4.4 Investment Return, Risk Metrics, and Portfolio Principles

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1.1 Philippine Corporate Formation and Capital Structure 1.2 Common and Preferred Shares 1.3 Stockholder Rights and Corporate Actions 1.4 Corporate Debt and Fixed Income Instruments

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4 Chapter 4: Financial Mathematics and Valuation Concepts

4.1 Time Value of Money and Interest Calculations 4.2 Bond Valuation and Yield Concepts 4.3 Equity Valuation Metrics and Financial Ratios 4.4 Investment Return, Risk Metrics, and Portfolio Principles

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10 Chapter 10: Risk Concepts and Categories

10.1 Risk, Uncertainty, and Objectives 10.2 Financial Risks: Market, Credit, and Liquidity 10.3 Non-Financial Risks: Operational, Strategic, and Reputational

11 Chapter 11: Risk Management Process

11.1 Risk Management: Coordinated Direction and Control 11.2 Risk Identification 11.3 Risk Analysis and Evaluation

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14 Chapter 14: Customer Due Diligence, Reporting & Record Keeping

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4.4 Investment Return, Risk Metrics, and Portfolio Principles

Key Takeaways Explain This Topic AI

Holding Period Return (HPR) captures total investment performance combining capital gains and cash distributions relative to the initial acquisition cost (HPR = (P_1 - P_0 + D) / P_0); across multiple periods, geometric mean return reflects true compound wealth accumulation, whereas arithmetic mean overstates multi-period returns.

Total investment risk is quantified by variance and standard deviation, which measure the dispersion of actual returns around the expected mean return; a higher standard deviation indicates greater historical volatility and wider dispersion of potential outcomes.

Total portfolio risk divides into systematic (market-wide, non-diversifiable) risk and unsystematic (firm-specific, diversifiable) risk; broad diversification across imperfectly correlated assets can substantially reduce unsystematic risk but does not guarantee its complete elimination.

Beta (β) measures an individual security's sensitivity to broad market movements; the Capital Asset Pricing Model (CAPM) establishes that an asset's expected return equals the risk-free rate plus a market risk premium scaled by Beta (E(R_i) = R_f + β_i * [E(R_m) - R_f]).

The Sharpe ratio measures excess return generated per unit of total risk ((R_p - R_f) / σ_p); Modern Portfolio Theory (MPT) demonstrates that combining imperfectly correlated assets (ρ < 1) reduces overall portfolio variance without a commensurate reduction in expected return.

Last updated: October 2026

4.4 Investment Return, Risk Metrics, and Portfolio Principles

Every investment decision in the capital markets embodies a fundamental trade-off: risk versus return . Rational investors demand higher expected returns to compensate for accepting greater uncertainty. For securities professionals preparing for the Philippine SEC Certification Examination Phase 1, understanding how to calculate historical returns, quantify dispersion, decompose systematic and unsystematic risks, and apply portfolio diversification principles is vital for advising retail and institutional clients.

Investment Return Measurements

Return measures the financial gain or loss generated on an investment relative to the capital committed.

Holding Period Return (HPR)

Holding Period Return (HPR) represents the total return generated over the entire timeframe an asset is held, irrespective of the calendar length of that period. Total return comprises two distinct components:

Capital Gain/Loss Yield : Price change relative to initial cost ( [ P 1 − P 0 ] / P 0 [P_1 - P_0] / P_0 [ P 1 ​ − P 0 ​ ] / P 0 ​ ).

Income Yield (Dividend or Coupon Yield) : Cash distributions received ( D / P 0 D / P_0 D / P 0 ​ ).

