Finance Chapter: Risk and Rates of Return

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the goal of a finance manager regarding risk and return?

Minimize return for a given level of risk.

Maximize risk for any level of return.

Minimize risk and return simultaneously.

Maximize return for a given level of risk. (correct)

How is investment risk defined?

The potential for return exceeding expectations.

The guaranteed return on an investment.

The level of investment in a single asset.

The chance that an unexpected outcome will occur. (correct)

What does a probability distribution indicate?

Only the most favorable outcomes of investments.

The likelihood of various outcomes occurring. (correct)

The direct relationship between risk and return.

The total returns of all investments.

What is the expected rate of return?

The rate of return expected from an investment over its life. Signup and view all the answers

Which state of the economy yields the highest rate of return for Martin Products?

Boom economy earning 110%. Signup and view all the answers

In the context of portfolio diversification, which statement is true?

Diversification can reduce systematic risk. Signup and view all the answers

What does a higher standard deviation of returns indicate?

Higher volatility in investment returns. Signup and view all the answers

What is risk aversion in investments?

The preference for certainty over uncertainty. Signup and view all the answers

What does the probability in investment states represent?

The likelihood of a certain economic state occurring. Signup and view all the answers

Which factor primarily affects an investor's decision when choosing a stock?

The risk associated with the stock's volatility. Signup and view all the answers

How is the expected return on a stock calculated?

Using the sum of the probabilities multiplied by the respective returns. Signup and view all the answers

Which stock is expected to have a higher risk indicated by its standard deviation?

Stock B with a standard deviation of 20.49%. Signup and view all the answers

What is the expected return on a portfolio comprised of both stocks A and B?

It is calculated as a weighted average of the expected returns. Signup and view all the answers

How is the risk associated with a portfolio typically mitigated?

Through diversifying investments across different assets. Signup and view all the answers

What does the standard deviation of a stock's return indicate?

The volatility or risk of the stock's returns. Signup and view all the answers

If an investor is risk averse, which stock would they likely prefer?

Stock A due to its lower standard deviation. Signup and view all the answers

What does a higher standard deviation indicate about the investment's returns?

Higher risk and more variable returns Signup and view all the answers

What is the formula for calculating the coefficient of variation?

Standard deviation divided by expected return Signup and view all the answers

How does diversification generally affect the risk of a portfolio?

It typically reduces overall risk Signup and view all the answers

In calculating expected return, how is it determined?

By multiplying each return by its probability and summing the results Signup and view all the answers

What is the variance a measure of in the context of investment returns?

The squared deviation of returns from the mean Signup and view all the answers

If an investor is risk-averse, how would they likely view an investment with high standard deviation?

As too risky for their portfolio Signup and view all the answers

Which of the following best describes the relationship between risk and expected return?

Higher risk is usually accompanied by higher expected returns Signup and view all the answers

Study Notes

Risk and Rates of Return

Finance managers aim to maximize return for a given risk level, or minimize risk for a given return level.
Investing risk is the chance of an unexpected outcome.
Risk and return on investments are measured with methods like standard deviation, variance and coefficient of variation.
Investors can reduce risk by diversification.

Lecture Objectives

Understanding investment risk
Measuring risk and return
Strategies to reduce risk

Defining and Measuring Risk

Risk is the probability that an unexpected outcome will occur.
Investment risk measures the degree of uncertainty associated with potential outcomes.

Probability Distribution

A probability distribution is a listing of all potential outcomes with assigned probabilities.
Probabilities must sum to 1.0 (100%).

Probability Distributions: Example

Example scenario: Rain or no rain
Rain probability: 40%
No rain probability: 60%

Probability Distributions: Example 2

Data from Martin Products & U.S. Electric
Shows rate of return probabilities contingent on economic scenarios: boom, normal or recession.

Expected Rate of Return

Expected return is the anticipated return on an investment over its lifetime.
It is calculated as the mean, or weighted average of possible returns.
Probabilities are the weights

Determining Expected Return: Example

Calculation of expected return for Martin Products and U.S. Electric.
Example tables illustrate probabilities and returns for various economic scenarios leading to expected return figures.

Formula for Expected Return

The formula for expected rate of return (r̂) involves summing the product of each possible return (rᵢ) and its probability (Prᵢ) of occurring. (r̂ = ∑(Prᵢrᵢ)

Measuring Risk: Methods

Standard deviation and variance serve to measure investment risk.
Coefficient of variation is another metric for measuring risk.

Measures of Risk

Risk reflects the chance that actual return deviates from the expected return.
Variance and standard deviation calculations are used to measure investment risk.

Comments on Standard Deviation

Standard Deviation (σ) measures the degree or level of risk.
Larger σ values represent a wider range of outcomes, less certain of predicted returns.

Calculating Standard Deviation/Variance: Example

Calculations for Martin Products' standard deviation and variance are detailed.
Example tables demonstrate the procedure.

