Risk & Return: Measuring, Comparing and Managing Financial Risk

TAKEAWAYS:

• Risk ≠ Return: Higher returns require higher risk; CAPM quantifies this tradeoff using beta and the market risk premium.
• Beta > 1: Stocks like NEPSE’s top performers (e.g., NMB Bank) move more than the market; beta < 1 (e.g., utility stocks) move less.
• Diversification: Combining uncorrelated assets (e.g., stocks + bonds) reduces unsystematic risk without sacrificing expected return.
• Real-world tools: Use Excel’s =STDEV.P(), =BETA(), or =IRR() to calculate metrics for Kathmandu Manufacturing Co. or Gandaki Hydropower’s projects.
• Risk types: Systematic (market-wide, e.g., inflation) vs. unsystematic (company-specific, e.g., a Daraz delivery strike).
• CAPM formula: $E(R_i)=R_f+{\beta }_i\times (R_m-R_f)$. Plug in NEPSE’s 10% average return and 4% risk-free rate (treasury bills) to find required returns.

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1. Definitions: Risk and Return in Finance

Risk is the probability and magnitude of losing money (or missing expected gains). Return is the compensation for taking that risk, measured as:

• Nominal return: $R=\frac{P_1-P_0+D}{P_0}$, where $P_0$ = initial price, $P_1$ = selling price, $D$ = dividends.
• Real return: Adjusts for inflation: $R_{\text{real}}=(1+R_{\text{nominal}})/(1+\text{inflation})-1$.

Types of Risk

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2. Measuring Risk: Standard Deviation and Variance

Risk is quantified by how much returns deviate from the mean. Use:

• Variance (${\sigma }^2$): Average of squared deviations. ${\sigma }^2=\frac{\sum (R_i-\bar{R}{)}^2}{n}$
• Standard Deviation ($\sigma$): Square root of variance (in percentage points).

Worked Example: NEPSE vs. Stock J

Calculations:

1. Mean returns: ${\bar{R}}_{\text{NEPSE}}=(15+10-5+20+10)/5=9.2\%$ ${\bar{R}}_J=(20+15+5+20+20)/5=16\%$

2. Variance for NEPSE: ${\sigma }^2=[(15-9.2{)}^2+(10-9.2{)}^2+(-5-9.2{)}^2+(20-9.2{)}^2+(10-9.2{)}^2]/5$ $=[33.64+0.64+193.64+118.84+0.64]/5=74.32$ ${\sigma }_{\text{NEPSE}}=\sqrt{74.32}=8.62\%$

3. Variance for Stock J: ${\sigma }_J^2=[(20-16{)}^2+(15-16{)}^2+(5-16{)}^2+(20-16{)}^2+(20-16{)}^2]/5$ $=[16+1+121+16+16]/5=36$ ${\sigma }_J=\sqrt{36}=6\%$

Interpretation:

• Stock J has lower volatility (6% vs. 8.62%) but higher average return (16% vs. 9.2%).
• Risk-return tradeoff: Stock J offers better compensation for its risk.

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3. Beta: Measuring Systematic Risk

Beta ($\beta$) measures how a stock’s returns move with the market. Formula: $${\beta }_i=\frac{\text{Covariance}(R_i,R_m)}{\text{Variance}(R_m)}$$

• $\beta =1$: Moves with the market (e.g., NEPSE index itself).
• $\beta >1$: More volatile than the market (e.g., NMB Bank: $\beta =1.3$).
• $\beta <1$: Less volatile (e.g., utility stocks like Nepal Electricity Authority).

Worked Example: Calculating Beta for Stock X Given:

• Market risk premium ($R_m-R_f$) = 6% (NEPSE avg return - treasury bill rate).
• Risk-free rate ($R_f$) = 4% (treasury bills).
• Stock X’s beta (${\beta }_X$) = 1.5.

Required Return Using CAPM: $$E(R_X)=R_f+{\beta }_X\times (R_m-R_f)$$ $$E(R_X)=4\%+1.5\times 6\%=4\%+9\%=13\%$$

Real-world tie-in:

• Gandaki Hydropower Company (GTC): If GTC’s stock has $\beta =1.2$, its required return is: $4\%+1.2\times 6\%=11.2\%$. Investors demand 11.2% to compensate for GTC’s systematic risk.

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4. Portfolio Risk: Diversification

Unsystematic risk can be eliminated by combining assets with low correlation. Example:

Portfolio Variance Formula: $${\sigma }_p^2=w_1^2{\sigma }_1^2+w_2^2{\sigma }_2^2+2w_1{w}_2{\sigma }_1{\sigma }_2{\rho }_{1,2}$$ Where:

• $w$ = weight of each stock in the portfolio.
• $\rho$ = correlation coefficient.

