Research Note

Funding the Goal, Not Maximising the Sharpe Ratio: A Guide to Liability-Aware Portfolio Insurance

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A practical guide to designing, simulating and rejecting goal-aware allocation rules using funding ratios, liability hedges, CPPI, gap risk and terminal shortfall.

Markets · Published 4 August 2026 · Updated 4 August 2026 · 8 min read

Goals-Based InvestingCPPILiability-Driven InvestingFunding RatioDuration MatchingPortfolio Insurance

A portfolio can have a good Sharpe ratio and still fail its investor.

The investor may need £500,000 in twelve years, a pension plan may need to meet a schedule of benefits, or an insurer may need assets that respond to rates in the same way as its liabilities. In each case the decisive outcome is not whether the portfolio was efficient in return–volatility space. It is whether the required cash was available when it was needed.

That changes the research question:

Which dynamic allocation rule gives the highest probability of meeting a future liability after inflation, interest-rate risk, transaction costs and gap risk are included?

This article is a guide to answering that question. It does not claim that CPPI, liability-driven investment or any other rule is universally superior. The reusable calculations are implemented in the investment-management-toolkit.

Begin with the liability

A future goal is economically similar to a liability: a required cash flow at a specified time. If liabilities $L_j$ occur at times $\tau_j$ and the appropriate annual discount rates are $y_j$ , their present value is

PV(L)=\sum_{j=1}^{J}\frac{L_j}{(1+y_j)^{\tau_j}}.

The funding ratio is

F_t=\frac{A_t}{PV_t(L)},

where $A_t$ is the current asset value.

This ratio reveals something that an asset-only chart hides. Cash can be stable in nominal value while the present value of the liability rises as interest rates fall. The asset account did not lose money, but the investor became less funded.

For an inflation-linked goal, the liability also changes with realised and expected inflation. A nominal floor is therefore not enough. The research model must state whether the goal is:

nominal or real;
a single terminal amount or a cash-flow schedule;
fixed or linked to wages, inflation or another index;
essential or aspirational; and
fully funded today or dependent on future contributions.

Without that specification, “capital protection” is only a slogan.

Separate the goal hedge from the performance engine

A useful conceptual split is:

Component	Job
Goal-hedging portfolio (GHP)	Respond to the liability’s main risk drivers
Performance-seeking portfolio (PSP)	Earn the risk premium needed to close the funding gap

For a fixed nominal payment, a matching zero-coupon bond is the cleanest theoretical GHP. For a schedule of cash flows, a bond portfolio can use cash-flow matching or duration matching. For a real liability, inflation-linked bonds may be closer to the economic exposure.

The PSP can be a diversified equity portfolio, risk-parity allocation, factor-based portfolio or another return-seeking strategy. The label does not make it safe. Its distribution, liquidity and correlation with the liability all matter.

The split prevents a common category error: evaluating the whole portfolio as if every asset has the same purpose. The hedge is judged by liability tracking. The PSP is judged by the quality and cost of the risk it contributes.

Duration matching is a local hedge

For a bond or liability with price $P$ and cash flows $CF_j$ , Macaulay duration is

D_M=\frac{\sum_j \tau_j\,PV(CF_j)}{P}.

Modified duration approximates the percentage price response to a small parallel yield change:

\frac{\Delta P}{P}\approx-D_{mod}\Delta y.

Matching asset and liability duration can stabilise the funding ratio against small parallel moves. It is not a complete hedge against:

large rate moves and convexity differences;
non-parallel yield-curve changes;
inflation surprises;
credit-spread changes;
defaults and downgrades;
liquidity differences; or
changing liability cash flows.

A research paper should therefore report key-rate or scenario sensitivities where the data permit, not only one duration number.

CPPI as a funding-rule template

Constant proportion portfolio insurance allocates to the risky portfolio as a multiple of the cushion above a floor. Black and Perold’s foundational CPPI analysis defines risky exposure as a constant multiple of wealth above the floor, subject to constraints.

Let wealth be $A_t$ , floor value $H_t$ , cushion $C_t$ and multiplier $m$ :

C_t=\max(A_t-H_t,0),

w^{PSP}_t =\min\left(w_{max},\max\left(0,\frac{mC_t}{A_t}\right)\right).

The remaining weight goes to the GHP.

The rule is intuitive:

when the portfolio is comfortably above the floor, it can take more PSP risk;
when the cushion shrinks, it sells risk;
at the floor, it should hold only the hedge.

