Experiment 003 · Asset allocation
Stocks, Bonds, and a Contextual Bandit
Follow one investor from age 22 through every quarter the shared data allows. Can a learning system build a better long-term path by choosing between U.S. stocks and bonds, or by continuously mixing the two?
intuition before equations
Two roads for the first $1,000
Stocks are usually the growth engine, while high-quality bonds are often the steadier counterweight. A fixed portfolio includes both. Here we ask whether an algorithm can use recent market information to choose the better investment for the next three months.
Broad exposure to large U.S. companies through the S&P 500.
Broad exposure to the U.S. investment-grade bond market.
Long-horizon backtest
What became of a lifetime of deposits?
Every path starts with $1,000 at age 22. The quarterly deposit also starts at $1,000 and then rises with inflation. This assumes the investor's wages, and therefore the amount available to invest, grow with the general price level. SPY and AGG stay put, 60/40 rebalances, the all-in bandit chooses one asset, and the contextual mix chooses an exact percentage of each.
Loading the frozen result…
Quarter by quarter
How did it split the money?
Each vertical slice is one quarter. Blue is the percentage in SPY and gold is the percentage in AGG. Hover or tap to see the exact mix and the all-in model’s choice.
how the machine thinks
Context changes the bet
A normal two-armed bandit remembers only which arm paid off. A contextual bandit also looks at the situation before choosing. We run it two ways: a classical all-in choice, plus a contextual semi-bandit that holds both assets and turns their scores into a continuously changing allocation.
- 01
Calculate the current signals
At the end of each quarter, calculate six signals using only the adjusted prices available on that date. No information from the next quarter is used.
- 02
Score both choices
SPY and AGG each have their own linear reward model. The score combines expected return with an uncertainty bonus.
- 03
Explore when unsure
The uncertainty bonus favors an asset in contexts the model has not seen often. The first two quarters also deliberately try one asset each.
- 04
Choose or blend
The all-in version takes the higher score. The mix uses both scores to select exact weights between 10% and 90%, then both held arms provide feedback.
- 05
Add the next deposit
After the quarter’s growth is measured, the investor contributes to every strategy before the next allocation executes. The deposit starts at $1,000 per quarter and rises with CPI over time.
- 06
Learn, then wait a day
Only completed-quarter returns update the models. Each new allocation executes one full trading session after its context is observed.
Six signals only
The information used each quarter
These six features summarize recent trend, risk, market stress, and diversification. We keep the list short because the quarterly dataset is not large.
for those who want the symbols
The Math Zone
The intuition is “predicted reward plus curiosity.” Let a be an asset arm, q a quarter, and xq the six-signal context plus an intercept.
What the model sees
Relative momentum at two horizons, a volatility gap, stock drawdown, stock-bond correlation, and relative trend distance.
Learned coefficients
Each asset maintains its own ridge-regression estimate of how context has related to its observed quarterly rewards.
LinUCB score
The first term exploits the larger predicted reward. The square-root term explores uncertainty. Here α = 0.075, fixed in advance.
Continuous stock weight
The logistic function turns the score gap into an exact allocation. A 10% floor keeps both assets present; T = 0.08 controls how strongly the mix reacts.
Quarterly reward
The selected or held ETFs’ adjusted close-to-close returns are observed only after the next quarter finishes.
The observed arms learn
The all-in bandit updates only its chosen arm. The mix holds both, so its semi-bandit model observes and updates both arm rewards.
The lifetime path
The deposit Cq starts at $1,000 and grows with CPI Iq, reflecting wages and investable income rising with the general price level. Growth happens first, then the deposit arrives. Reallocation costs 0.10% times turnover.
What this analysis can tell us
This is one historical path with two modern ETFs, and it should not be treated as a retirement recommendation. The investor reaches age 44 because that is where the available snapshot ends. We do not project any future results. AGG limits the shared history because it launched in September 2003. ETF adjusted prices provide a useful approximation of total returns, but they are not a point-in-time institutional index dataset. The test also ignores taxes and fund tracking differences. Finally, market relationships can change, so the result depends on the particular period tested.
Asset descriptions come from State Street’s SPY materials ↗ and iShares’ AGG materials ↗. The diversification framing follows the SEC’s Investor.gov guide ↗. Momentum horizons are informed by the published time-series momentum research ↗, while the changing diversification role of correlation is discussed by the Federal Reserve ↗. The learning rule is the disjoint linear model from the original LinUCB paper ↗. Quarterly contributions grow using the monthly seasonally adjusted CPI-U from the U.S. Bureau of Labor Statistics via FRED ↗. This experiment is for education and is not investment advice.