Risk and Return: Types, Measurement, Trade-offs and Real Applications

TAKEAWAYS:

• Risk and return are inversely related: higher risk demands higher expected return to compensate investors.
• Risk types include market risk, default risk, inflation risk, and liquidity risk—each requires different mitigation strategies.
• Measuring risk: standard deviation (volatility) and beta (systematic risk) are key metrics in financial analysis.
• Capital Asset Pricing Model (CAPM) links risk (beta) to expected return: $E(R_i)=R_f+{\beta }_i(E(R_m)-R_f)$.
• Portfolio diversification reduces unsystematic risk but cannot eliminate market risk.
• Real-world applications: banks use risk-return trade-offs for loan pricing, NEPSE investors analyze stock betas, and fintech apps (e.g., Khalti) incorporate risk models for digital transactions.

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1. Introduction to Risk and Return

Risk is the uncertainty about future outcomes, while return is the compensation expected for bearing that risk. Investors demand higher returns for higher risk. This principle underpins all financial decisions—from buying stocks to lending money.

Key Definitions

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2. Types of Risk

Risk can be categorized based on its source and impact. Understanding these helps investors and businesses make informed decisions.

A. Financial Risks

1. Market Risk (Systematic Risk)

   • Definition: Risk from overall market movements (e.g., inflation, recessions).
   • Cannot be diversified away.
   • Example: If global oil prices rise, all airlines (e.g., Yeti Airlines) face higher fuel costs.

2. Default Risk (Credit Risk)

   • Definition: Risk that a borrower (e.g., a company or government) fails to repay a loan or meet obligations.
   • Measured by credit ratings (e.g., AAA to D in Nepal’s banking sector).
   • Example: If Global IME Bank defaults on bonds, investors lose money.

3. Inflation Risk

   • Definition: Risk that money’s purchasing power erodes over time.
   • Example: If inflation is 7% but your fixed deposit gives 5%, you lose 2% real return.

4. Liquidity Risk

   • Definition: Risk of not being able to sell an investment quickly without losing value.
   • Example: Trading Nepal Investment Bank’s bonds during a market crash may force you to sell at a loss.

5. Interest Rate Risk

   • Definition: Risk that changes in interest rates affect investment values (e.g., bonds).
   • Example: If NBR raises repo rates, existing bonds lose value.

B. Business Risks

1. Operational Risk

   • Definition: Risk from internal processes (e.g., fraud, errors, system failures).
   • Example: Ncell’s network outage during peak hours loses revenue.

2. Regulatory Risk

   • Definition: Risk from changes in laws or regulations.
   • Example: New SEBON rules forcing banks to hold more capital reduce profits.

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3. Measuring Risk

A. Standard Deviation (Volatility)

• Measures how much returns fluctuate from the average.
• Formula: $$\sigma =\sqrt{\frac{\sum (R_i-\bar{R}{)}^2}{N}}$$ where $R_i$ = individual return, $\bar{R}=$ average return, $N=$ number of observations.
• Interpretation: Higher standard deviation = higher risk.
• Example:
  • Stock A: Returns = [10%, 12%, 8%, 15%], $\sigma =2.5\%$.
  • Stock B: Returns = [5%, 20%, -5%, 10%], $\sigma =8.2\%$.
  • Stock B is riskier despite same average return (10%).

B. Beta (Systematic Risk)

• Measures stock’s sensitivity to market movements.
• Formula: $$\beta =\frac{\text{Covariance}(R_i,R_m)}{\text{Variance}(R_m)}$$ where $R_i=$ stock return, $R_m=$ market return.
• Interpretation:
  • $\beta =1$: Moves with the market (e.g., Nepal Bank Limited).
  • $\beta >1$: More volatile than the market (e.g., Nepal Investment Bank).
  • $\beta <1$: Less volatile (e.g., NMB Bank).
• Example: If NEPSE index rises by 5%, a stock with $\beta =1.5$ is expected to rise by 7.5%.

C. Value at Risk (VaR)

• Estimates maximum potential loss over a given time at a confidence level (e.g., 95%).
• Example: A bank might say, “There’s a 5% chance we lose Rs 50 million in a month.”

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4. Risk-Return Trade-off

Investors cannot have high returns without taking risk. The relationship is visualized by the Efficient Frontier (a curve showing optimal portfolios offering the highest return for a given risk level).

Visual: Efficient Frontier

• Low risk (e.g., fixed deposits): Safe but low returns (~5-7% in Nepal).
• Moderate risk (e.g., bonds): Balanced (e.g., Nepal Government Bonds at ~8-10%).
• High risk (e.g., stocks): Volatile but high growth potential (e.g., Nepal Stock Exchange averages ~12% long-term).

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5. Capital Asset Pricing Model (CAPM)

CAPM explains how risk and return are linked in equilibrium. It calculates the expected return of an asset based on its beta and market conditions.

CAPM Formula

$$E(R_i)=R_f+{\beta }_i[E(R_m)-R_f]$$

• $E(R_i)$: Expected return of the asset.
• $R_f$: Risk-free rate (e.g., Nepal Rastra Bank’s 90-day Treasury bill at 6%).
• ${\beta }_i$: Beta of the asset.
• $E(R_m)$: Expected market return (e.g., NEPSE’s historical average of 10%).

