Quote from: d5000 on September 22, 2024, 09:33:49 PM

First I'd like to ask @virginorange: do you still think the original formula holds? I repeat it here:

Quote

e^[ 5,8323 * ln(Date - 03.Jan.2009) - 39,296 ]

The formula is estimated to minimize the square difference between the daily bitcoin prices and the trend (ls-estimation). However since we work in ln-time earlier data points carry more weight.

As a result the formula is pretty sticky and does not change a lot with recent data points. One day this will be the downfall of the trend model since the model will show a change in trend very late.

To check if the trend has already broken down I estimated the slope of different sub sections of our curve.

We don't see a different slope before and after 2017. Both intervals have a slope of 5.7.
However dividing our curve into segments bottom to bottom or top to top gave us much less stable results.

Quote from: d5000 on September 22, 2024, 09:33:49 PM

I personally consider it a tiny bit too optimistic, because I believe that the price in early 2024 may have been an "overshoot". I have experimented a bit with the formula and got that the following values would be currently quite close:

e^[ 5,82 * ln(Date - 03.Jan.2009) - 39,4 ]

Which gives me the current price of ~ € 58358.60 and is thus very close to the actual price. (Of course we don't know if we're currently above or below the trend but I think my point becomes clear ...).

You optimize the formula to our recent history. I optimized the formula over the total price history of Bitcoin. Optimizing for only a shot time span gives you unstable results depending on where we are in the bull/bear-cycle.

Our model will break down one day. Therefore I have implemented model maintenance triggers. We should question our model, when the Bitcoin price goes lower than trend*e⁻1 or when we don't reach a euphoria phase for a long time (more than 1600-1700 days after the last euphoria).

Quote from: virginorange on April 23, 2024, 11:12:58 AM

Model maintenance triggers:

My DCA management can be easily implemented in excel and does not cause much of a headache or costs a lot of time. However I'm very dependent on my model to continue to describe the Bitcoin price behavior. Therefore I have to check, if my model is still correct.

...

❶ Maintenance trigger "new top found":

in theory the trigger looks like this:

   1st trigger:
   Bitcoin price = trend +750 days
   2nd trigger:
   [Bitcoin price 10% below all time high] and [S&P 90d volatility > S&P 500d volatility] or
   [Bitcoin price 50% below all time high]

I will then check, if the slope is still slightly below 6.

A significantly lower slope would require a new hedonistic optimization to get a new bitcoin allocation (e.g. 50% instead of 66%).

I will also check how far above trend the Bitcoin price went, to set a new trading trigger for the next cycle (e.g. 500 days overvaluation instead of 750 days or switiching form days overvaluation to ln overvaluation).

❷ Maintenance trigger "new top missed":

trigger:
no euphoria since 1621 or 1677 days

❸ Maintenance trigger "new bottom found":

   1st trigger:
   Bitcoin price = 40% below trend
   2nd trigger:
   [Bitcoin price 10% above 12 months low] and [S&P 90d volatility < 90% S&P 500d volatility] or
   [Bitcoin price 50% above 12 months low]

I will then check, if the slope is still slightly below 6. Also I will check the picture of undervaluation and volatility to re-calibrate our trading triggers and our maintenance triggers.

❹ Maintenance trigger "bottom broken":

   trigger:
   crushing with high volatility through the floor or
   gradually lower and lower bottoms

Currently we are around 25% blow trend, which does not seem to be unusual. Since Bitcoin volatility is low we are certainly not breaking our model for reason ❹. The new euphoria should arrive summer 2026 latest. Otherwise we would have to evaluate our model. So I can't confirm a model break down.

Quote from: d5000 on September 22, 2024, 09:33:49 PM

I'm however not good at math, so it's not completely clear for me how I'd adjust it to get lower values in the future preserving the approximate curve until now (or if this is even possible with that formula).

I used more sophisticated statistics programs during university and also one of my previous jobs, however for Bitcoin price trend estimation excel is enough. Excel offers a simple least squares regression. You only have to ln-transform the time values and the price values and excel can calculate a simple line for the trend. The results you can then transform back.