The combined formula is: H P R = P 1 − P 0 + D P 0 = P 1 − P 0 P 0 + D P 0 HPR = \frac{P_1 - P_0 + D}{P_0} = \frac{P_1 - P_0}{P_0} + \frac{D}{P_0} H PR = P 0 ​ P 1 ​ − P 0 ​ + D ​ = P 0 ​ P 1 ​ − P 0 ​ ​ + P 0 ​ D ​

Where:

• P 0 P_0 P 0 ​ = Initial purchase price
• P 1 P_1 P 1 ​ = Ending market price (or sale price)
• D D D = Total cash dividends or interest coupons received during the holding period
• Annualized Return

Because holding periods vary across investments (e.g., 90 days vs. 3 years), returns must be annualized to enable valid comparisons:

Compound Annual Growth Rate (CAGR) : Annualized Return = ( 1 + H P R ) 1 / t − 1 = ( 1 + H P R ) 365 Days − 1 \text{Annualized Return} = (1 + HPR)^{1/t} - 1 = (1 + HPR)^{\frac{365}{\text{Days}}} - 1 Annualized Return = ( 1 + H PR ) 1/ t − 1 = ( 1 + H PR ) Days 365 ​ − 1

Arithmetic vs. Geometric Mean Return

When evaluating historical investment performance over multiple consecutive years, analysts use two divergent averaging methodologies:

Arithmetic Mean : The simple numerical average of annual returns: R ˉ arithmetic = ∑ t = 1 n R t n \bar{R}_{\text{arithmetic}} = \frac{\sum_{t=1}^n R_t}{n} R ˉ arithmetic ​ = n ∑ t = 1 n ​ R t ​ ​

Geometric Mean (Compound Annual Return) : The constant rate that compounds the initial capital to the final terminal wealth: R geometric = [ ∏ t = 1 n ( 1 + R t ) ] 1 / n − 1 = [ ( 1 + R 1 ) ( 1 + R 2 ) ⋯ ( 1 + R n ) ] 1 / n − 1 R_{\text{geometric}} = \left[ \prod_{t=1}^n (1 + R_t) \right]^{1/n} - 1 = \left[ (1 + R_1)(1 + R_2)\cdots(1 + R_n) \right]^{1/n} - 1 R geometric ​ = [ ∏ t = 1 n ​ ( 1 + R t ​ ) ] 1/ n − 1 = [ ( 1 + R 1 ​ ) ( 1 + R 2 ​ ) ⋯ ( 1 + R n ​ ) ] 1/ n − 1

The Mathematical Volatility Drag

Whenever annual returns exhibit volatility, the geometric mean is strictly less than the arithmetic mean ( R geom ≤ R arith R_{\text{geom}} \le R_{\text{arith}} R geom ​ ≤ R arith ​ ). The difference between them widens as return volatility increases.

Classic Illustrative Example :

An investor purchases a PSE-listed mining stock at Php 100:

In Year 1, the stock surges +50% to Php 150.

In Year 2, the stock plunges -50% to Php 75.

Arithmetic Mean : [ ( + 50 % ) + ( − 50 % ) ] / 2 = 0.0 % [(+50\%) + (-50\%)] / 2 = \mathbf{0.0\%} [( + 50% ) + ( − 50% )] /2 = 0.0%

Actual Investor Wealth : The investor started with Php 100 and ended with Php 75, suffering an actual -25% total loss over 2 years.

Geometric Mean : ( 1 + 0.50 ) ( 1 − 0.50 ) − 1 = 1.50 × 0.50 − 1 = 0.75 − 1 = 0.8660 − 1 = − 13.40 % \sqrt{(1 + 0.50)(1 - 0.50)} - 1 = \sqrt{1.50 \times 0.50} - 1 = \sqrt{0.75} - 1 = 0.8660 - 1 = \mathbf{-13.40\%} ( 1 + 0.50 ) ( 1 − 0.50 ) ​ − 1 = 1.50 × 0.50 ​ − 1 = 0.75 ​ − 1 = 0.8660 − 1 = − 13.40% per year.

Important

Exam Rule: Which Mean to Use?

Use the Geometric Mean when evaluating past multi-period compound performance and terminal wealth accumulation.

Use the Arithmetic Mean as the unbiased statistical estimator of expected return in a single upcoming future period.

Quantifying Investment Risk: Variance and Standard Deviation

Risk in modern finance is defined as the dispersion, uncertainty, or volatility of actual outcomes around the expected mean return.

