Mathematical Risk Framework

Overview of Nexxore's mathematical risk management methodology, including Sharpe Ratio optimization, Value at Risk (VaR), Conditional Value at Risk (CVaR), and drawdown controls.


Overview

Nexxore differentiates itself through rigorous quantitative risk management. Every strategy is optimized not just for returns, but for risk-adjusted returns. The Risk Agent continuously monitors all positions and enforces strict limits.


Core Risk Metrics

Metric
Purpose
Nexxore Target

Sharpe Ratio

Risk-adjusted returns

> 2.0

Sortino Ratio

Downside-adjusted returns

> 2.5

VaR (95%)

Max daily loss threshold

< -3%

CVaR (95%)

Expected loss in tail events

< -5%

Max Drawdown

Largest peak-to-trough

< -10%

Beta

Market correlation

< 0.1 (DN strategies)


Sharpe Ratio

The Sharpe Ratio measures risk-adjusted returns, ensuring that returns justify the volatility taken.

Formula

Sharpe=RpRfσpSharpe = \frac{R_p - R_f}{\sigma_p}

Where:

  • $R_p$ = Portfolio return

  • $R_f$ = Risk-free rate

  • $\sigma_p$ = Portfolio volatility (standard deviation)

Interpretation

Sharpe Ratio
Quality
Action

< 0

Losing money

Avoid

0 - 1.0

Below average

Review strategy

1.0 - 2.0

Good

Acceptable

2.0 - 3.0

Very Good

Target range

> 3.0

Excellent

Optimal

Nexxore Target: All strategies must maintain Sharpe > 2.0


Sortino Ratio

Unlike Sharpe, Sortino only penalizes downside volatility, making it more relevant for asymmetric return profiles.

Formula

Sortino=RpRfσdSortino = \frac{R_p - R_f}{\sigma_d}

Where: $\sigma_d$ = Downside deviation (volatility of negative returns only)

When to Use

Ratio
Best For

Sharpe

Symmetric return distributions

Sortino

Strategies with positive skew, options-based approaches

Nexxore uses both metrics for comprehensive risk assessment.


Value at Risk (VaR)

VaR measures the maximum expected loss over a given time period at a specified confidence level.

Definition

"With 95% confidence, we will NOT lose more than X% over the specified time period."

Example

VaR (95%, 1 day) = -2.1%

  • 95% of days: Loss ≤ 2.1%

  • 5% of days: Loss > 2.1% (tail risk)

Limitations

VaR tells you the threshold but not what happens beyond it. This is why Nexxore primarily uses CVaR.


Conditional Value at Risk (CVaR)

CVaR (also called Expected Shortfall) measures the average loss in the tail—what happens when things go wrong.

Formula

CVaRα=E[LLVaRα]CVaR_{\alpha} = E[L | L \ge VaR_{\alpha}]

Why CVaR > VaR

Metric
What It Tells You

VaR (95%)

"Loss won't exceed X, 95% of the time"

CVaR (95%)

"When losses DO exceed X, expect Y on average"

CVaR is more conservative and captures tail risk better. Nexxore uses CVaR as the primary risk constraint.

Risk Agent CVaR Enforcement

The Risk Agent monitors CVaR continuously:

Condition
Action

CVaR within limits

Normal operation

CVaR approaching limit (80%)

Warning alert

CVaR at limit (90%)

Reduce new position sizes

CVaR breached (100%)

Halt trading, force hedge


Maximum Drawdown

Maximum Drawdown (MDD) measures the largest peak-to-trough decline in portfolio value.

Formula

MDD=TroughPeakPeak×100%MDD = \frac{Trough - Peak}{Peak} \times 100\%

Drawdown Limits by Strategy

Strategy Type
Max Drawdown
Recovery Time Target

Conservative (DN)

-5%

< 30 days

Moderate

-10%

< 60 days

Aggressive

-20%

< 90 days


Beta & Correlation

Portfolio Beta

Beta measures systematic risk—how much the portfolio moves relative to the market.

βp=Cov(Rp,Rm)Var(Rm)\beta_p = \frac{Cov(R_p, R_m)}{Var(R_m)}

Interpretation

Beta
Meaning

β = 1.0

Moves with the market

β > 1.0

More volatile than market

β < 1.0

Less volatile than market

β = 0

Market neutral

β < 0

Inverse correlation

Nexxore Targets

Strategy
Target Beta

Delta-Neutral

< 0.1

Alpha Strategies

0.3 - 0.7


Risk-Adjusted Performance Comparison

Strategy
APY
Volatility
Sharpe
Max DD
CVaR

DN Yield

12%

3%

2.67

-3%

-2.1%

Moderate Alpha

25%

12%

1.75

-10%

-6.5%

Aggressive

45%

25%

1.64

-20%

-12.3%

HODL ETH

35%*

60%

0.52

-55%

-35%

Historical average, highly variable

Key Insight: Higher returns ≠ better risk-adjusted returns. The DN Yield strategy has the best Sharpe despite lower APY.


Risk Agent Implementation

The Risk Agent continuously monitors all metrics and takes automated action.

Monitoring Frequency

Check
Frequency

Portfolio value

Every block (~12s)

Rolling volatility

Every block

VaR/CVaR recalculation

Every block

Drawdown from peak

Every block

Delta neutrality

Every block

Alert Levels

Level
Threshold
Action

Warning

80% of limit

Log alert, notify manager

Caution

90% of limit

Reduce position sizes 50%, tighten stops

Critical

100% of limit

Halt new positions, force hedge, emergency alert


Summary

Nexxore's risk framework ensures that all strategies maintain institutional-grade risk management:

  1. Sharpe > 2.0 — Returns must justify volatility

  2. CVaR-based limits — Tail risk is actively managed

  3. Continuous monitoring — Every block, every position

  4. Automated enforcement — No human bottleneck in risk management


Next Steps

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