The True Value¶

Learning objectives

After reading this chapter you will be able to:

Explain price discovery with the simulation as the example: a price looking for a value nobody on the exchange can see
Describe how the true values move, in words and in numbers
Say who pulls prices toward the values and who pushes them away
Measure how far the market is from its values, and change that
Read and change every setting of the market model

Prerequisites: A Market That Runs Itself.

Price and value¶

A share's price is the last price two traders agreed on. Its value is what the share is really worth — on a real exchange, what the company's future earnings are worth today. Nobody knows the value exactly. Some traders have a good estimate of it and trade on the difference: they buy when the price is below their estimate, sell when it is above. Their orders pull the price toward the value. Everyone else — traders who follow momentum, who need cash, who simply guess — pushes the price around. The price you see is the outcome of that tug of war, and the process by which it finds the value is called price discovery.

On a real exchange nobody can check how well price discovery works, because the value is never revealed. In the simulation it exists: pm-market-sim keeps a true value for every share and moves it the way company values move. You, as the instructor, can see it; the students cannot; the AI traders that trade on value see it through errors of their own. So you can watch the gap between price and value open and close — and show it to a class after the fact.

How the values move¶

Every second of continuous trading, each share's value takes a small random step. The step is a mix of four things:

Ingredient	What it is	In the `s300-sim` example
The market	One random move shared by every share	each share follows it with weight `beta_market`, 0.35–0.60 by sector
The sector	One random move per industry sector	weight `beta_sector`, 0.35–0.60
The share itself	Its own random move	the rest of its volatility
Jumps	Now and then a sudden move: an unannounced event	0.05 a day per share, size ±4 % (σ)

Plus a slow drift (5 % a year), news (next chapter) and an overnight move when the market reopens. The size of the random steps is the share's volatility: 30 % a year by default, 18 % for the calmest sectors (consumer staples, utilities), 35 % for technology and energy, and spread a little around its sector for each share.

What that means in a day:

	Typical size (one standard deviation)
A whole trading day, volatility 30 %	1.9 %, about 2.1 % with the jumps
One hour of continuous trading	0.7 %
One minute	0.1 %
The overnight move (20 % of a day's variance)	0.85 %
A jump (once in 20 trading days per share)	4 %

So on a typical day a share's value ends within about ±2 % of where it started, one day in twenty more than ±4 %; across the 300 shares, about 15 jump somewhere every day.

Shares move together. Two shares in the same sector move together with a correlation of about beta_market² + beta_sector² — 0.56 for two technology shares — and two shares in different sectors with about the product of their market betas, around 0.3. A bad day for the market is a bad day for most shares; a bad day for energy is a bad day for all 16 energy shares.

The day has a rhythm. Real markets are busiest after the open and before the close; so is the model. The values move about twice as fast (in variance) right after the open and before the close as at midday, averaging one day's worth over the day.

Only during trading. The values move only while the exchange trades continuously — not in the auctions, not at night. The night's move arrives in one step when the market reopens, so the opening auction has a new value to find.

Where the values start

On the first day each share's value starts at the engine's previous close, or, on a brand-new exchange, at the share's last price in the configuration — so price and value start equal. From then on pm-market-sim saves the values every 10 seconds (market_sim_state.json) and continues from them after any restart.

Who pulls, who pushes¶

Pulls the price toward the value	Pushes it away
`MM01`, the market maker: every second it moves its own price 30 % of the remaining way to the value (`--anchor-sim 0.3`) and re-quotes around it	`noise-retail`, `market-taker`, `iceberg-seller`: orders in random directions
22 `value-investor`s: buy when the price is more than 0.4 % below their view of the value, sell when above	`trend-follower`s and `scalper`s: buy what rose, sell what fell — they amplify moves
8 `institutional`s: the same with a 0.6 % threshold, in big orders worked over three minutes	`contrarian`s and `auction-player`s: fade moves; they pull toward the recent price, not the value
	Every value trader's own error: each sees the value through a bias of its own (about ±1 %)

The value traders do not see the value exactly. Each one has, per share, a persistent error drawn at random (standard deviation 1 % for value investors, 0.8 % for institutions) and redrawn now and then. That is why two value traders disagree about a price, and trade with each other — and why the market as a whole has a better estimate of the value than any single trader.