Expected Return

Given a set of n n n mutually exclusive economic scenarios, each with probability p i p_i p i ​ and anticipated return R i R_i R i ​ , the Expected Return ( E ( R ) E(R) E ( R ) ) is: E ( R ) = ∑ i = 1 n p i R i E(R) = \sum_{i=1}^n p_i R_i E ( R ) = ∑ i = 1 n ​ p i ​ R i ​

Variance and Standard Deviation

Variance ( σ 2 \sigma^2 σ 2 ) : The probability-weighted sum of squared deviations from the expected return: σ 2 = ∑ i = 1 n p i [ R i − E ( R ) ] 2 \sigma^2 = \sum_{i=1}^n p_i \left[ R_i - E(R) \right]^2 σ 2 = ∑ i = 1 n ​ p i ​ [ R i ​ − E ( R ) ] 2

Standard Deviation ( σ \sigma σ ) : The square root of variance, returning risk to the same percentage units as the return: σ = σ 2 = ∑ i = 1 n p i [ R i − E ( R ) ] 2 \sigma = \sqrt{\sigma^2} = \sqrt{\sum_{i=1}^n p_i \left[ R_i - E(R) \right]^2} σ = σ 2 ​ = ∑ i = 1 n ​ p i ​ [ R i ​ − E ( R ) ] 2 ​

Under a normal distribution curve:

• 68.26% of annual returns fall within E ( R ) ± 1 σ E(R) \pm 1\sigma E ( R ) ± 1 σ
• 95.44% of annual returns fall within E ( R ) ± 2 σ E(R) \pm 2\sigma E ( R ) ± 2 σ
• 99.74% of annual returns fall within E ( R ) ± 3 σ E(R) \pm 3\sigma E ( R ) ± 3 σ
• Systematic vs. Unsystematic Risk

Total risk (measured by standard deviation σ \sigma σ ) consists of two distinct components: Total Risk = Systematic (Market) Risk + Unsystematic (Firm-Specific) Risk \text{Total Risk} = \text{Systematic (Market) Risk} + \text{Unsystematic (Firm-Specific) Risk} Total Risk = Systematic (Market) Risk + Unsystematic (Firm-Specific) Risk Portfolio Risk (σ)

• ▲
• │ Total Risk
• │ .---------------
• │ /
• │ / Unsystematic (Diversifiable Risk - reduced through broad diversification)
• │ / Risk
• │/─────────────────── Constant Systematic Risk (Non-diversifiable)
• │
• └────────────────────────► Number of Stocks in Portfolio
• Comparison of Risk Dimensions

Feature Unsystematic Risk Systematic Risk

Alternative Terminology Specific, Idiosyncratic, Diversifiable Risk Market Risk, Non-Diversifiable, Undiversifiable Risk

Root Causes Executive departure, labor strikes, product recalls, corporate litigation, factory fires. Inflation surges, BSP interest rate hikes, GDP contractions, currency shocks, global pandemics.

Scope of Impact Confined strictly to a single company or narrow industrial sub-sector. Simultaneously affects all securities across the entire macroeconomic system.

Mitigation Strategy Substantially reduced through broad diversification across imperfectly correlated holdings, but never guaranteed to be exactly zero. Cannot be eliminated through diversification within that asset class; mitigated only by asset allocation or hedging.

Market Pricing Zero compensation . Efficient capital markets do not reward investors for bearing diversifiable risk. Compensated . Expected returns are directly tied to an asset's exposure to systematic risk.

Beta ( β \beta β ) and the Capital Asset Pricing Model (CAPM)

Because investors can diversify much firm-specific risk at comparatively low cost, equilibrium pricing models such as CAPM focus on non-diversifiable systematic risk. Beta ( β \beta β ) measures the sensitivity of a security's returns relative to movements in the broad market benchmark (such as the Philippine Stock Exchange Index - PSEi).