Example: A portfolio with 50% NMB Bank and 50% Global Ime: $${\sigma }_p^2=0.5^2\times 10^2+0.5^2\times 8^2+2\times 0.5\times 0.5\times 10\times 8\times 0.3$$ $$=25+16+6=47$$ $${\sigma }_p=\sqrt{47}=6.85\%$$ Result: Portfolio risk (6.85%) < individual risks (10% and 8%).

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5. Capital Asset Pricing Model (CAPM)

CAPM links risk and return for efficient markets. Key assumptions:

1. Investors are rational and seek to maximize returns for a given risk.
2. All assets are perfectly divisible.
3. No taxes or transaction costs.

CAPM Equation: $$E(R_i)=R_f+{\beta }_i(R_m-R_f)$$ Where:

• $E(R_i)$ = Expected return of asset $i$.
• $R_f$ = Risk-free rate (e.g., 4% for Nepal’s treasury bills).
• $R_m$ = Expected market return (e.g., NEPSE’s 10% historical avg).
• ${\beta }_i$ = Stock’s beta.

Worked Example: Kathmandu Manufacturing Co. (KMC)

• KMC’s stock has $\beta =1.2$.
• Current NEPSE return ($R_m$) = 10%, risk-free rate ($R_f$) = 4%.
• Required return for KMC: $E(R_{\text{KMC}})=4\%+1.2\times (10\%-4\%)=4\%+7.2\%=11.2\%$.

Interpretation:

• KMC’s stock should offer 11.2% to compensate for its risk.
• If KMC offers only 8%, investors will sell it (undervalued).
• If KMC offers 15%, investors will buy it (overvalued).

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6. Risk and Return Tradeoff

The Security Market Line (SML) plots expected return vs. beta:

Expected Return (%)
   ^
15 |               *
   |              /
10 |             /
   |            /
5  |-----------*---------> Beta
   |          /
   |         /
0  |________/

• Above SML: Overpriced (buy).
• Below SML: Underpriced (sell).
• On SML: Fairly priced.

Real-world Application: NEPSE Stocks

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In the Real World

1. eSewa and Khalti (Digital Payments)

   • Risk: Cybersecurity breaches (unsystematic risk).
   • Return: High growth potential ($\beta \approx 1.4$) justifies investor returns.
   • CAPM Use: Khalti’s investors demand $4\%+1.4\times 6\%=12.4\%$ return.

2. Daraz (E-commerce)

   • Risk: Supply chain disruptions (systematic) + driver strikes (unsystematic).
   • Diversification: Daraz holds cash reserves (liquidity risk management) and uses algorithms to balance inventory (operating risk).

3. Nepal Rastra Bank (NRB) and Interest Rates

   • Risk-free rate: NRB’s policy rate (currently ~6%) sets $R_f$.
   • CAPM for Banks: If a bank’s stock has $\beta =0.9$, its required return is $6\%+0.9\times 4\%=9.6\%$. Banks like NMB Bank must offer this to attract investors.

4. Gandaki Hydropower Company (GTC)

   • Project Risk: High initial cost but stable returns ($\beta \approx 0.7$ due to government contracts).
   • CAPM Calculation: $4\%+0.7\times 6\%=8.2\%$. GTC’s 7% actual return suggests it’s undervalued.

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7. Limitations of CAPM

Alternative Models:

• Arbitrage Pricing Theory (APT): Uses multiple factors (e.g., inflation, oil prices).
• Fama-French 3-Factor Model: Adds size and value factors.

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Exam Tip

1. CAPM is the star: Always use $E(R)=R_f+\beta (R_m-R_f)$. Memorize:

   • $R_f$ = Risk-free rate (given in exams, e.g., 4%).
   • $R_m-R_f$ = Market risk premium (given or assume 6% for NEPSE).
   • $\beta$ = Given or calculate from covariance/variance.

2. Risk vs. Return: Exams test your ability to compare assets. Example:

   • Stock A: $\sigma =12\%$, $E(R)=15\%$.
   • Stock B: $\sigma =8\%$, $E(R)=10\%$.
   • Answer: Stock A offers better risk-return tradeoff (higher Sharpe ratio).

3. Diversification: If asked how to reduce risk, say:

   • Combine stocks with low correlation (e.g., banks + hydropower).
   • Avoid putting all funds in NEPSE (systematic risk remains).

4. Numerical traps:

   • Always check if returns are nominal or real.
   • For beta, use market returns, not individual stock means.
   • Standard deviation is in percentage points, not decimals.

5. Real-world questions:

   • If asked about Kathmandu Manufacturing Co., assume:
     • $\beta =1.1$, $R_m=10\%$, $R_f=4\%$.
     • Calculate required return and compare to actual returns.
   • For Gandaki Hydropower, highlight low beta (stable cash flows) vs. high-return but risky stocks.

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