Chapter 8 Risks and Rates of Return

Summary

The video explains how to calculate a stock's expected return and assess its risk. Using Mike's company stock as an example, it demonstrates computing the expected return by weighting potential outcomes based on different economic scenarios. It then shows how to measure risk through standard deviation and the coefficient of variation, which standardizes risk per unit of return. Finally, the video introduces the Capital Asset Pricing Model (CAPM), illustrating how to calculate a stock’s required return using the risk-free rate, market return, and beta, highlighting the impact of market-related risk. The content combines practical calculations with clear financial concepts for investors.

Takeaways

• 📈 The expected return is the weighted average of possible investment outcomes based on their probabilities.
• 💡 Mike identifies three possible economic states for next year: strong, normal, and weak.
• 🔢 The probabilities for each state are: strong 30%, normal 40%, and weak 30%.
• 💰 Stock returns for each economic state are: strong 80%, normal 10%, and weak -60%.
• 🧮 Expected return is calculated by multiplying each state's probability by its corresponding return and summing the results, yielding 10% for Mike’s stock.
• ⚠️ Standard deviation measures stand-alone risk by quantifying the variability of returns from the expected return, calculated as 54.22% for Mike’s stock.
• 📊 Coefficient of variation standardizes risk per unit of return and is calculated by dividing standard deviation by expected return, giving a value of 5.42.
• 🏦 The Capital Asset Pricing Model (CAPM) determines a stock’s required return based on risk-free rate, market return, and beta.
• 📉 CAPM adjusts for systematic risk using beta, reflecting how a stock’s returns move with the market.
• 💹 Using CAPM with a risk-free rate of 6%, market return of 11%, and beta of 2, Mike’s required return is 16%, higher than the expected return, indicating higher perceived risk.

Q & A

What is the expected rate of return for an investment?

The expected rate of return is the rate anticipated to be realized from an investment, calculated as the weighted average of the probability distribution of all possible outcomes.

What are the three possible states of the economy considered in Mike's analysis?

The three possible states are strong, normal, and weak.

How does Mike calculate the expected return for his stock?

Mike multiplies the probability of each economic state by the expected stock return for that state, then sums these products to get the expected return.

What is the expected return for Mike's stock given the probabilities and returns provided?

The expected return is 10%, calculated as (0.3 × 0.8) + (0.4 × 0.1) + (0.3 × -0.6) = 0.10 or 10%.

How is the standard deviation used to measure the risk of a stock?

Standard deviation measures the stock's standalone risk by showing how much the actual returns deviate from the expected return. It is calculated using the variance, which accounts for the probability-weighted squared differences from the expected return.

What is the standard deviation of Mike's stock returns?

The standard deviation is approximately 54.22%, indicating the degree of variability or risk around the expected return.

What is the coefficient of variation and why is it useful?

The coefficient of variation (CV) is the standard deviation divided by the expected return. It provides a standardized measure of risk per unit of expected return, allowing comparison across different investments.

How is the CAPM formula structured for calculating the required return?

The CAPM formula is: Required Return = Risk-free rate + Beta × (Market Return − Risk-free rate). It calculates the return required for a stock considering market risk.

Using CAPM, what is the required return for Mike's stock with a beta of 2, risk-free rate of 6%, and market rate of 11%?

The required return is 16%, calculated as 0.06 + 2 × (0.11 − 0.06) = 0.16 or 16%.

Why does CAPM use the beta coefficient in determining required return?

Beta measures the extent to which a stock's returns move with the overall market. CAPM uses it to adjust the required return for the stock’s market-related risk beyond standalone risk.

What is the difference between expected return and required return?

Expected return is the average return an investor anticipates based on probabilities, while required return is the minimum return an investor expects based on risk, typically calculated using models like CAPM.

Why might an investor use both expected return and standard deviation when evaluating a stock?

Expected return indicates potential gain, while standard deviation shows the risk or volatility. Using both provides a fuller picture of risk-adjusted investment potential.