How do I use the sovereign bond adjusted CAPM for international valuations?

Question

AcadiFi · Accepted Answer

The sovereign bond adjusted CAPM embeds country risk directly into the cost of equity by augmenting the standard CAPM with a sovereign spread component.

Standard CAPM:
ke = Rf_mature + β × ERP_mature

Sovereign-adjusted CAPM (additive CRP):
ke = Rf_mature + β × ERP_mature + λ × CRP

Where:
- Rf_mature = US 10Y Treasury (default-free benchmark)
- λ (lambda) = company's exposure to country risk (1.0 default for fully-local firm; <1 for export-heavy or multinational)
- CRP = sovereign default spread, optionally scaled by equity/bond volatility

Alternative (multiplicative):
ke = Rf_mature + β × (ERP_mature + CRP)
Treats CRP as part of market premium rather than an add-on.

Worked example — valuing São Paulo-based retailer Varejo Azul:
- Rf_mature = 4.25% (US 10Y)
- β_unlevered = 0.85 (sector beta)
- β_levered = 1.05 (post D/E adjustment)
- ERP_mature = 5.0%
- Brazil sovereign spread (USD): 275 bps
- Volatility scalar: 1.32
- CRP = 2.75% × 1.32 = 3.63%
- λ = 0.90 (export small portion, mostly domestic)

ke = 4.25% + 1.05 × 5.0% + 0.90 × 3.63%
ke = 4.25% + 5.25% + 3.27% = 12.77%

Currency consideration:
If cash flows are in BRL, convert ke to BRL using Fisher: (1+ke_BRL) = (1+ke_USD) × (1+inflation_BRL)/(1+inflation_USD)

BRL inflation 4.5%, US inflation 2.5%: ke_BRL ≈ (1.1277 × 1.045/1.025) − 1 = 14.97%

When to prefer additive vs multiplicative:
- Additive (λ × CRP): captures idiosyncratic country exposure
- Multiplicative (β × ERP_EM): assumes country risk is systematic and beta-scaled

Most CFA curriculum and practitioner work uses additive for flexibility.

How do I use the sovereign bond adjusted CAPM for international valuations?

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