A Quantamental Estimation Model for Institutional Risk Adjustment

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Theoretical Foundations and Literature Review

• Proxy Theory (Damodaran, 2009): Public comps estimate private asset volatility.

• Geltner & Mei (2002): Temporal smoothing masks private asset variance.

• NCREIF Volatility Studies: Longitudinal REIT and PE data on smoothing bias.

• Dispersion Analytics (MSCI): Geography and liquidity impact observed volatility.

• STR/CoStar RevPAR Volatility Studies: Empirical hospitality cash flow data.

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Bay Street’s Model: Calculating Synthetic Volatility

Bay Street Synthetic Volatility (BSV) Formula:

BSV_private = Vol_proxy REIT × Dispersion Multiplier × Leverage Adjustment

Step 1: Proxy Selection

Each private deal is mapped to a comparable public REIT based on geography, asset type, and business model.

Step 2: Dispersion Multiplier

• 1 (Low): U.S., UK, Singapore → 1.0x

• 2 (Medium): Portugal, UAE, Thailand → 1.2x

• 3 (High): India, Indonesia, Mexico → 1.5x

Step 3: Leverage Adjustment

Volatility is adjusted for capital structure using:
Leverage Adjustment = 1 + (LTV_deal − LTV_proxy) × κ
(Default κ = 0.75)

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Integration into Bay Street Metrics

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4.1 BAS: Bay Adjusted Sharpe

BAS = AHA ÷ Synthetic Volatility

4.2 LSD: Liquidity Stress Delta

BSV >15% and LSD >1% triggers flags for exit degradation risk.

4.3 Optimizer Inputs

BSV feeds portfolio optimizer constraints and Efficient Frontier models in Streamlit.

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Case Study: Two Deals with Same IRR, Different Volatility

• Deal A (Portugal): IRR 15.0%, Proxy Vol 13.0%, Dispersion 1.2, Leverage 68%, BSV 20.2%, AHA 5.2%, BAS 0.26

• Deal B (USA): IRR 15.0%, Proxy Vol 11.0%, Dispersion 1.0, Leverage 50%, BSV 11.0%, AHA 5.2%, BAS 0.47

Conclusion: Same IRR, but Deal B is superior risk-adjusted.

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Strategic Implications for LPs and Investment Committees

• Improved Deal Comparability: BSV normalizes public and private evaluations.

• Volatility as Pricing Factor: LPs can price IRR based on estimated risk.

• Negotiation Leverage: Higher BSV supports tighter deal structures.

• Post-Investment Monitoring: Drift outside volatility bands triggers IC review.

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Conclusion: Making the Invisible Quantifiable

Bay Street’s Synthetic Volatility model transforms the opaque risk of private hospitality investments into a measurable, institutional-grade input. It strengthens underwriting, enables portfolio optimization, and increases LP transparency. Future initiatives include dynamic recalibration against REIT betas, validation against realized IRRs, and expansion into dynamic exit horizon modeling.

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