Quant Modelling [HFT] All modules
7 Module 07

Portfolio Construction & Risk Management

A great signal can still lose money if it is held badly. This module covers how quants spread capital across assets, why correlation drives diversification, and the risk metrics that decide whether a strategy is actually worth running.

Exam: Risk & Evaluation Source: Session 7 Core skill

Why portfolios exist

A portfolio is simply a collection of positions held at the same time. We build portfolios instead of betting everything on one idea for three connected reasons:

๐Ÿงฏ

Reduce concentration risk

Avoid having one asset decide your entire outcome.

๐Ÿ’ธ

Spread capital

Distribute money across many assets and ideas.

โš–๏ธ

Improve risk-adjusted returns

Earn more return per unit of risk, not just more return.

โ˜… Core idea

The goal is not to maximise return at any cost. It is to maximise return per unit of risk. A portfolio is the tool that lets us shape risk deliberately instead of accepting whatever one asset hands us.

Concentration risk

Concentration risk is what happens when too much capital sits in one asset. It is a double-edged sword: a single position makes large gains possible, but it makes equally large losses possible. If that one asset gaps down, there is nothing to cushion the blow.

โ–ฒ The trap

Concentration looks brilliant right up until it does not. The same factor that delivered an outsized gain can deliver an outsized loss. You are not being paid extra for that risk โ€” you are just exposed to it.

Diversification

Diversification means spreading risk so that no single outcome dominates the portfolio. By reducing dependence on one asset's fate, we get a result that is more stable than any of its parts.

๐Ÿ“‰

Lower volatility

Independent ups and downs partially cancel out.

๐ŸงŠ

Reduced concentration risk

No single asset can sink the whole book.

ใ€ฐ๏ธ

Smoother returns

The equity curve gets steadier, less jagged.

๐Ÿ—๏ธ

Better stability

Performance is more robust to surprises.

โ—† Portfolio A vs Portfolio B

Portfolio A โ€” 100% Apple. Every move in Apple is the whole story. One earnings miss and the account swings hard.

Portfolio B โ€” diversified basket. Apple is one name among many. A bad day for one stock is softened by the others, so the combined return is smoother and the downside is contained.

Correlation intuition

Here is the catch that trips up most beginners: diversification depends on correlation, not on the number of assets. Correlation measures whether assets move together.

๐Ÿ”—

Correlation = 1

Perfect co-movement. The assets rise and fall in lockstep, so holding both is the same as holding one โ€” no diversification benefit.

๐ŸŽฒ

Low correlation

Assets move differently. When one dips, another may hold or rise, so their swings partly cancel โ€” better diversification.

โ˜… Remember

More assets โ‰  more diversification. Twenty tech stocks that all move together are barely more diversified than one. What you want is assets whose returns are weakly related, so their risks offset.

flowchart TB
  subgraph HIGH[High correlation โ‰ˆ 1]
    direction LR
    X1([Asset X]) --- Y1([Asset Y])
  end
  subgraph LOW[Low correlation]
    direction LR
    X2([Asset X]) --- Y2([Asset Y])
  end
  HIGH --> R1[Move together โ†’ risk adds up โ†’ NO benefit]
  LOW --> R2[Move differently โ†’ risk offsets โ†’ diversified]
  classDef s fill:#eef2ff,stroke:#4f46e5,stroke-width:1px,color:#3730a3;
  classDef d fill:#ecfdf5,stroke:#0d9488,color:#0d9488;
  class X1,Y1,X2,Y2,R1 s
  class R2 d
      
Diversification is a function of correlation: only weakly related assets actually reduce portfolio risk.

Portfolio allocation

Allocation is the decision of how much capital goes into each asset โ€” the set of weights. These weights determine how the portfolio behaves. Two common starting points:

pie showData
  title Equal weight (5 assets)
  "Asset A" : 20
  "Asset B" : 20
  "Asset C" : 20
  "Asset D" : 20
  "Asset E" : 20
        
Equal weight: every asset gets the same 20%. Simple and neutral.
pie showData
  title Weighted (conviction-based)
  "Asset A" : 40
  "Asset B" : 25
  "Asset C" : 15
  "Asset D" : 10
  "Asset E" : 10
        
Weighted: more capital to higher-conviction names (40/25/15/10/10).