Worked Example: CAPM for a Nepali Stock

Scenario: You’re analyzing Cement India Nepal Limited (CINL) stock.

• Risk-free rate ($R_f$) = 6% (NBR’s 90-day bill).
• Market return ($E(R_m)$) = 10% (NEPSE’s average).
• CINL’s beta ($\beta$) = 1.3 (from historical data).

Calculation: $$E(R_{CINL})=6\%+1.3\times (10\%-6\%)=6\%+5.2\%=11.2\%$$ Interpretation: CINL’s expected return is 11.2%, reflecting its higher risk (beta > 1).

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6. Portfolio Diversification

Diversification reduces unsystematic risk (company-specific risk) but not systematic risk (market risk).

How It Works

• Single Stock: High risk (e.g., investing only in Nepal Investment Bank).
• Diversified Portfolio: Mix of stocks, bonds, and cash to smooth returns.
• Example: A portfolio with Nepal Bank, Global IME, and NMB reduces risk vs. holding just one.

Visual: Diversification Impact

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7. Real-World Applications

A. Banking and Loan Pricing

• Example: Nepal Bank Limited charges higher interest rates for business loans (riskier) than home loans (less risky).
• Risk Premium: If a loan has a 10% default risk, the bank adds a 2-3% premium to the interest rate.

B. Stock Market Investments (NEPSE)

• Example: Nepal Investment Bank’s stock has a beta of 1.5. Investors expect higher returns (e.g., 12-14%) because it’s riskier than NMB Bank (beta ~0.8).
• Dividend Discount Model (DDM): Used to value stocks based on expected dividends and risk. $$P_0=\frac{D_1}{R-g}$$ where $D_1=$ next dividend, $R=$ required return (from CAPM), $g=$ growth rate.

C. Fintech Apps (Khalti, eSewa)

• Risk Management: These apps use credit scoring models to assess borrowers’ risk before approving loans.
• Example: If your Khalti Loan application shows high beta (unstable income), you get a higher interest rate (e.g., 18% vs. 12%).

D. Government Bonds (Nepal Rastra Bank)

• Risk-Free Proxy: NBR’s bonds are considered risk-free (beta = 0).
• Inflation Hedging: Bonds with inflation-linked returns protect investors from purchasing power loss.

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8. Worked Numerical Example: Risk and Return for a Kathmandu Retail Shop

Scenario: Kathmandu Mart, a small retail shop in Thapathali, is deciding whether to expand. The owner has two options:

1. Option A: Invest in a new store (high risk, high return).
2. Option B: Buy government bonds (low risk, low return).

Given Data

Calculations

1. Risk-Return Trade-off:

   • Option A offers 2x the return but with 7.5x the volatility.
   • Option B is safer but yields only 8% (below inflation if it’s >8%).

2. CAPM Validation:

   • Assume:
     • Risk-free rate ($R_f$) = 6% (NBR’s bond).
     • Market return ($E(R_m)$) = 12% (Nepal’s GDP growth proxy).
   • For Option A: $$E(R_A)=6\%+1.8\times (12\%-6\%)=6\%+10.8\%=16.8\%$$ The owner’s expected 20% seems high—this suggests either:
     • The store has unique competitive advantages (e.g., prime location).
     • The owner is risk-seeking.

3. Diversification Suggestion:

   • Instead of all-in on Option A, the owner could:
     • Invest 60% in the store and 40% in bonds to balance risk and return.

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9. Advantages and Disadvantages of Risk Management

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10. Exam Tip

1. Memorize Key Formulas:

   • CAPM: $E(R_i)=R_f+{\beta }_i(E(R_m)-R_f)$.
   • Standard Deviation: $\sigma =\sqrt{\frac{\sum (R_i-\bar{R}{)}^2}{N}}$.
   • Beta: $\beta =\frac{\text{Cov}(R_i,R_m)}{\text{Var}(R_m)}$.

2. Practice Numerical Problems:

   • Past exam questions often test:
     • Calculating expected returns using CAPM.
     • Comparing risk using standard deviation/beta.
     • Portfolio diversification scenarios.

3. Real-World Connections:

   • Link theories to Nepal’s context:
     • How Nepal Rastra Bank manages inflation risk.
     • Why Nepal Investment Bank’s stock has a higher beta than NMB Bank’s.
     • How Khalti uses risk models for loans.

4. Common Pitfalls:

   • Ignoring systematic risk: Diversification can’t eliminate market risk.
   • Misapplying CAPM: Ensure you use the correct $R_f$ and $E(R_m)$.
   • Overlooking inflation: Always adjust nominal returns for inflation in long-term analyses.

5. Diagram-Based Questions:

   • Expect questions on:
     • Efficient Frontier (plot risk vs. return).
     • Risk decomposition (systematic vs. unsystematic).
     • CAPM graph (Security Market Line).

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11. Summary Table: Risk and Return Metrics

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12. Quick Revision Checklist

Before the exam, ensure you can: ✅ Define risk premium, beta, and standard deviation. ✅ Explain the difference between systematic and unsystematic risk. ✅ Apply CAPM to calculate expected returns. ✅ Interpret a beta value (e.g., $\beta =0.8$ vs. $\beta =1.5$). ✅ Describe how diversification reduces risk. ✅ Relate Nepal’s financial environment (NEPSE, NBR, banks) to risk-return concepts.