Portfolio basics for a small account

ExpertDuration 35 minTools Python 3, numpy, pandas

Why this lesson

One working strategy is fragile; a couple of genuinely different ones are sturdier — but only if you combine them without fooling yourself. The two ways small accounts get portfolio construction wrong are equal and opposite: stacking strategies that are secretly the same bet (so you think you’re diversified and you’re not), and pushing size past the point where your own footprint kills the edge. This lesson gives you the three tools that matter at small scale — correlation caps, honest risk combination, and a capacity estimate — and skips the institutional machinery you don’t need yet.

Watch

Segment: 3:56–16:25 — vol-targeted sizing through the silver crashwatch full video

Watch for: A real-money worked example: volatility-targeted sizing kept Carver's account-level loss near 3% through a violent silver crash while non-vol-adjusted CTAs lost far more. Sizing by volatility is the portfolio's first line of defence.

Segment: 41:24–46:00 — the degenerate optimizer, honestlywatch full video

Watch for: A from-scratch mean-variance optimizer returning a degenerate 100%-into-one-strategy 'solution' — and Wong's honesty that this is realistic optimizer behaviour, not a mistake, which is why small accounts should prefer constraints over raw optimization.

The explainer

Combine risk, don’t add it. Two strategies each risking 2% of the account do not combine to 4% of portfolio risk — unless they are perfectly correlated. Combined volatility depends on how the two move together: if they are uncorrelated, the portfolio’s risk is meaningfully less than the sum, because their bad days don’t always coincide; if they are strongly correlated, you get almost no diversification and the risk really is close to additive. The arithmetic is the two-asset volatility formula (below in the exercise), and its lesson is blunt: the diversification benefit lives entirely in the correlation. Assume two strategies are independent when they are actually 0.8 correlated and you have badly understated your real risk. Carver’s practical warning is that correlation is far less predictable than volatility — roughly R-squared 0.2 versus 0.35 — so estimate it on a slower rolling window (say six months) than volatility (about one month), and never trust a single point estimate.

Correlation clustering caps. The subtle danger is not two openly-similar strategies — it is several strategies that look different (different names, different entry rules) but are the same underlying bet. Tim Rea, running 100+ systems across 25 markets, is candid that “there’s many ways to define a breakout,” and that whole clusters of his systems go correlated in the same market phase. A correlation cluster is a group of positions or strategies that move together; a clustering cap limits how much total risk any one cluster may hold, so that ten variations on one idea can’t quietly assemble into a single concentrated position that one event ends. At small scale you don’t need a formal clustering algorithm — you need the discipline of grouping your strategies by what they actually bet on and capping each group.

Combine without double-counting. Derek Wong’s from-scratch treatment is the honest one for our purposes. He reframes momentum and mean-reversion as positive-skew versus negative-skew return distributions — classify by evidence, not by the story you tell about the entry — then treats each strategy as a “security” so their returns can be combined directly. The instructive moment is the failure: a naive Markowitz mean-variance optimizer hands back a degenerate solution, ~100% into a single strategy, and he refuses to call it a bug. It is what unconstrained optimizers do — they pile into whatever backtested best, which is exactly the overfitting you’ve spent Level 3 avoiding, now wearing a portfolio hat. The small-account response is not a fancier optimizer; it is constraints (position floors, equal-ish weights, capped cluster risk) and robustness over raw optimization. This is where forecast combination lives as an awareness term: the institutional approach (Carver’s) blends multiple rules’ forecasts into one position with fixed, sensible weights rather than optimized ones — you should know the idea exists, and know that for a small account the sensible default is simple, roughly equal weighting inside each uncorrelated cluster.

The capacity ceiling. Finally, size has a hard limit that has nothing to do with whether the edge is real. As your order size grows, your own trading moves the price against you — market impact — and slippage rises with size along a slippage curve. Past some point, the extra size’s slippage cost exceeds the edge per trade, and the strategy stops making money at that size even though it works fine smaller. That point is the capacity ceiling. For a small retail account this is usually not your binding constraint — you are too small to move a major FX pair — but it becomes real fast on thin instruments, at the session-open spread spikes where breakout systems fire, or if you scale aggressively. The simple model: estimate slippage as a rising function of size, multiply by trade frequency, and find the size where cumulative slippage cost crosses your gross edge. Above that line, adding capital lowers your return. Knowing roughly where your ceiling sits stops you from mistaking “I got too big” for “my edge died” (the differential diagnosis from Lesson 3.5).

