyperbolic Secant distribution (m = -0.014, s = 0.055), which is similar to a Normal distribution, but has significantly higher kurtosis (peak). Ideally, we would want the "No Call" set to have a mean close to zero, and this is what occurs: if it were greatly skewed to the right or left, this would suggest that our criteria for selecting Beats and Misses needed adjusting.

With this historical summary as a backdrop, we now look to the current period (Q1:2017).

**Taiwan Forecasts for Q1:2017**

From an analysis standpoint, Taiwan public companies present an intriguing data set as they report revenues on a monthly basis to the Taiwan Stock Exchange. The companies themselves report full financials, including revenues, on a quarterly basis. We have nearly 15 years of this monthly data.

Our models can generate forecasts at any time, but as each month of the quarter is reported, we utilize a Bayesian process that incrementally assimilates this data as it becomes available and then produces updated forecasts. With the January and February components of Q1 now reported, we now have updated forecasts for all 355 companies, as shown in Figure 6 below.

Investors unfamiliar with this process and/or strict strong-market-efficiency adherents might think this information is quickly assimilated. The short answer is: it's not. We would have them look again at Figure 1 above. If this information was being correctly utilized, we would not have 92% success in predicting upside and downside surprises over four years and 5,000 forecasts. Furthermore, it's never just about the data, but how to model it to correctly predict real-world scenarios and actual results.

**Figure 6: Taiwan Q1:2017 Forecast Count by Sector and Type**

*Source: RAD Advisors*

**What's Going On In Apple's Supply Chain?**

Several important Apple (NASDAQ:AAPL) suppliers, including (alphabetically) ASE (NYSE:ASX) (2311 TT), Catcher (OTC:CHERF) (2474 TT), Cheng Uei (Foxlink) (2392 TT), Hon Hai (Foxconn (OTC:FXCOF)) (2317 TT), Largan (OTC:LGANF) (3008 TT), Pegatron (OTC:PGTRF) (4938 TT), Quanta (2382 TT), and TSMC (NYSE:TSM) (2330 TT) have forecast probabilities that could impact AAPL.

**Figure 7: Q1:2017 Revenue Forecasts for Key Apple Suppliers**

*Source: RAD Advisors*

Of the 13 suppliers listed in Figure 3 above, we have statistically identified calls for three (Miss at TSMC and Beats at Flexium and Quanta). However, important names such as Catcher, Hon Hai, and Pegatron have a high probability of missing, based on our models.

First, TSMC. Apple is one of TSMC's largest customers, if not the largest; other important TSMC customers include Broadcom (NASDAQ:AVGO), Nvidia (NASDAQ:NVDA), Qualcomm (NASDAQ:QCOM), and Texas Instruments (NYSE:TXN). In its first two months of Q1, TSMC has reported NT$148.039bn. From this, we know that it has to print at least NT$91.045bn in March in order to meet current Street expectations of NT$239.085bn, which would represent M/M growth of 27.47%. The question becomes: how reasonable is it for TSMC to achieve this growth? What is the probability of it happening?

There are many ways to answer this question, and we'll look at a few. First is the idea of seasonality. Many Taiwan companies have very seasonal M/M growth patterns. In fact, on a country-wide basis, March is historically the month with the strongest M/M growth. For TSMC, we can measure what this growth has been over many different periods.

**Five Years.** On a five-yr seasonal basis, TSMC has historically posted March M/M revenue growth of +11.32% (s=5.26%). The necessary M/M growth of +27.47% in order to meet Street expectations would represent 3.07 standard deviations above the norm: in other words, there is a 99.89% probability of it not happening, based on this five-yr seasonal view. Is this view the right one? We don't know, which is why we take multiple views.

**All Years (seasonal).** We have 15 years of monthly data for TSMC (and many other Taiwan companies, insofar as they have an operating history of that length). On a 15-year seasonal basis, TSMC has averaged +9.38% M/M in March (s=6.67%). The necessary M/M growth of +27.47% in order to meet Street expectations would represent 2.71 standard deviations above the norm: in other words, there is a 99.67% probability of it not happening, based on this 15-yr seasonal view. These two seasonal views give us very similar results.