But the floor must be economically defined. For a future goal, $H_t$ should be connected to the present value of the protected liability, not merely 80% of initial nominal wealth.

A moving drawdown floor

Another variant protects a proportion of the highest wealth reached:

H_t=\max\left(H^{goal}_t,(1-d)\max_{s\le t}A_s\right),

where $d$ is the allowed drawdown. This crystallises some gains but can force the strategy to de-risk after a fall. It protects a path-dependent account value, which is not always the same as protecting the underlying goal.

The floor is not a guarantee

Discrete rebalancing creates gap risk. If the risky asset falls far enough between rebalances, wealth can jump through the floor before the strategy can sell. Cont and Tankov analyse CPPI in the presence of jumps in asset prices, where this issue becomes explicit.

Other ways the apparent protection can fail include:

the GHP does not match the liability;
the “safe” asset has credit or duration risk;
trading is delayed or markets close;
transaction costs increase during the rebalance;
leverage or borrowing becomes unavailable;
the model understates volatility and jump frequency;
inflation changes the goal faster than the hedge; and
contributions arrive later than assumed.

For that reason, report both floor violations and their severity. A strategy with one 1% breach is different from one with a 20% breach, even if each is counted as one failure.

Define the strategy comparison before simulation

A useful comparison includes simple and complex rules:

Strategy	Allocation logic	Why include it
Cash or matched bond	Fully hedged	Protection baseline
Fixed mix	Constant PSP/GHP weight	Low-complexity benchmark
Glidepath	PSP weight changes with time	Common lifecycle rule
Funding-ratio bands	Adjust at specified thresholds	Limits turnover
CPPI	PSP weight is a multiple of cushion	Dynamic protection rule
Drawdown-floor CPPI	Floor follows peak wealth	Path protection
Dynamic-programming rule	Optimises goal probability	Model-intensive benchmark

Goals-based research has proposed dynamic policies that directly maximise the probability of reaching terminal wealth. Das, Ostrov, Radhakrishnan and Srivastav present a dynamic allocation algorithm for that objective. Dempster and co-authors compare holistic dynamic planning with conventional practices in Life Cycle Goal Achievement or Portfolio Volatility Reduction?.

The dynamic optimiser is not automatically the winner. It has more assumptions and more opportunities to overfit. Fixed mix and matched bonds are necessary benchmarks precisely because they are difficult to improve upon honestly after costs.

Simulate assets and liabilities together

A liability-aware study cannot simulate equity while leaving the discount rate fixed. At minimum, scenarios should jointly represent:

PSP returns;
the yield curve or relevant discount rate;
GHP returns;
inflation where the goal is real;
contributions and withdrawals; and
transaction costs.

There are three complementary scenario families.

Historical paths

Historical replay preserves realised cross-asset relationships and real crises. It is transparent but contains only one sequence of events. Start dates can dominate conclusions.

Use rolling start cohorts and report the distribution of outcomes rather than one backtest beginning at a favourable date.

Resampled paths

Block bootstrap preserves short-run dependence better than independently drawing months. Vary the block length and show sensitivity. Resampling cannot create economic states absent from the historical sample.

Parametric scenarios

Equity returns may be represented with stochastic volatility or jump processes; rates may use a short-rate or term-structure model; inflation can be linked to rates and growth. The benefit is controlled stress. The cost is model risk.

A Cox–Ingersoll–Ross-style short-rate process is often written

dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t,

where $\kappa$ controls mean reversion, $\theta$ the long-run level and $\sigma$ the volatility. It is a teaching model, not a complete modern curve engine. If used, calibrate it point in time and disclose which yield-curve dynamics it cannot reproduce.

The strongest study shows conclusions across historical, resampled and parametric scenarios instead of asking one simulation to carry the whole claim.

Use goal-native performance measures

Sharpe ratio can remain a diagnostic, but it should not be the objective.

For terminal wealth $A_T$ and goal $G_T$ , report:

Probability of success

p_{goal}=\Pr(A_T\ge G_T).

Expected monetary shortfall

ES_{goal}=\mathbb{E}\left[(G_T-A_T)^+\right].

Conditional failure severity

CFS=\mathbb{E}\left[G_T-A_T\mid A_T<G_T\right].

Also report:

terminal funding-ratio distribution;
worst 5% terminal wealth;
floor-breach probability and severity;
maximum drawdown;
upside surplus conditional on success;
turnover and cost;
time spent fully de-risked; and
contribution sensitivity.