Whichever scheme you choose, weights must sum to 100% of the capital you are deploying.

โ–ฆ Quick check

If three positions are weighted 50% + 30% + 20%, they sum to 100% โ€” a fully invested portfolio with no leftover cash and no leverage.

The construction pipeline

Building a portfolio is a repeatable pipeline that turns raw assets into a measurable result:

flowchart LR
  A([Assets]) --> B([Returns])
  B --> C([Weights])
  C --> D([Portfolio])
  D --> E([Performance])
  classDef s fill:#eef2ff,stroke:#4f46e5,stroke-width:1px,color:#3730a3;
  classDef d fill:#ecfdf5,stroke:#0d9488,color:#0d9488;
  class A,B,C,D s
  class E d
      
Assets โ†’ Returns โ†’ Weights โ†’ Portfolio โ†’ Performance. Each stage feeds the next.

What is risk?

โ–ฃ Definition โ€” Risk

Risk is uncertainty about future outcomes. We cannot know tomorrow's return in advance, so risk measures how widely the actual result might differ from what we expect.

Risk shows up in several forms, and a good risk process watches all of them:

๐ŸŒ

Market risk

The whole market moves against you (a broad selloff).

๐Ÿญ

Sector risk

One industry (e.g. tech) takes a hit you are over-exposed to.

๐Ÿ’ง

Liquidity risk

You cannot exit a position without moving the price.

๐Ÿง 

Strategy risk

Your specific edge stops working as the market adapts.

Risk metrics

To compare strategies fairly we need numbers, not feelings. These four metrics are the backbone of strategy evaluation.

Volatility

Volatility measures how much returns vary around their average โ€” it is the standard deviation of returns. Higher volatility means higher uncertainty: a stable portfolio drifts gently, while an unstable one swings wildly even if both end at the same place.

โ–ฆ Reading it

Two strategies can post the same average return, yet the one with lower volatility is more dependable. Volatility is the raw "risk" number that feeds into nearly every other metric below.

Sharpe ratio

The Sharpe ratio answers the key question: how much return am I getting per unit of risk? Higher is better โ€” it means more reward for the same wobble.

Sharpe ratio $$ S = \dfrac{R_p - R_f}{\sigma_p} $$

where $R_p$ is the portfolio return, $R_f$ the risk-free rate, and $\sigma_p$ the portfolio volatility. (When the risk-free rate is ignored for a quick comparison, it is just return divided by volatility.)

Worked example Higher return is not always better
  1. Strategy A returns 10% with volatility 5%: $S_A = \dfrac{10\%}{5\%}$.
  2. Strategy B returns 15% with volatility 15%: $S_B = \dfrac{15\%}{15\%}$.
  3. Compute: $S_A = 2.0$ and $S_B = 1.0$.
Strategy A wins. Despite a lower headline return, A earns twice the return per unit of risk โ€” that is the whole point of risk-adjusted thinking.
Self-check: A strategy returns 12% with volatility 6%. What is its Sharpe ratio?
Ignoring the risk-free rate, $S = \dfrac{12\%}{6\%} = \mathbf{2.0}$. A Sharpe of 2 is strong โ€” the strategy delivers two units of return for every unit of risk taken.

Maximum drawdown

Maximum drawdown (MDD) is the largest peak-to-trough decline the portfolio suffers before recovering. It answers the gut-level question: "what is the worst pain I would have lived through?"

Maximum drawdown $$ \text{MDD} = \dfrac{\text{Trough} - \text{Peak}}{\text{Peak}} $$

The cycle is always Peak โ†’ Decline โ†’ Recovery. A strategy can have a fine average return yet a brutal drawdown that would have forced you (or your investors) to quit at the bottom.

Win rate

Win rate is the fraction of trades that make money:

Win rate $$ \text{Win rate} = \dfrac{\#\text{ winning trades}}{\#\text{ total trades}} $$
โ–ฒ Why a high win rate can mislead

A strategy can win 90% of the time and still lose money if the rare losses are huge. Imagine 9 wins of \$10 and 1 loss of \$200: that is a 90% win rate and a net loss of \$110. Profitability depends on win size, not just win frequency.

