I can do that, but the code is pretty complicated and computationally intensive. If you want a specific utility function calculated, you can always ask me. I think this is a very interesting and under-studied research subject, but it's hard to come up with utility functions that actually reflect actual investor goals. My best guess is that utility is approximately linear to the expected retirement years, that approach results in quite aggressive asset allocations.redstar wrote: ↑Mon Jul 27, 2020 10:01 pmThis thread was very informative and interesting, thank you. I think my utility function is not well defined, and I probably should spend some time thinking about what an appropriate one is. I really enjoyed the AA charts you generated. Would you be willing to share any of that code to mess with other possible scenarios?Uncorrelated wrote: ↑Sun Jul 26, 2020 12:30 amI have attempted to calculate optimal asset allocations for different utility functions. I tried optimizing for the fastest (on average) way to reach a certain number, or maximize the number of retirement years. You can view it in this topic. I don't know how well this utility function matches your goals, but the point is that a different utility function results in very different asset allocations. These scenario's were calculated without leverage.
I am confident that the desire to retire earlier results in an asset allocation that is more aggressive than lifestyle investing with a fixed retirement date suggests, but I'm not sure how much more aggressive.
I think I know that paper you're talking about. But it's not particularly relevant to this user, as it didn't investigate early retirement motives.Steve Reading wrote: ↑Mon Jul 27, 2020 10:27 pmUncorrelated will answer that better, he showed me once a paper that used a specific strategy to target a specific nest egg. It still uses leverage and everything but ramps down differently. That might be a better fit for you. I seem to recall it was complex, not as simple as just an equation you plug into at any time, regardless of time horizon or current assets.
I only brought up a nest egg target as a rough estimate as to when you might be done with Phase 1 and then could sit down and actually factor in SS, future wages, etc. But the above strategy might ramp you down before so if that's what you prefer and ultimately want to use, I would use that strategy since the beginning.
Hopefully he'll link the paper, I never saved it :/
As far as I'm aware of, the topic I linked is the only place on the internet that discusses optimal portfolio models in the context of early retirement goals...
I use 16% for volatility and 5-6% for future ERP. I don't think there are good reasons to use different estimates for different geographic regions. If you want an active sector or geographic region tilt, you can use mean variance optimization to determine the optimal ratio. This is too difficult to do by hand.redstar wrote: ↑Fri Jul 31, 2020 10:36 amWould anyone be able to check my math on computing the Samuelson Share? I'm looking for a 55% US / 45% Intl. weight of equity (close to market weight). My initial guess at an RRA is 3.
For risk/reward inputs into calculation, the authors suggest CAPE and VIX, but this tells me to have a 0% stock allocation? So I looked at Vanguard's August 2020 estimates for equity returns and volatility instead. Are these reasonable to use or are there better numbers here?
US Stock Return: 4% - 6% (I'll use 5%)
US Stock Volatility: 16.4%
Intl. Stock Return: 7% - 9% (I'll use 8%)
Intl. Stock Volatility: 18.3%
So now I need the equity risk premium for each asset class. What should I be comparing to? The t-bill rate is 0.10%, I can earn 1% in the savings account I have, or should I be comparing to bonds in general? (I'll use 1% below for now)
Leverage Amount: 150%
Borrowing Cost above 100% at IB: 1.59%
Effective US ERP after borrowing = (5%+(5%-1.59%)*(50%))/150% - 1% = 3.47%
Effective Intl. ERP after borrowing = (8%+(8%-1.59%)*(50%))/150% - 1% = 6.47%
US Samuelson Share = 3.47% / ((16.4% ^ 2)*3) * 55% US equity ratio = 23.65%
Intl. Samuelson Share = 6.47% / ((18.3% ^ 2)*3) * 45% Intl equity ratio = 28.98%
Total Samuelson Share (all equity) = 52.63%
I think I'm failing to account for expense ratios and stuff here, but overall does this look right for factoring in multiple equity types, borrowing cost, and some risk-free rate?
IIRC Ayres and Nalebuff use the 10-year t-bill rate for the risk free rate as some sort of compromise. I usually use 1 or 3 month t-bills. I have not read the book so I don't know what the exact definition of samuelson share is, your math looks reasonable.