Three tools, one theme: at portfolio level, the account is killed by hidden sameness (correlation you ignored) and hidden size (capacity you exceeded). Measure both honestly and a small book of a few real, uncorrelated edges will outlast a big pile of the same bet.

Do it

Combine two strategies’ risk honestly, then find a rough capacity ceiling from a slippage curve.

import numpy as np

# --- Part 1: combine two strategies' risk WITHOUT double-counting ---
vol_a = 0.02      # strategy A: 2% daily volatility of returns
vol_b = 0.02      # strategy B: 2% daily volatility
w_a, w_b = 0.5, 0.5

def portfolio_vol(va, vb, wa, wb, corr):
    return np.sqrt((wa*va)**2 + (wb*vb)**2 + 2*wa*wb*va*vb*corr)

for corr in (0.0, 0.5, 0.9, 1.0):
    pv = portfolio_vol(vol_a, vol_b, w_a, w_b, corr)
    naive_sum = w_a*vol_a + w_b*vol_b       # the WRONG way (just adding)
    print(f"corr={corr:>4}:  true portfolio vol={pv:.4f}   naive additive={naive_sum:.4f}   "
          f"diversification saved={(naive_sum-pv)/naive_sum:.0%}")
# At corr=0 you keep ~29% risk reduction; at corr=1.0 diversification vanishes.

# --- Part 2: capacity ceiling from a simple slippage curve ---
gross_edge_per_trade = 3.0            # $ per micro-lot of gross edge before slippage
def slippage_cost(size_lots):
    # market impact: slippage rises with size (toy super-linear curve, $ per trade)
    return 0.8 * size_lots + 0.05 * size_lots**2

sizes = np.arange(1, 60)
net_edge = gross_edge_per_trade * sizes - slippage_cost(sizes) * 1  # net $ per trade at each size
best = sizes[np.argmax(net_edge)]
ceiling = sizes[np.argmax(net_edge < 0)] if np.any(net_edge < 0) else sizes[-1]
print(f"\nnet edge peaks at size ~{best} lots; capacity ceiling (net edge -> 0) near {ceiling} lots")
print("above the ceiling, adding capital LOWERS total return — that's the wall, not a dead edge")

Read Part 1’s output as the whole point of the lesson: the money you save by diversifying is the correlation term, and it disappears as correlation goes to 1. Read Part 2 as the reason you cannot infinitely scale a working edge.

Terms introduced

Terms introduced in this lesson

• Correlation clustering
• Forecast combination
• Capacity / market impact

Each term links to the glossary, where it is defined by the way you just used it.

Check

Check yourself

1. Why can't you just add two strategies' individual risks together to get portfolio risk?

   Because brokers cap total risk automaticallyBecause addition is only valid for three or more strategiesBecause risk is measured in different units per strategyBecause their correlation matters — combined volatility depends on how they move together, and is usually LESS than the sum

2. Correlation clustering caps exist to prevent…

   Holding positions overnightTrading more than one instrument at a timeSeveral 'different' strategies that are secretly the same bet from stacking into one concentrated, undiversified positionUsing volatility targeting

3. In Derek Wong's worked example, a naive mean-variance optimizer put ~100% into one strategy. He treated this as…

   A reason to add more leverageA bug in the codeProof that optimization never worksRealistic optimizer behaviour that shows why you need constraints (position floors) or more robust methods, not raw Markowitz

4. A capacity ceiling from a slippage curve is the point where…

   The broker refuses more ordersYou run out of marginYour position size grows large enough that your own market impact / slippage eats the edge, so the strategy stops working at THAT sizeCorrelation reaches 1.0

Check answers

You can move on when you can… combine two strategies’ risk with the correlation term instead of adding them, cap correlated clusters so secretly-identical bets can’t concentrate, explain why a naive optimizer’s degenerate solution argues for constraints over raw Markowitz on a small account, and estimate a capacity ceiling from a slippage curve.

Mark this lesson complete

Go deeper

• Robert Carver, Systematic Trading (Parts 3–4) and Leveraged Trading — volatility targeting, forecast combination, and portfolio construction as one coherent framework.
• Carver, position sizing when markets break — the listener Q&A on estimating realized correlation from strategy P&L is the practical how-to for Part 1.
• Derek Wong, combining quantitative strategies — the full code-backed walkthrough, degenerate optimizer and all.
• Carver, Following the Trend — diversified portfolio economics when you eventually run many instruments.