ARIMA For Options Investing

In many intro time series classes, you come across the autoregressive integrated moving average (ARIMA) forecasting technique. But you only took economics or finance so you can infiltrate the capitalist beast and make out like a tapeworm. How does ARIMA make my bank account go arriba?

A lot of people fail when trying to use ARIMA to day-trade or swing-trade, so they instead opt for training a neural network with 1 million billion trillion parameters, increasing their electricity bill beyond whatever returns they may hope to make. But if you have patience, if you can suffer through the existential pain that is another year or two on this blighted rock, you may prefer this easier ARIMA options.

  1. Pick a stock deemed fairly safe.
  2. Download monthly price data. There is a trade-off in periodicity. Daily/weekly data is noisy, and quarterly/annual data leads to issues with estimation and structural change. I think monthly is a good balance.
  3. Choose an interval that has fairly linear price action – or price action that can be made linear with log or Box-Box transformations.
  4. Forecast 1-3 years out.
  5. Find an option that capitalizes on those forecasts while fitting your risk-reward tolerance.

Example: MSFT

> r <- auto.arima(y, seasonal = FALSE)
> r
Series: y
ARIMA(1,2,2)

Coefficients:
ar1 ma1 ma2
0.5817 -1.8075 0.8448
s.e. 0.1891 0.1126 0.1038

sigma^2 estimated as 49.56: log likelihood=-209.05
AIC=426.11 AICc=426.81 BIC=434.61
> forecast(r)
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
May 2021 264.3469 255.3247 273.3692 250.5486 278.1453
Jun 2021 268.8622 257.4521 280.2723 251.4120 286.3125
Jul 2021 274.3771 261.4216 287.3326 254.5634 294.1908
Aug 2021 280.4733 266.2047 294.7420 258.6513 302.2954
Sep 2021 286.9078 271.3407 302.4749 263.0999 310.7156
Oct 2021 293.5389 276.5900 310.4879 267.6178 319.4601
Nov 2021 300.2845 281.8231 318.7459 272.0503 328.5187
Dec 2021 307.0966 286.9715 327.2217 276.3180 337.8753
Jan 2022 313.9475 292.0015 335.8935 280.3840 347.5110
Feb 2022 320.8209 296.8991 344.7426 284.2357 357.4060
Mar 2022 327.7073 301.6615 353.7532 287.8736 367.5410
Apr 2022 334.6014 306.2913 362.9115 291.3049 377.8979
May 2022 341.4999 310.7940 372.2058 294.5393 388.4605
Jun 2022 348.4010 315.1759 381.6261 297.5876 399.2145
Jul 2022 355.3036 319.4434 391.1639 300.4601 410.1472
Aug 2022 362.2071 323.6025 400.8117 303.1664 421.2478
Sep 2022 369.1111 327.6588 410.5634 305.7153 432.5069
Oct 2022 376.0154 331.6173 420.4134 308.1144 443.9163
Nov 2022 382.9198 335.4825 430.3571 310.3707 455.4689
Dec 2022 389.8243 339.2584 440.3903 312.4903 467.1584
Jan 2023 396.7289 342.9483 450.5096 314.4786 478.9793

Let’s be conservative and check out options for Jan 2023, assuming it hits the lower 80% interval, $343 (no, I am not assuming this is the lower 10th percentile in some posterior distribution, you Bayesian bastards).

I am liking the 330/335 Bull Call Spread option below. Assuming MSFT is at least $330 in Jan 2023 (which is probably conservative based on the model), 510% is a good return.

In the name of risk aversion, I am also happy with the 285/290 call spread. MSFT must be at least $286 in Jan 2023 (only about 10% up from today), and we get a 252% return. Beats the hell out of any savings account I know of.

Be sure to diversify.

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