Teaching material · 2018

Portfolio Construction Techniques

Fernando Ruiz, CAIA · Asset Allocation Course
Contents
  1. Asset allocation by risk profile
  2. Total return asset allocation — shortfall risk
  3. Simplified techniques: Elton-Gruber-Padberg algorithm
  4. Active management relative to a benchmark
  5. Core-satellite investing
  6. Dynamic core-satellite (CPPI)

1. Asset allocation by risk profile

Suppose we must define the asset allocation for three investor profiles investing in equities (MSCI All Country), fixed income (JPM Hedge Global Bond Index) and hedge funds (CSFB/Tremont Hedge Fund Index).

  • Conservative investor: target return of 4%
  • Moderate investor: target return of 7.5%
  • Aggressive investor: target return of 10%

The equity return distribution exhibits high kurtosis and negative skewness. Hedge fund returns show very high kurtosis. Fixed income is closest to normality. Mean-variance optimisation based on these distributions may therefore lead to incorrect results.

Alternative optimisation frameworks

A
VaR minimisation — Minimise the Cornish-Fisher adjusted VaR subject to an expected return constraint.
B
Expected Shortfall (CVaR) — Minimise conditional VaR subject to expected return ≥ 0%.
C
Lower Partial Moment (LPM) — Minimise LPM with a = 3 and target return = 0%.

2. Total return asset allocation — shortfall risk

Leibowitz and Kogelman's shortfall risk framework defines an investor's risk profile through two parameters:

  • A minimum return threshold (Rtarget) below which the investor considers a loss to have occurred.
  • A maximum probability that portfolio return falls below that threshold for a given horizon.

Under normality, if a fraction of the portfolio is invested in the risk-free asset rf and the rest in a risky asset, the weight allocated to the risky asset is:

w_risky = [μ_risky - R_target - Φ⁻¹(p*) · σ_risky] / [μ_risky - r_f]

The shortfall risk is a special case of LPM (a=0). Its weakness is that it does not indicate how adverse a loss might be — only its probability. Expected Shortfall is a more complete measure and satisfies coherent risk measure properties.

Empirical result: a portfolio dynamically managed to keep shortfall probability below 5% generated an annualised return of 4.64% vs. 3.96% for a static 50/50 buy-and-hold strategy (1999–2008).

3. Simplified techniques: Elton-Gruber-Padberg algorithm

Sharpe first proposed a simplified approach: choose the 20 assets with the highest Treynor ratio and assign equal weights of 5%. The EGP algorithm formalises this idea.

EGP with Treynor ratio (market model)

1
Compute the Treynor ratio for each asset: (μ_i − r_f) / β_i
2
Rank assets from highest to lowest Treynor ratio.
3
Compute the cut-off values C_i. The last asset whose Treynor ratio exceeds its C_i defines C*.
4
Include all assets above C*. Compute Z_i scores and normalise to obtain portfolio weights X_i.

EGP with Sharpe ratio (constant correlation)

When CAPM is not appropriate, an alternative version uses the Sharpe ratio and assumes a constant pairwise correlation ρ across all assets. The cut-off C_i is recomputed accordingly, and the Sharpe ratio replaces Treynor as the selection criterion.

4. Active management relative to a benchmark

Active management seeks to generate alpha relative to a benchmark through timing (tactical asset allocation) and security selection. The key measures are:

Alpha
Excess return generated by active decisions: α = R_P − R_B, where R_P and R_B are portfolio and benchmark returns respectively.
Tracking error
Standard deviation of alpha. Larger active positions and riskier holdings increase tracking error.
Information ratio
Alpha divided by tracking error. Measures the quality of active management: return per unit of active risk.
Ex-ante tracking error
TE² = (X_P − X_B)' · Σ · (X_P − X_B). Used to set maximum TE limits in mandates (typically 4–8% for equities).

Fund biases: size and style

Equity funds are typically classified by capitalisation bias (Large Cap, Mid Cap, Small Cap) and style (Value, Growth, Blend). These biases drive behaviour relative to the benchmark and explain a significant portion of tracking error.

5. Core-satellite investing

The core-satellite approach divides the portfolio into two components:

  • Core — passively managed relative to the benchmark (zero or minimal TE), implemented via ETFs or index funds.
  • Satellite — actively managed strategies with high TE (hedge funds, concentrated managers, niche specialists).

The total portfolio tracking error equals the satellite's TE weighted by its allocation:

TE_total = w_satellite × TE_satellite

Example: an investor with a 2.5% TE target can either build a single active portfolio with TE = 2.5%, or allocate 80% to a passive core and 20% to a satellite manager with TE = 12.5%.

6. Dynamic core-satellite (CPPI)

The dynamic core-satellite applies Constant Proportion Portfolio Insurance (CPPI) logic to active management. The core plays the role of the risk-free asset; the satellite plays the role of the risky asset.

The key parameters are:

  • Floor (F_t) — minimum acceptable portfolio value, typically set at 90% of the benchmark: F_t = k × B_t
  • Cushion (C_t) — difference between portfolio value and floor: C_t = P_t − F_t
  • Multiplier (m) — determines the satellite allocation: S_t = m × C_t

As the satellite generates alpha, the cushion grows and its allocation increases. If it underperforms, the cushion shrinks and the allocation decreases — protecting against excessive underperformance relative to the benchmark.

Alternative floor definitions include: capital guarantee, benchmark protection floor, maximum drawdown floor, and trailing performance floor.