CVaR Optimization

While the AI agents in the Confluence Engine provide insights into where the market might go, the CVaR optimizer determines how Tharwa should act on that information.

CVaR, or Conditional Value at Risk, is a quantitative method that focuses on what happens when things go wrong. Instead of optimizing for average returns or historical volatility, it asks:

“What are the worst-case outcomes and how do we structure the portfolio to survive them?”

This makes CVaR particularly suited for managing stablecoin backing, where preserving principal is just as important as earning yield.

Why CVaR?

Most DeFi protocols still rely on outdated financial metrics:

• Volatility tells you how much an asset moves, but not in which direction.

• Sharpe Ratio balances return against volatility, but doesn’t distinguish between upside and downside risk.

• VaR (Value at Risk) estimates the maximum loss at a given confidence level, but doesn’t quantify what happens beyond that point.

CVaR takes it one step further.

CVaR focuses on the average loss in the worst 5% of scenarios.

That makes it more conservative, more relevant during high-stress periods, and more robust for risk-aware asset allocation.

How Tharwa Uses CVaR

1. Input Signals from AI Agents The AI layer delivers asset-level packets with updated sentiment, fundamentals, and forward-looking risks.

2. Portfolio Simulation The optimizer simulates thousands of portfolio permutations using recent performance data and projected correlations.

3. Tail-Risk Filtering Portfolios are ranked not by raw return, but by how they perform in the 5% worst-case outcomes. The optimizer penalizes allocations that expose the system to sharp drawdowns or high downside variance.

4. Rebalancing Decision Once a set of optimal weights is selected, the protocol either recommends reallocation (manual review phase) or executes changes autonomously (future phase).

This means that even if an asset looks strong in normal conditions, its weight may be reduced if it behaves poorly in downside scenarios.

Example: CVaR vs. Semivariance

In backtesting with a portfolio of gold, UAE real estate, oil, and T-bills:

• The semivariance-optimized portfolio produced slightly higher returns but exposed users to larger drawdowns (−8.05% worst-case).

• The CVaR-optimized portfolio delivered slightly lower peak returns, but significantly reduced tail losses (−5.59%).

Over time, the CVaR-based strategy generated better risk-adjusted performance, particularly during volatile or crisis periods.

CVaR Portfolio Optimization Logic

function LOAD_AND_PREPROCESS_ASSET_DATA(asset_list, csv_file, start_date)
    for each asset in asset_list do
        if asset == 'UAE_RealEstate' then
            data ← load_csv(csv_file)
            price_index ← parse_and_clean(data)
            returns[asset] ← compute_monthly_returns(price_index)
        else
            prices ← download_from_yahoo_finance(asset, start_date)
            returns[asset] ← compute_monthly_returns(prices)
        end if
    end for
    aligned_returns ← align_on_common_dates(returns)
    return aligned_returns
end function

function BUILD_CVaR_OPTIMIZATION(returns_matrix, mean_returns, params)
    n_assets ← number of assets in returns_matrix
    T ← number of time periods in returns_matrix
    w ← optimization variables (weights for each asset)
    VaR, z ← auxiliary variables for CVaR

    objective ← maximize(mean_returns ⋅ w)

    constraints ← {
        sum(w) = 1,
        w ≥ 0,
        w ≤ params.max_weight,
        z ≥ 0,
        z ≥ (-returns_matrix @ w) - VaR,
        VaR + 1/(params.alpha * T) * sum(z) ≤ -params.cvar_limit
    }

    problem ← define_optimization_problem(objective, constraints)
    return problem
end function

function MAIN()
    returns ← LOAD_AND_PREPROCESS_ASSET_DATA(all_assets, uae_csv_file, start_date)
    mean_returns ← compute_columnwise_means(returns)
    problem ← BUILD_CVaR_OPTIMIZATION(returns, mean_returns, params)
    optimal_weights ← solve_optimization_problem(problem)
    output(optimal_weights)
end function

Figure: CVaR pseudocode representing the portfolio simulation and filtering logic used in backtesting (gold, UAE real estate, oil, sukuk).

CVaR Optimization – Mathematical Formulation

The pseudocode logic described above is based on the Rockafellar and Uryasev convex reformulation of Conditional Value at Risk (CVaR), which defines it as:

$$\text{CVaR}_\alpha = \min_{\text{VaR} \in \mathbb{R}} \left[ \text{VaR} + \frac{1}{\alpha T} \sum_{t=1}^{T} \max(L_t - \text{VaR}, 0) \right]$$

Where:

• Lₜ: Loss in period t (positive for losses, negative for gains)

• VaR: Value at Risk, the loss threshold at confidence level α

• α: Confidence level (e.g., 0.05 for 95% confidence)

• T: Number of time periods

• max(Lₜ − VaR, 0): Excess loss beyond VaR (only losses greater than VaR are counted)

Optimization Objective

$$\max_{w, \text{VaR}, z} \quad \mu^\top w$$

Where:

• μ: Vector of expected returns for each asset (monthly return)

• w: Portfolio weights (capital allocation)

• μᵀw: Expected return of the portfolio

• z: Auxiliary vector for CVaR loss tracking

$$\begin{aligned} w^\top \mu &\geq \text{min\_return} \\ \mathbf{1}^\top w &= 1 \quad \text{(fully invested)} \\ w &\geq 0 \quad \text{(no shorting)} \\ w &\leq w_{\text{max}} \quad \text{(individual asset cap)} \\ \text{CVaR}_\alpha(w) &\leq -c \quad \text{(tail-risk threshold)} \end{aligned}$$

Together, these constraints ensure the portfolio not only seeks high returns, but also stays within defined risk bounds and asset allocation limits.

Key Benefits

• Protects Against Black Swans CVaR doesn’t just model volatility. It prepares for the outliers — the moments when most systems fail.

• Works in Real-World Markets Useful across multiple asset classes (e.g., oil, real estate, sovereign debt) where traditional volatility metrics don’t apply cleanly.

• Balances Yield and Preservation Portfolios can still earn, but without sacrificing downside protection. This makes it ideal for stablecoin collateral or long-term vault strategies.

• Completely Transparent CVaR simulations and optimization results can be published on-chain or made available in performance dashboards for DAO and investor review.

Summary

Most DeFi systems optimize for yield, not survival. Tharwa flips that logic by using CVaR to prioritize resilience first, then build return on top of it.

This is how the Confluence Engine maintains stability in a world that doesn’t always cooperate. It doesn’t just react to volatility. It plans for it.