How close does the market get?¶

The yardstick is the gap ln(price / value) — for small gaps the same as the percentage difference — across all 300 shares, summarised as its root mean square (RMS). Measured on the s300-sim set-up at real speed on a 2-vCPU machine, minute by minute from the fifth to the sixteenth minute of continuous trading:

Measure	Value
RMS gap, all shares	about 0.3 % (0.21–0.43 % from one minute to the next)
Median absolute gap	about 0.04 %
Shares more than 2 % away	2 of the 300 on average, never more than 5

In other words half the prices sit within a few hundredths of a percent of their value, and a handful of shares — usually ones that just jumped, or a thinly traded one — are a percent or two away; those few make up most of the RMS. The gap is what keeps the value traders busy: if it were zero, they would have nothing to trade.

To see the gap yourself:

# From the host
docker exec edumatcher-sim pm-market-sim --status --id OPS01

# From the container
pm-market-sim --status --id OPS01

pm-market-sim: RUNNING seq=4120 symbols=300 open_rumours=0
symbol        value        mid  mid/value
LHX           62.63      65.63     +4.79%
GPN           28.51      27.61     -3.19%
...

It lists the shares furthest from their value. For every share, ask the API with the instructor's key:

curl -s -H "Authorization: Bearer key-ops01-3e34rs" http://localhost:8080/api/v1/admin/sim

The answer holds the model's state and the latest value of every share. The same data streams on the WebSocket /api/v1/admin/sim. Only ADMIN keys get an answer; a student's key is refused.

Changing the model¶

The model's settings are in market_sim.yaml, deployed next to the engine configuration (in the container /data/ref_data/market_sim.yaml; how to deploy your own copy: The Simulation Container or A Complete Set-up by Hand).

version: 1
seed: 301
step_sec: 1.0
overnight_fraction: 0.2
defaults: {vol: 0.30, drift: 0.05, jump_rate: 0.05, jump_mean: 0.0,
           jump_std: 0.04, beta_market: 0.5, beta_sector: 0.4}
sectors:
  TECH: {vol: 0.35, beta_market: 0.6, beta_sector: 0.45}
  # ... ten more
symbols:
  AAPL: {sector: TECH, vol: 0.392}
  # ... 299 more
news: { ... }   # next chapter

A share's settings are defaults, overridden by its sector's, overridden by its own line.

Setting	Range	Raise it and	Lower it and
`vol`	0–3	values wander further each day; prices lag them more; value traders trade more	a calm market where prices hug the values
`drift`	−1–1	values creep up (a bull market); at 0.05 it is invisible within a day	negative: a slow bear market
`jump_rate`	0–10	more sudden moves the news never announced; more large gaps	0: values only diffuse
`jump_std`	0–1	bigger surprises
`jump_mean`	−1–1	jumps mostly up (positive) or down (negative)
`beta_market`	0–1	shares move together; a market-wide day is visible in every book	shares independent
`beta_sector`	0–1	sectors move as blocks
`overnight_fraction`	0–5	bigger gaps at the open; busier opening auctions	0: the open continues the close
`step_sec`	0.01–60	coarser steps, fewer value messages	smoother values, more messages
`seed`	any integer ≥ 0	a different but repeatable path
`initial` (per symbol)	> 0	start a share at a chosen value: the market finds it from its old price

beta_market² + beta_sector² must not exceed 1 for any share; the rest of its variance is its own.

Recipes¶

You want	Change in `market_sim.yaml`
A calm market for a first lesson	`defaults: {vol: 0.15, jump_rate: 0.0}`, and the sectors' `vol` down too
A volatile market	every `vol` × 2, `jump_rate: 0.2`
A crash day	inject a market headline with impact −0.08 (next chapter) rather than changing the model
Mispriced shares to find	`initial` for a few shares, 10 % away from their last price: watch the value traders close the gap
Independent shares	`beta_market: 0` and `beta_sector: 0` everywhere
The same day again	the same `seed`, a fresh data directory

Restart after a change: the model reads market_sim.yaml when it starts. A share's values carry on from where they were; only how they move from now on changes (except initial, which applies only to a share without a saved value).

The market maker's anchor¶

The strongest single force toward the value is the market maker. With --anchor-sim 0.3 it moves its own price 30 % of the way to the value every second, so that price reaches a new value within a few seconds; its quotes follow as soon as the price has moved more than 15 ticks (--drift-ticks). The value traders then trade against prices that are already about right.

Without it, the value traders do all the pulling. That is a more interesting market to watch — prices wander further, rumours move them — but with one caveat: a market maker that is not anchored, and simply re-quotes around its own last mid, is worse than none. It refills the same prices whatever happens, and informed traders cannot move it. In a test the gap grew from under 1 % to 2–4 % within minutes. Either anchor the market maker or stop it; Tuning the Traders shows how.