Two strategies can have the same success probability but very different failure severity. An investor deciding between them needs both.

Implement the rules without same-period knowledge

At rebalance time $t$ , the allocation must be based on wealth and liability values known before the return over $t$ to $t+1$ .

from investment_research_toolkit import (
    cppi_backtest,
    fixed_mix_backtest,
    funding_ratio,
    present_value,
    terminal_goal_metrics,
)

liability_pv = present_value(liability_cashflows, annual_discount_rates)
current_funding = funding_ratio(asset_value, liability_pv)

cppi = cppi_backtest(
    risky_returns,
    goal_hedge_returns,
    multiplier=3.0,
    floor_fraction=0.90,
    drawdown_limit=0.15,
)

metrics = terminal_goal_metrics(terminal_values, goal=500_000)

The toolkit’s CPPI function calculates the risky weight before applying each period’s returns. A full empirical study should add explicit rebalancing dates, liability repricing, taxes, spreads and market impact.

Transaction costs alter the strategy, not just the result

A common mistake is to calculate the ideal allocation every day and subtract a constant cost at the end. Costs feed back into wealth, the cushion and the next allocation.

If $\Delta w_{i,t}$ is the trade in asset $i$ and $c_{i,t}$ its proportional cost, the wealth update should include

Cost_t=A_t\sum_i c_{i,t}|\Delta w_{i,t}|.

For illiquid or stressed assets, costs should increase with volatility, spread or trade size. Funding-ratio bands can reduce churn by trading only when the desired allocation leaves a tolerance region.

Research on the original CPPI rule explicitly considers transaction costs and borrowing constraints. Any modern comparison that omits them tests an idealised control rule, not an implementable strategy.

Stress the assumptions that make protection look easy

Run designed shocks, not only Monte Carlo averages:

Overnight equity gap: PSP falls 20% before rebalancing.
Inflation shock: the real liability rises while nominal bonds fall.
Rate rally: liability present value rises faster than the GHP.
Rate sell-off: long-duration hedge loses value while the goal horizon shortens.
Correlation break: PSP and GHP fall together.
Contribution failure: expected cash inflows are delayed or absent.
Liquidity shock: costs and slippage multiply during de-risking.
Whipsaw: repeated reversals force sell-low/buy-high CPPI trading.

The objective is not to make every strategy survive every scenario. It is to understand which assumption causes each failure.

Keep calibration separate from judgment

Parameters such as multiplier, rebalance frequency, floor fraction and risk budget should be chosen on a training period or from economic constraints. If the multiplier is selected from the full sample because it maximises realised success, the simulation has been optimised to one known history.

Use an expanding or rolling design:

estimate parameters on past data
          ↓
freeze the allocation rule
          ↓
simulate or replay the next period
          ↓
record realised wealth and costs
          ↓
advance the information set

Preserve a final period that is not used for parameter changes. If researchers keep revisiting that period, it is no longer out of sample.

What would make a strategy unacceptable?

Define rejection gates before comparing results. For example:

success probability does not beat fixed mix by a meaningful margin;
lower average shortfall is purchased with unacceptable severe breaches;
performance depends on one starting date or one rate regime;
turnover makes the improvement disappear;
the strategy remains fully de-risked after common shocks;
the GHP fails to track the liability under plausible curve moves;
success requires leverage unavailable to the intended investor; or
small parameter changes reverse the ranking.

A complex strategy that is only marginally better than a matched bond plus fixed PSP allocation should probably lose on governance.

A minimal credible research protocol

Start with one well-defined goal:

Set a real terminal liability and contribution schedule.
Use a diversified equity PSP and duration-appropriate bond GHP.
Compare matched bond, 60/40, glidepath, CPPI and drawdown-floor CPPI.
Replay multiple historical start cohorts.
Add block-bootstrap and rate/inflation stress scenarios.
Charge costs at every rebalance.
Freeze parameters before the final test period.
Rank strategies by success probability and failure severity.

Only then add Black–Litterman views, regime forecasts or dynamic programming.

The final decision should be understandable without a stochastic-control textbook: what is the goal, how much is currently funded, what risks can close the gap, what protects the minimum, and under which shocks does the plan fail?

That is the difference between optimising a portfolio and financing an outcome.

For the asset-only construction problem that this framework extends, see From Sharpe Ratios to Portfolio Weights. For leakage-safe model selection, see Sparse Factors Without Backtest Theatre.