Journal number 1 ∘ Beka Darakhvelidze ∘
A Methodological Framework for Modified CAPM Estimation

doi.org/10.52340/eab.2026.18.01.12.

This study addresses a critical gap in emerging market finance by systematically analyzing and comparing alternative methodological approaches for estimating each component of the Capital Asset Pricing Model (CAPM) in data-constrained environments. While the theoretical foundation of CAPM remains elegant and logically consistent, substantial debate persists among finance scholars regarding the optimal estimation methodology for each variable, The problem becomes more acute in developing markets where sovereign yields may embed default risk, equity indices may be illiquid or economically unrepresentative, and reliable time-series data may be scarce or structurally unstable. The framework presented here systematizes the selection and adjustment of each input variable under such constraints. Risk-free rates are constructed using either credit-rating-implied default spreads or market-based CDS spreads, with explicit discussion of reinvestment risk and instrument choice. Beta estimation is implemented using regression-based methods for listed firms and a pure-play (bottom-up) methodology for private firms, including unlevering and relevering via Hamada-style adjustments and, where appropriate, conversion to a “total beta” relevant for non-diversified investors. The market risk premium is evaluated through historical, survey-based, and implied approaches, and a modified historical strategy is defended when local market benchmarks are infeasible. Finally, country risk premium estimation is formalized through rating-based default spreads in data-thin markets and volatility-scaled default spreads in deeper emerging markets. The contribution is a defensible, internally consistent methodological architecture that bridges asset-pricing theory and valuation practice in data-constrained environments.

Keywords: Modified CAPM, Cost of equity, Emerging markets, Frontier markets, Risk-free rate, Beta, Market risk premium, Country risk premium, CDS, Credit ratings, Bottom-up beta, Total beta.
JEL Codes: G12, G15, G32, C13, F34

Introduction

The modified CAPM widely applied in practice and research, remains deceptively simple in form yet highly sensitive in implementation. The model’s key inputs: risk-free rate, beta, market risk premium (equity risk premium), and country risk premium can each be estimated using multiple competing methodologies. Even within the financial economics community, input construction is debated vigorously, and where consensus is absent, practitioners frequently rely on subjective preference when operationalizing the model (Roll, 1977; Blume, 1975). These methodological disagreements become systematically more consequential in emerging and frontier markets. In such settings, government bonds may not be default-free and may embed political and credit risk; equity indices may be missing, illiquid, or not representative of a true market portfolio; and stable and sufficiently long time-series data may be difficult to obtain. These constraints can render “textbook” implementations fragile and, in extreme cases, economically misleading. Accordingly, this article presents a structured methodological framework designed explicitly for emerging-market valuation contexts. The framework is grounded in a pragmatic principle: rather than forcing a single canonical estimator under conditions where its assumptions fail, the analyst must adopt an approach that is theoretically coherent yet empirically feasible, and that transparently justifies each methodological choice in light of local market infrastructure.

Methodological Framework and Model Architecture

The methodological focus is the construction of the modified CAPM inputs required for cost-of-equity estimation:
• Risk-free rate (Rf): must approximate default-free and reinvestment-risk-free cash flows, subject to instrument availability and sovereign credit quality.
• Beta (β): must measure sensitivity to systematic risk for diversified investors, and may require modification to reflect total risk for non-diversified marginal investors in certain emerging-market contexts.
• Market risk premium / equity risk premium (MRP / ERP): may be infeasible to estimate locally due to index limitations, implying the need for alternative approaches (historical, survey-based, implied) and/or a modified “base premium + country risk” construction.
• Country risk premium (CRP): must capture non-diversifiable country-specific risks that are empirically not spanned by beta in segmented or partially integrated markets (Harvey, 2001).
Two implementation constraints dominate the framework:
• Instrument integrity: inputs should be derived from investable, economically meaningful benchmarks where possible (e.g., liquid sovereign yields, CDS spreads, widely used indices).
• Cross-country comparability: input estimation should preserve comparability across countries by enforcing coherent maturity, currency, and sampling conventions when feasible, while transparently documenting unavoidable deviations.