MetricWhat it measuresBetter when
VolatilityVariability of returns (std dev)Lower
Sharpe ratioReturn per unit of riskHigher
Max drawdownWorst peak-to-trough lossSmaller (closer to 0)
Win rateShare of profitable tradesHigher โ€” but only with healthy win/loss size

Position sizing & risk control

Sizing answers a deceptively simple question: how much should we buy? The amount you actually put at risk is set by your position size and where your stop sits:

Dollars at risk $$ \text{Risk} = \text{Position size} \times \text{Stop-loss }\% $$

This is the lever that controls how much a single bad trade can cost you, independent of the signal itself.

Worked example Capital allocation
  1. Total capital is โ‚น100,000.
  2. You allocate 10% to this position: $0.10 \times โ‚น100{,}000$.
  3. Position size $= โ‚น10{,}000$.
A 10% allocation puts โ‚น10,000 into the trade. If your stop-loss is 5%, the dollars at risk are $โ‚น10{,}000 \times 5\% = โ‚น500$.
โ˜… Why sizing matters

Good signal + bad sizing = bad outcome. The world's best edge will still blow up an account if every trade is oversized. Sizing converts a probabilistic edge into a survivable strategy.

Exposure control

The aim is to avoid hidden concentration โ€” situations where positions that look independent are secretly the same bet. Holding ten technology names feels diversified, but it is really one large bet on the tech sector.

flowchart TB
  P([Portfolio capital]) --> S1([Technology])
  P --> S2([Healthcare])
  P --> S3([Financials])
  P --> S4([Energy])
  S1 -.->|cap per sector| L([Position & sector limits])
  S2 -.-> L
  S3 -.-> L
  S4 -.-> L
  classDef s fill:#eef2ff,stroke:#4f46e5,stroke-width:1px,color:#3730a3;
  classDef d fill:#ecfdf5,stroke:#0d9488,color:#0d9488;
  class P,S1,S2,S3,S4 s
  class L d
      
Spreading capital across sectors and capping each one keeps a single industry from dominating the book.

The risk-control toolkit

๐Ÿ“

Position limits

A maximum size per position and per sector, so no single bet grows too large.

๐Ÿ›‘

Stop losses

Pre-set exits that protect capital and cap the downside on any one trade.

๐Ÿ“‰

Drawdown limits

If the portfolio falls past a threshold, cut exposure to preserve capital.

๐Ÿ‘๏ธ

Exposure monitoring

Continuously track where risk actually sits, not where you assume it does.

Combining strategies

Just as we diversify across assets, we can diversify across ideas. Running several uncorrelated strategies together reduces dependence on any one edge โ€” this is diversification applied one level up.

๐Ÿš€

Momentum

Ride assets that are trending strongly.

โ†ฉ๏ธ

Mean reversion

Fade overreactions back toward normal.

โšญ

Pairs trading

Trade the spread between two related assets.

โœฆ Portfolio of strategies

When momentum struggles, mean reversion may shine. Combining them diversifies your ideas and reduces strategy risk โ€” the same logic as diversifying assets, applied to the edges themselves.

โ–ฆ Industry perspective

Professional desks formalise all of this into a risk management function: continuous exposure monitoring and stress testing (asking "what happens in a crash?") sit alongside every strategy that goes live.

Self-check: You hold 15 stocks but they are all semiconductor names. Are you well diversified?
No. Because they are highly correlated (they move together with the chip cycle), this is effectively one concentrated sector bet. Remember: more assets โ‰  more diversification โ€” low correlation is what matters.
Self-check: Strategy A returns 8% with 4% volatility; Strategy B returns 20% with 20% volatility. Which has the better Sharpe?
$S_A = 8/4 = 2.0$ versus $S_B = 20/20 = 1.0$. Strategy A is twice as efficient on a risk-adjusted basis, even though B has the bigger raw return.

Key takeaways

โ˜… Remember
  • Diversification matters โ€” spreading capital lowers volatility and concentration risk.
  • Correlation matters โ€” only weakly correlated assets actually diversify; more assets alone do not.
  • Risk matters โ€” measure it with volatility, Sharpe, max drawdown and win rate, not just return.
  • Position sizing matters โ€” a good signal with bad sizing still loses; risk = size ร— stop-loss %.
  • Risk management matters โ€” limits, stops, drawdown caps and exposure monitoring keep you in the game.