Calculating Beta

β i = Cov ( R i , R m ) σ m 2 = ρ i , m σ i σ m σ m 2 = ρ i , m × σ i σ m \beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \frac{\rho_{i,m} \sigma_i \sigma_m}{\sigma_m^2} = \rho_{i,m} \times \frac{\sigma_i}{\sigma_m} β i ​ = σ m 2 ​ Cov ( R i ​ , R m ​ ) ​ = σ m 2 ​ ρ i , m ​ σ i ​ σ m ​ ​ = ρ i , m ​ × σ m ​ σ i ​ ​

Where:

Cov ( R i , R m ) \text{Cov}(R_i, R_m) Cov ( R i ​ , R m ​ ) = Covariance between security i i i and market m m m

• σ m 2 \sigma_m^2 σ m 2 ​ = Variance of the market benchmark
• ρ i , m \rho_{i,m} ρ i , m ​ = Correlation coefficient between security i i i and the market
• σ i , σ m \sigma_i, \sigma_m σ i ​ , σ m ​ = Standard deviations of security i i i and the market

Interpreting Beta Values :

β = 1.0 \mathbf{\beta = 1.0} β = 1.0 : The stock possesses average market risk; moves in tandem with the PSEi.

β > 1.0 \mathbf{\beta > 1.0} β > 1.0 : Aggressive Stock . More volatile than the market (e.g., property developers, tech startups with β = 1.4 \beta = 1.4 β = 1.4 ).

β < 1.0 \mathbf{\beta < 1.0} β < 1.0 : Defensive Stock . Less volatile than the market (e.g., regulated electric utilities like Meralco, consumer staple food manufacturers with β = 0.7 \beta = 0.7 β = 0.7 ).

β = 0.0 \mathbf{\beta = 0.0} β = 0.0 : Asset is completely uncorrelated with market movements (e.g., default-free Philippine Treasury bills).

β < 0.0 \mathbf{\beta < 0.0} β < 0.0 : Rare asset moving inversely to the broad market (e.g., gold mining equities or inverse hedging instruments).

The CAPM Equation

Formulated by William Sharpe, John Lintner, and Jan Mossin, the Capital Asset Pricing Model (CAPM) determines the required rate of return for any risky asset based on its systematic risk: E ( R i ) = R f + β i × [ E ( R m ) − R f ] E(R_i) = R_f + \beta_i \times \left[ E(R_m) - R_f \right] E ( R i ​ ) = R f ​ + β i ​ × [ E ( R m ​ ) − R f ​ ]

Where:

E ( R i ) E(R_i) E ( R i ​ ) = Required or expected rate of return on security i i i

R f R_f R f ​ = Risk-free rate of return (conventionally proxied in the Philippines by benchmark sovereign debt, such as 91-day T-Bills or 10-year FXTNs)

E ( R m ) E(R_m) E ( R m ​ ) = Expected return on the market portfolio (represented by the PSEi)

[ E ( R m ) − R f ] \left[ E(R_m) - R_f \right] [ E ( R m ​ ) − R f ​ ] = Market Risk Premium (MRP) , representing the excess compensation investors demand for holding equities over riskless sovereign debt

β i × [ E ( R m ) − R f ] \beta_i \times \left[ E(R_m) - R_f \right] β i ​ × [ E ( R m ​ ) − R f ​ ] = Asset's individual risk premium

Jensen's Alpha ( α \alpha α )

Alpha ( α \alpha α ) measures excess return earned beyond what is predicted by the CAPM: α = R actual − E ( R i ) \alpha = R_{\text{actual}} - E(R_i) α = R actual ​ − E ( R i ​ )

α > 0 \alpha > 0 α > 0 : Security generated superior risk-adjusted return (undervalued, beat the benchmark).

α < 0 \alpha < 0 α < 0 : Security underperformed given its systematic risk level.

Risk-Adjusted Performance: The Sharpe Ratio

Evaluating performance purely on nominal returns is dangerous; a portfolio manager who generates 15% return by taking triple the risk of the market may be destroying risk-adjusted value.

