19 Chapter 8 Risk and return

Conceptual Questions

1. 1. Risk is measured by two key factors: probability and magnitude of outcomes. Higher probability of a negative outcome increases overall risk. The magnitude of loss or gain also affects risk: a small loss is less risky than a large loss, even if they have the same probability.
   2. Systematic risk (market risk) affects the entire economy or market, such as recessions, inflation, interest rate changes, and geopolitical risks. This type of risk cannot be eliminated through diversification. Unsystematic risk (firm-specific risk) is unique to a company or industry, such as management changes, lawsuits, or product failures. This risk can be reduced by holding a diversified portfolio of stocks across different sectors.
   3. Diversification reduces unsystematic risk by spreading investments across different asset types (stocks, bonds, real estate, etc.). Diversification does not eliminate systematic risk since market-wide factors (e.g., recessions) impact all assets. For example, if an investor owns stocks in both the technology and healthcare industries, a downturn in tech stocks may be offset by stability in healthcare stocks.
   4. Expected return is the weighted average of possible returns based on probability. It represents the long-term average return of an investment. Standard deviation measures risk by showing how much returns deviate from the expected return. A higher standard deviation means higher risk because returns fluctuate more. For example, if Investment A has an expected return of 10% and a standard deviation of 8%, while Investment B also has an expected return of 10% but a standard deviation of 15%, Investment B is riskier because its returns are more volatile, even though the expected returns are the same.
   5. Beta measures how sensitive an asset is to market movements. A beta greater than 1 means the stock is more volatile than the market (e.g., tech stocks). A beta less than 1 means the stock is less volatile than the market (e.g., utilities, consumer staples). A beta of 1 means the stock moves in line with the market. For example, if the market increases by 5%, a stock with a beta of 1.5 would be expected to rise by 7.5% (1.5 × 5%).
   6. The Capital Asset Pricing Model (CAPM) formula is Expected Return = Risk-Free Rate + Beta × (Market Return – Risk-Free Rate). This helps determine the fair return on an asset given its risk (beta). The Security Market Line (SML) represents CAPM graphically. If an asset lies above the SML, it is undervalued (offering a higher return than required for its risk).

Short Calculations

1. Expected Return Calculation: Given probability and returns: Recession (20%) → -10%, Normal Growth (50%) → 6%, Boom (30%) → 15%. Using the formula:

E(R) = (0.20 × -10%) + (0.50 × 6%) + (0.30 × 15%) = -2% + 3% + 4.5% = 5.5%

2. Standard Deviation Calculation:

σ = √[(0.20 × (-10% – 5.5%)²) + (0.50 × (6% – 5.5%)²) + (0.30 × (15% – 5.5%)²)]

= √[(0.20 × 240.25) + (0.50 × 0.25) + (0.30 × 90.25)]

= √(48.05 + 0.125 + 27.075) = √75.25 = 8.68%

3. Portfolio Expected Return Calculation: Stock A has an expected return of 8%, Stock B has an expected return of 12%, and portfolio weights are 50% in A and 50% in B. Using the formula:

E(R_p) = (0.5 × 8%) + (0.5 × 12%) = 4% + 6% = 10%

4. Beta Calculation: Given market variance = 0.04 and stock covariance with the market = 0.06. Using the formula:

β = Covariance of stock and market / Variance of market

β = 0.06 / 0.04 = 1.5

5. CAPM Expected Return: Given risk-free rate = 3%, market return = 10%, and beta = 1.2. Using the formula:

E(R) = 3% + 1.2 × (10% – 3%)

= 3% + 1.2 × 7% = 3% + 8.4% = 11.4%

Scenario-Based Problems

1. Diversification Decision: Adding bonds to a portfolio can reduce overall risk because bonds typically have low or negative correlation with stocks. If stocks decline, bonds may hold steady or increase in value.

2. Interpreting Beta Values: A stock with beta 1.8 will experience larger fluctuations than the market. If the market drops 5%, this stock will likely decline 9% (1.8 × 5%). A stock with beta 0.6 will move less, only dropping 3% (0.6 × 5%).

3. Investment Choices & Risk: Stock A has low risk (standard deviation of 8%), making it suitable for risk-averse investors. A well-diversified portfolio can help balance risk and return.

4. Applying CAPM in Decision-Making: Required return = 11.2%. If a project is offering 11%, it is slightly below the required return, meaning it may not be worth investing in.

5. Refining Investment Strategies: Investment A has a higher beta, making it more volatile. A risk-averse investor should consider a lower-beta investment.

Interactive Challenge

1. Risk Classification Exercise: Recession impacts all industries → Systematic Risk. Pharmaceutical company lawsuit → Unsystematic Risk. Interest rate increase → Systematic Risk. CEO resignation → Unsystematic Risk.

2. Portfolio Allocation: A balanced portfolio could be structured as 40% stocks, 30% bonds, 20% real estate, and 10% cash to maintain stability while growing investments.