**No seasonality.** What if we don't believe that TSMC's business is seasonal at all? For this view, which in some ways is more statistically robust as it incorporates 12x more data, we look at all of TSMC's M/M growth rates over the past 15 years. The average is 1.48% (s=11.08%). The necessary M/M growth of +27.47% in order to meet Street expectations would represent 2.35 standard deviations above the norm: in other words, there is a 99.05% probability of it not happening, based on this nonseasonal view.

Our modeling process looks at many other cuts and periods of the data, as well as other inputs. Could TSMC post +27.47% M/M growth in March? It is, of course, possible. Over the entire 180 months (15 years * 12 months) for which we have data, TSMC has eclipsed this growth rate just twice: July 2015 (+35.02%), and April 2009 (+59.65%), when it was coming out of the ugly period of zero orders at the end of the financial crisis of 2008. So it could happen. The question, however, is: how likely is it? What is the probability, based on a robust modeling process like ours with a very good historical track record?

Growth of +27.47% M/M would rank in the 99th percentile over the entire 15-year history of TSMC's data; this too bolsters our confidence in our forecast of a 99.7% probability of a miss. Of course, if analysts were to lower TSMC's estimates, our forecast probability would also decline (assuming no other inputs).

We don't know if the apparent weakness at TSMC is due to AAPL, some of its other aforementioned customers, or some combination thereof. But as shown in Figure 7, it's worth noting that other AAPL suppliers, including Hon Hai, Pegatron, and Catcher, also have a high probability of missing, even if there is no outright call per se. Conversely, we are forecasting Beats for both Flexium and Quanta. As it relates to Apple, Quanta only manufactures MacBooks, not iPhones.

**Figure 8: Q1:2017 Revenue Forecasts for Key Nike Suppliers**

*Source: RAD Advisors*

While only Feng Tay (9910 TT) and Eclat (1476 TT) have outright calls (both for Miss), other Nike (NYSE:NKE) suppliers such as Pou Chen and Far Eastern have high probability of misses. As always, there are other company relationships involved, but at minimum, these could indicate negative data points for Nike that could hit the market in the next month or so.

**Availability of Data on Bloomberg Terminal**

Our custom, highly predictive data is available for use on the Bloomberg terminal, where it can be combined with virtually all of Bloomberg's data in functions such as EQS (screening). A handful of use cases follow. Contact rad@radadvisors.com for more information.

With a forecast success rate of 92% over the past four years, Taiwan forecast data can be used as a proxy for upside and downside surprises over the next 30 or more days. As a data set, forecast probability can be appended to any single or multiple valuation metric(s) for the purposes of long/short idea generation. Figure 9 below shows Beat probability vs. 12-month forward P/E. A very low beat probability (i.e., a very high miss probability) coupled with high P/E could be a potential short idea. Conversely, a high beat probability (i.e., a low miss probability) may justify a high P/E on the long side.

**Figure 9: Forecast Probability vs. P/E**

*Source: RAD Advisors, Bloomberg*

Similarly, Figure 10 below shows Beat probability vs. EV/EBITDA. A very low beat probability (i.e., a very high miss probability) coupled with high EV/EBITDA could be a potential short idea. Conversely, a high beat probability (i.e., a low miss probability) may justify a higher EV/EBITDA on the long side.

**Figure 10: Forecast Probability vs. EV/EBITDA**

*Source: RAD Advisors, Bloomberg*

**Model Methodology**

RAD Advisors employs several types of models combined in a proprietary ensemble process, including cross-validated multiple linear regression, various seasonal models (ARIMA, etc.), and probabilistic Monte Carlo simulations. We have also developed several genetic algorithms in our model building process. We believe that our ensemble process provides levels of accuracy that might otherwise not be achieved utilizing a single methodology. As with any predictive modeling technique, errors do occur, but we endeavor to always improve with a thorough post-mortem of errors (and successes). Figure 11 below breaks down our Taiwan forecast results by quarter over the past four years, which range from a low of 81.8% (Q2:2015) to a high of 97.0% (Q2:13), averaging 91.8%.

**Figure 11: Forecast Success by Quarter, Q1:2013-Q4:2016**

*Source: RAD Advisors*

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.