Measuring Risk: Coefficient of Variation

Calculated as standard deviation divided by expected return.
Useful for comparing investments with differing risk and returns.

Example 1 (Stock Returns)

Illustrative table to demonstrate a probability distribution for returns of different stocks A and B
Data presented in a table format with states of the economy, associated probabilities, and returns for different stocks.

Required Calculations

Expected return and standard deviation calculation for each stock.
Purpose is to aid investment decision-making.

Portfolio Risk and Return

Portfolio is a collection of assets, such as stocks and bonds, owned by a person or entity.
Most investors do not hold individual stock investments, but instead portfolios.

Expected Return on a Portfolio

Expected return for a portfolio (r̂p) is computed as the weighted average expected rate of return from individual stocks comprising the portfolio..
Weights reflect the proportion invested in different stocks.

Portfolio Returns

Expected return on a portfolio represents the weighted average expected return on the stocks within that portfolio.
Formula: r̂p = Σ(Wᵢr̂ᵢ) where Wᵢ represents the proportion of the portfolio invested in stock i.

Portfolio Risk and Return: Example

Previous calculations for Expected return and variance (Stock A & B)
Details on results for stock A & B.
Example showing how to calculate standard deviation on Stock A and Standard Deviation on Stock B.

Example 2 on Portfolio

Example table showing states of the economy, probabilities, returns for stock A and B.

Solutions: Expected Return on Portfolio

How to determine the Expected Return for a portfolio.
Example of a specific portfolio involving investment proportions for stocks A and B.

Measuring Risk-Portfolio

Standard deviation calculation for portfolios is slightly more complicated.
Requires derivation of a new probability distribution of the portfolio's returns for calculations.
Formula details illustrating method.

Example Continued (Portfolio)

Calculating Portfolio risk and return for a specific stock portfolio.
Data about specific portfolio scenarios.
Example details of probabilities, associated returns, and the calculated portfolio variance.

Portfolio Coefficients: Variance

Portfolio variance calculation for a particular portfolio scenario involving two stocks (e.g., Stock A and B.)
Illustrates the calculation's steps for a stock portfolio.

Portfolio Coefficients: Beta

Portfolio beta: weighted average of individual securities' betas in a portfolio.
Formula provided to illustrate calculation methodology.

Risk Reduction: Portfolio

Diversification reduces portfolio risk.
Stocks that are not perfectly correlated reduce portfolio risk through diversification.
Riskiness of the portfolio reduces as the number of stocks in the portfolio increases.

Total Risk = Systematic + Unsystematic Risk

Total investment risk is comprised of components that cannot be eliminated through diversification (Systematic), and components that can (Unsystematic).
Systematic Risk: Market risk
Unsystematic risk: Firm-specific.

Firm-Specific Risk

Type of risk specific to a particular firm.
Includes events like product failures, management scandals, or loss of key employees..
Can be reduced by diversification.

Market Risk

Market Risk (Systematic risk) involves economic factors impacting all firms (e.g., overall economic health, interest rates, inflation).
Not reducible through diversification.
Measured using the beta coefficient.

Beta Coefficient

beta coefficient represents the stock's sensitivity to market reactions.
Average stock has a Beta coefficient of 1.0.
Beta > 1 indicates the stock's volatility is higher than the market average.

The Concept of Beta

beta coefficient: a measure of the extent to which a stock's returns move along wit the stock market.
Beta = 0.5 means stock only half as volatile
Beta = 1.0 indicates the stock is as volatile as the market average
Beta = 2.0 indicates the stock is twice as reactive as the market average.

Capital Asset Pricing Model (CAPM)

Model describing the relationship between risk and required return.
Required return is the risk-free rate plus a risk premium based on the systematic risk of the security.

The Required Rate of Return for a Security (CAPM)

formula illustrating the required rate of return based on the risk-free return, market risk premium (calculated by subtracting the risk-free rate from the market return), and the stock's beta.
Shows that the required rate of return will be higher if the relevant beta is higher.

The Relationship Between Risk and Rates of Return

Definitions and notations relevant to CAPM.

Market Risk Premium

Market risk premium is the additional return needed to compensate investors for average market risk.

Security Market Line (SML)

Graphical representation showing the relationship between risk (beta) and required rate of return.
Shows the risk-return trade-off for individual securities in the market.

Portfolio Beta Coefficients

Portfolio beta is the weighted average of the individual securities' betas.
Illustrating the calculation process.

What have we Learned

Meaning of risk in investing
How risk and return are measured
Methods for investors to reduce risk (diversification)
Actions investors take when investment return doesn't match required return.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers the essential concepts of investment risk and the measurement of return in finance. It explores strategies for minimizing risk while maximizing returns, and includes understanding probability distributions related to investment outcomes. Test your knowledge on risk assessment and management in financial contexts.