6. Portfolio Construction

A trader thinks in trades. A portfolio manager thinks in allocations across strategies and assets. This chapter is about getting from “I have 5 ideas” to “I have a coherent, risk-balanced book.”

Why portfolio construction matters

Two strategies, each with 15% CAGR / 20% drawdown, run together with low correlation can yield ~15% CAGR / 12% drawdown. That’s a better Sharpe without sacrificing return. Free lunch via diversification.

The covariance / correlation matrix

For N strategies (or stocks), you need:

• Mean returns $\mu_i$.
• Volatilities $\sigma_i$.
• Pairwise correlations $\rho_{ij}$.

Portfolio variance: $\sigma_p^2 = \sum_i w_i^2 \sigma_i^2 + 2\sum_{i<j} w_i w_j \sigma_i \sigma_j \rho_{ij}$

Diversification works only when $\rho < 1$. The lower (or more negative), the better.

Mean-variance optimization (Markowitz)

The classical method: for a given target return, find weights that minimize variance.

Output: an efficient frontier of optimal portfolios.

Why pure Markowitz often fails in practice

• Estimates of $\mu$ are notoriously noisy → optimizer puts huge weights on the highest-mean asset.
• Correlation matrices are unstable, especially in crises.
• Result: very concentrated, high-turnover portfolios that underperform live.

Fix: Use shrinkage estimators (Ledoit-Wolf), Black-Litterman with priors, or simpler heuristics below.

Risk parity

Rather than equal capital weights, equal risk contributions.

$w_i \cdot \sigma_i \approx w_j \cdot \sigma_j \quad \forall i, j$

A high-vol asset gets a smaller weight; a low-vol asset gets a larger one. Each contributes the same to portfolio risk.

Example

• Strategy A: $\sigma = 30\%$
• Strategy B: $\sigma = 10\%$

Equal capital (50/50) → A dominates the risk. Risk parity → B gets 75% capital, A gets 25%, both contribute equal vol.

This is what Bridgewater’s “All Weather” portfolio is built on.

The Kelly criterion (multi-asset version)

For multiple correlated bets, the optimal fraction matrix is: $\mathbf{f}^* = \Sigma^{-1} \boldsymbol{\mu}$

(where $\Sigma$ is covariance, $\boldsymbol{\mu}$ is excess returns vector).

Same caveat as single-asset Kelly: full Kelly is too aggressive. Use fractional Kelly (¼ to ½).

Volatility targeting

Pick a portfolio vol target (e.g., 15% annualized). Scale leverage up/down to maintain it.

target_vol = 0.15
realized_vol = compute_30d_vol(portfolio)
leverage = target_vol / realized_vol

Pros:

• Smoother equity curve.
• Reduces blow-up risk (auto-deleverages in crises).

Cons:

• Procyclical when vol spikes mid-trade (forces selling at bad prices).
• Adds turnover.

Most professional CTA / hedge funds run vol-targeted books.

Position sizing for a multi-strategy book

For each strategy, decide:

1. Capital allocation — % of total capital.
2. Risk allocation — % of total daily VaR / vol budget.
3. Max drawdown trigger — auto-deleverage if breached.

A simple framework:

Strategy	Capital %	Vol target	Stop-loss (DD trigger)
Momentum (long equity)	40%	18%	−20%
Mean reversion / pairs	25%	8%	−10%
Short premium options	20%	12%	−12%
Long vol / tail hedge	5%	30%	(no stop, hedge)
Cash	10%	0%	—

Total portfolio vol target ≈ ~15%, with explicit drawdown circuit breakers per sleeve.

Correlation in crisis

“When you need diversification most, you have it least.”

In normal times, strategies might be uncorrelated. In a crisis (March 2020, August 2024 carry-trade unwind), everything correlates. Long equity, short vol, mean-reversion — all hit at once.

Defense:

• Maintain a small always-on long-vol sleeve (cheap OTM puts on Nifty).
• Hold meaningful cash (5–20%).
• Have non-equity diversifiers (gold, bonds, USD-denominated).

These positions lose money 95% of the time. The 5% they pay off, they save the entire portfolio.

Factor exposure

Even an “actively managed” portfolio is often a closet-bet on standard factors:

Factor	Description	Long-term premium
Market (β)	Long equity index	Yes
Size	Small-cap minus large-cap	Modest
Value	Cheap minus expensive (low P/B)	Yes (long history)
Momentum	Past winners minus losers	Yes (strongest)
Quality	High ROE/low debt minus opposite	Yes
Low volatility	Low-vol stocks beat high-vol risk-adjusted	Yes

Run a regression of your portfolio returns on these factors. Most “alpha” turns out to be hidden factor exposure. Genuine alpha (residual after factors) is rare.

If your strategy is just “long momentum + long quality,” you don’t need fancy backtests — buy the relevant factor ETFs and save costs.

Rebalancing

Even great portfolios drift. Rebalance:

• Time-based: quarterly or monthly.
• Threshold-based: when a position drifts > 5% from target.
• Vol-targeted: continuous rebalancing to maintain vol budget.

Trade-off: more frequent → tighter to plan but higher costs.

A practical multi-strategy portfolio (₹50L example)

Capital ₹50L, target portfolio vol 12%:

Sleeve	Strategy	Capital	Notes
Long equity	Momentum top-15 NSE	₹15L	Quarterly rebalance
Long equity	Pullback swing trading	₹10L	Active
Stat arb	Pairs trading (banks)	₹8L	Always-on
Options	Short Nifty/Bank Nifty weekly condors	₹6L (margin)	Weekly cycle
Tail hedge	Long monthly OTM Nifty puts	₹0.5L	Always rolling
Cash	Liquid funds	₹10.5L	Dry powder + buffer

Expected combined: ~14–18% CAGR with ~12–15% max DD if regimes are normal. A regime change can hurt — but no single sleeve can blow up the whole book.

Drawdown management

Pre-define what happens at each drawdown level:

Portfolio DD	Action
5%	Normal — no action
10%	Reduce active exposure by 25%
15%	Reduce by 50%, switch off worst-performing strategies
20%	Move to 70% cash, only run highest-conviction sleeve
25%	Stop trading entirely. Full review. Don’t restart for 30 days.

This is a discipline mechanism. Without pre-commitment, you’ll over-trade out of drawdowns and dig deeper.

Tracking & attribution

Every month, decompose returns:

• Total portfolio return.
• Per-sleeve contribution.
• Per-strategy P&L.
• Per-factor exposure.

This tells you what actually made/lost money — not what you think did. Often surprising.

Reading list

• Active Portfolio Management — Grinold & Kahn (the institutional bible).
• The Intelligent Asset Allocator — William Bernstein.
• Asset Management — Andrew Ang (factor investing).
• Expected Returns — Antti Ilmanen (very deep).