The Sharpe Ratio Formula

Developed by Nobel laureate William Sharpe, the Sharpe Ratio measures the excess return generated per unit of total risk (standard deviation): Sharpe Ratio = R p − R f σ p \text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p} Sharpe Ratio = σ p ​ R p ​ − R f ​ ​

Where:

• R p R_p R p ​ = Realized or expected portfolio return
• R f R_f R f ​ = Risk-free rate
• σ p \sigma_p σ p ​ = Standard deviation of portfolio returns (total risk)
• Sharpe Ratio vs. Treynor Ratio

Metric Denominator (Risk Measure) Risk Captured Appropriate Portfolio Application

Sharpe Ratio Standard Deviation ( σ p \sigma_p σ p ​ ) Total Risk (Systematic + Unsystematic) Undiversified portfolios , single mutual funds, total client wealth allocations

Treynor Ratio Beta ( β p \beta_p β p ​ ) Systematic Risk Only Well-diversified sub-portfolios added to an already fully diversified holding

Modern Portfolio Theory (MPT) and Diversification

Introduced by Harry Markowitz in 1952, Modern Portfolio Theory (MPT) mathematically proved that investors can reduce portfolio risk without sacrificing expected return by combining assets with imperfect correlations.

Two-Asset Portfolio Expected Return and Variance

Expected Return of a Two-Asset Portfolio : E ( R p ) = w 1 E ( R 1 ) + w 2 E ( R 2 ) E(R_p) = w_1 E(R_1) + w_2 E(R_2) E ( R p ​ ) = w 1 ​ E ( R 1 ​ ) + w 2 ​ E ( R 2 ​ )

Variance of a Two-Asset Portfolio : σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2 w 1 w 2 Cov 1 , 2 \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \text{Cov}_{1,2} σ p 2 ​ = w 1 2 ​ σ 1 2 ​ + w 2 2 ​ σ 2 2 ​ + 2 w 1 ​ w 2 ​ Cov 1 , 2 ​ σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2 w 1 w 2 σ 1 σ 2 ρ 1 , 2 \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \rho_{1,2} σ p 2 ​ = w 1 2 ​ σ 1 2 ​ + w 2 2 ​ σ 2 2 ​ + 2 w 1 ​ w 2 ​ σ 1 ​ σ 2 ​ ρ 1 , 2 ​

Where w 1 , w 2 w_1, w_2 w 1 ​ , w 2 ​ are portfolio weights ( w 1 + w 2 = 1 w_1 + w_2 = 1 w 1 ​ + w 2 ​ = 1 ), and ρ 1 , 2 \rho_{1,2} ρ 1 , 2 ​ is the correlation coefficient between Asset 1 and Asset 2 (ranging from − 1.0 -1.0 − 1.0 to + 1.0 +1.0 + 1.0 ).

The Power of Correlation ( ρ \rho ρ )

Perfect Positive Correlation ( ρ = + 1.0 \rho = +1.0 ρ = + 1.0 ) : No risk reduction occurs; portfolio standard deviation is simply the weighted average of individual asset standard deviations.

Imperfect Correlation ( ρ < + 1.0 \rho < +1.0 ρ < + 1.0 ) : Diversification benefits occur . Portfolio standard deviation is strictly less than the weighted average of individual standard deviations.

Perfect Negative Correlation ( ρ = − 1.0 \rho = -1.0 ρ = − 1.0 ) : All risk can theoretically be completely eliminated, creating a riskless portfolio.

Practical Exam Traps & Regulatory Context

Warning

Exam Trap: Confusing Standard Deviation with Beta Always verify whether an exam question asks for total risk or systematic risk :

If the question asks for total risk , the metric is Standard Deviation ( σ \sigma σ ) .

If the question asks for market/systematic risk , the metric is Beta ( β \beta β ) .

Do not plug standard deviation into the CAPM formula, and do not use Beta in the denominator of the Sharpe ratio.

Note

Regulatory Context: Collective Investment Schemes Under SEC Memorandum Circulars governing Mutual Funds (Investment Companies under RA 2629) and BSP regulations governing Unit Investment Trust Funds (UITFs), investment managers are bound by statutory single-issuer concentration limits (conventionally capping exposure to a single corporate entity at 10% to 15% of Net Asset Value). This regulatory constraint enforces unsystematic risk diversification by law.