Risk-Free Rate Estimation in Emerging Markets

The risk-free rate constitutes the foundational building block of CAPM, representing both the time value of money and the opportunity cost of investing in risky assets (Schmidt, 2020). Theoretically, a risk-free asset must satisfy two critical criteria: (1) absence of default risk, ensuring the expected cash flows materialize with certainty, and (2) absence of reinvestment risk, guaranteeing the realized return matches the expected return regardless of interest rate movements. In developed markets, long-term zero-coupon government bonds most closely approximate these theoretical requirements (Courtois et al., 2018). The issuing government possesses monetary sovereignty, - the discretion to print currency in extremis, which minimizes nominal default probability. Additionally, zero-coupon structure eliminates reinvestment risk by avoiding intermediate cash flows. However, these conditions rarely hold in emerging and frontier markets, where sovereign default risk may be substantial, government bonds of appropriate maturity may not exist, or secondary markets may lack liquidity (Erb et al., 1996).

Direct Local Government Bond Approach. When an emerging market government issues long-term local currency bonds with adequate liquidity and reasonable trading history, the direct approach uses these yields as the starting point, subsequently adjusting for embedded default risk. The adjustment typically employs either:

Formula N 2

This approach might be used for instance for Brazil and India, where active sovereign CDS trading provides reliable spread data. CDS spreads offer several advantages over credit ratings: they reflect current market perceptions of default risk, update continuously as new information arrives, and aggregate diverse market participants\\' assessments. Advantages: Market-based measurement captures real-time risk perceptions. CDS spreads respond dynamically to macroeconomic developments, political events, and global risk sentiment shifts, providing more timely risk adjustments than periodic rating revisions. Limitations: CDS spreads exhibit substantial volatility, particularly during crisis periods, potentially introducing excessive noise into cost of capital estimates (Damodaran, 2012). Additionally, CDS markets may not exist or lack liquidity for smaller emerging markets and frontier economies. A practical concern involves currency denomination, CDS contracts typically reference USD-denominated sovereign debt, potentially creating currency mismatch issues when estimating local currency discount rates.
Build-Up Approach. When local government bonds are either non-existent or unreliable due to thin trading or embedded default risk, the build-up method constructs a synthetic risk-free rate by starting from a developed market benchmark and adjusting for relevant risk differentials:

Advantages: CIRP-based rates are market-determined, reflecting the collective expectations of foreign exchange and interest rate market participants. The approach avoids relying on potentially biased credit ratings. Limitations: Implementation requires liquid forward markets for the relevant maturity (10 years), which typically do not exist for smaller emerging market currencies. Where forward markets exist only for short tenors (e.g., 1 year), extrapolation to longer maturities introduces additional assumptions and potential error.
Methodological Selection Criteria. Our framework applies the following decision hierarchy for risk-free rate estimation:
1. If liquid local currency government bonds exist with 10+ years maturity and reasonable trading volumes: Use direct approach with default spread adjustment (rating-based or CDS-based depending on CDS market availability).
2. If government bonds exist but CDS markets are absent: Apply credit rating-based default spread adjustment.
3. If government bond markets are illiquid or non-existent: Consider build-up or CIRP approaches depending on forward market development.

1. Return frequency: Weekly returns represent the optimal balance in emerging markets. Daily returns introduce microstructure noise and non-synchronous trading bias (Roll, 1977), while monthly or quarterly observations provide insufficient data points for reliable estimation. Weekly frequency mitigates microstructure issues while maintaining adequate sample size.
2. Observation period: Empirical evidence suggests 5-10 years of data provides the best trade-off between parameter stability and capturing current risk characteristics (Blume, 1975). Shorter periods yield unstable estimates with wide confidence intervals; longer periods may incorporate outdated business model or capital structure information.
3. Currency consistency: Returns for both the individual stock and market index must be calculated in identical currency. Currency mismatches conflate beta with foreign exchange exposure, producing biased systematic risk estimates.
4. Market index selection: The index should represent the broadest feasible equity market portfolio. However, local indices in emerging markets often suffer from concentration (few stocks dominate), illiquidity, and short histories, potentially yielding unreliable betas.
Beta estimation for private firms: the pure-play (bottom-up) approach
The pure-play or bottom-up approach addresses beta estimation for private companies or firms in illiquid markets through a four-stage process: Stage 1: Identify comparable publicly traded firms. Select companies with similar operating characteristics: industry classification, business model, operational leverage, and market capitalization. This stage requires balancing comparability against sample size, overly restrictive criteria yield too few comparables with unreliably estimated average betas, while overly loose criteria introduce heterogeneity that biases results (Damodaran, 2012). Stage 2: Unlever comparable company betas. Observed betas reflect both business risk and financial leverage. To isolate business risk, we apply Hamada\\'s (1972) unlevering formula:

This produces a company-specific beta reflecting both industry business risk and the target firm\\'s financial leverage policy. Critical assumption: The pure-play method implicitly assumes comparable companies possess similar operating leverage (fixed versus variable cost structures). This assumption rarely holds perfectly in practice. Operating leverage differences affect beta independently of financial leverage, but data limitations frequently prevent explicit adjustment. Researchers must acknowledge this limitation and consider its potential materiality based on industry characteristics.
Alternative Approach: Accounting Beta. Accounting beta represents an alternative methodology particularly relevant for emerging markets with underdeveloped equity markets. The approach regresses accounting-based performance measures (net income, EBITDA, ROE, ROA) against corresponding market-wide benchmarks:

Appeal: The methodology is conceptually straightforward and empirically grounded. If investors historically earned 5-6% excess returns on equities, this suggests future expectations may center around similar magnitudes. Critical sensitivities: Measurement period length. U.S. data from 1926-2020 suggests approximately 6% historical premium, while the most recent 20 years yields 3-4%, illustrating substantial period-dependence (Damodaran, 2012). Arithmetic versus geometric averaging. Arithmetic means provide unbiased estimates of expected single-period returns but overstate long-horizon compound returns. Geometric means accurately capture compounding but understate expected single-period returns. Inclusion of crisis periods. Different economic regimes (boom, recession, crisis) generate vastly different realized premia, making the sample period choice critical. Standard error considerations: Even in developed markets with century-long data, historical ERP estimates exhibit wide confidence intervals:

Solving for (cost of equity) and subtracting the risk-free rate yields implied ERP. This approach incorporates market prices and forward-looking expectations, but requires assumptions about dividend growth rates and payout policies, introducing substantial subjectivity.
While acknowledging these alternatives\\' value, data constraints and transparency considerations led us to adopt the modified historical approach (global premium plus country risk) as our primary methodology.
Country Risk Premium: Capturing Emerging Market-Specific Risks
Campbell Harvey\\'s (2001) seminal research demonstrated empirically that traditional beta inadequately captures country-specific risks in emerging markets. Systematic risk exposure measured by beta primarily reflects sensitivity to global market movements, but fails to adequately price political risk, institutional weaknesses, regulatory uncertainty, currency convertibility constraints, and expropriation risk that characterize emerging economies. Consequently, explicitly incorporating a country risk premium (CRP) into cost of equity estimation becomes essential for emerging markets (Damodaran, 2003, 2012; Erb et al., 1996).
For example, for Georgia and Armenia, we can employ sovereign credit rating-based default spreads as country risk premia. The methodology proceeds as follows:
1. Obtain sovereign credit rating. International rating agencies (Fitch, Moody\\'s, S&P) assign ratings reflecting sovereign default probability.
2. Map rating to default spread. Each rating level corresponds to an empirically observed spread between bonds of that rating and equivalent-maturity risk-free benchmarks (U.S. Treasuries).
3. Add default spread to base ERP.
Example: If Georgia holds a BB rating, the corresponding default spread might be 250 basis points (2.5%). Adding this to a 6% U.S. equity risk premium yields 8.5% total ERP. Rationale and advantages: Credit ratings provide standardized, internationally comparable sovereign risk measures. Rating agencies aggregate diverse information sources, fiscal metrics, political stability indicators, institutional quality assessments, into a single risk measure. Data are readily available and updated regularly. Limitations and critiques: Lagging indicators: Rating changes typically follow market-perceived risk changes by months. The 2008 financial crisis and COVID-19 pandemic demonstrated that rating downgrades often occurred well after sovereign spreads had already widened substantially. Incomplete risk capture: Ratings primarily assess default risk on fixed-income securities. Equity investors face additional risks—political instability, expropriation, regulatory arbitrariness, corruption—that ratings may underweight (Damodaran, 2003). (3) Potential bias. The 2008 crisis revealed conflicts of interest and pro-issuer bias among rating agencies, raising questions about rating reliability and independence. Acknowledging these limitations, we view rating-based CRP as a pragmatic, transparent starting point, a conservative minimum estimate of country-specific risk rather than a comprehensive measure.
For instance, for Brazil and India, sovereign CDS spreads can be employed rather than credit ratings:

 

Data and Estimation Strategy
Because the article is methodology-centered, the data strategy is articulated as an implementable protocol rather than a dataset claim. The framework’s core data conventions include:
• Risk-free rate inputs: 10-year sovereign yields in the valuation currency where possible; default adjustment via ratings-based spreads in data-thin markets and CDS in deeper markets.
• Beta estimation (listed firms): weekly logarithmic total returns over a 5–10 year window; currency alignment between asset and market returns; regression-based beta via market model (Jensen, 1969).
• Beta estimation (private firms): peer identification; unlevering via Equation and relevering via Equation arithmetic averaging of unlevered betas; optional conversion to total beta via Equation when marginal investors are plausibly non-diversified (Bekaert & Harvey, 2003; Damodaran, 2012).
• CRP scaling: volatility computed on consistent frequency and horizon (e.g., 36–60 monthly observations as discussed) to balance sample adequacy with structural change risk.
Methodological Limitations and Threats to Validity
The framework explicitly treats emerging-market cost-of-capital estimation as a sequence of constrained optimizations rather than a single “correct” estimator. The principal limitations are:
1. Risk-free rate purity is unattainable in many emerging markets: sovereign yields embed credit and liquidity risk; ratings lag conditions; CDS can be volatile and unavailable (Damodaran, 2012).
2. Forward-market approaches are maturity-limited: CIRP is theoretically grounded but requires liquid long-tenor forwards not present in many frontier markets.
3. Inflation-based conversions are assumption-intensive: expected inflation is regime-dependent; resulting risk-free rates can be sensitive to forecast error.
4. Pure-play beta depends on peer quality and operating leverage assumptions: peer selection is partly judgmental; operating leverage heterogeneity can bias betas.
5. Accounting beta is susceptible to managerial discretion and low frequency: annual reporting reduces inference power and can confound market-risk interpretation.
6. Total beta may overstate risk if investors are partially diversified: correlation and volatility instability can amplify estimation noise.
7. CRP estimation is imperfectly identified: rating-based spreads may understate equity-relevant risks, while volatility-scaling can overreact during crises (Damodaran, 2012, 2023).

Conclusion

This study contributes to emerging markets finance literature by developing and justifying a systematic, pragmatic framework for cost of equity estimation in data-constrained environments. Rather than advocating a single "correct" methodology, we recognize that optimal approaches depend on country-specific characteristics including financial market development, data availability, and institutional infrastructure. Our analysis yields several important conclusions for both research and practice:
Methodological flexibility is essential. A one-size-fits-all approach to emerging market cost of equity estimation proves both theoretically unjustifiable and practically infeasible. Frontier markets like Georgia and Armenia require different methodological adaptations than more developed emerging markets like Brazil and India. The appropriate methodology must be matched to local market conditions.
Transparency matters more than precision. Given the inherent uncertainty in cost of capital estimation, clearly documenting methodological choices, underlying assumptions, and limitations provides more value than spurious precision. Practitioners benefit from understanding the range of defensible estimates and the sensitivity to key assumptions.
Country risk premium is material and necessary. Standard CAPM beta inadequately captures emerging market risks. Explicitly incorporating country risk premia through either rating-based default spreads or market-based CDS measures substantially improves model realism. The choice between rating-based and CDS-based approaches should depend on data availability and market development.
Local market data frequently proves inadequate. For frontier markets, illiquid local stock markets cannot support reliable regression-based beta estimation. Pure-play methodologies using international comparables provide more robust systematic risk estimates, though at the cost of potentially overlooking country-specific operating conditions.
The theory-practice gap requires pragmatic bridging. Financial theory provides valuable conceptual foundations, but practical implementation in emerging markets inevitably requires compromises. Acknowledging these compromises explicitly, justifying them with reference to empirical constraints, and testing robustness enhances credibility.

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1. Capital Asset Pricing Model (CAPM)

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