Finance Chapters 10 and 11 Quiz

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Questions and Answers

What is the standard deviation for small stocks, according to the data provided?

12.0%

3.1%

25.0%

38.8% (correct)

What relationship is observed between risk and return in investments?

Higher return indicates lower risk.

Return and risk are unrelated.

Greater return corresponds with greater risk. (correct)

Lower return leads to stable risk.

What are excess returns commonly compared against?

The standard deviation of corporate bonds.

Average returns of large stocks.

The historical volatility of small stocks.

The average return for Treasury bills. (correct)

What is the expected return based on?

A weighted average of possible returns. Signup and view all the answers

Which of the following is true about Treasury bills?

They are a benchmark for risk-free returns. Signup and view all the answers

What was the realized annual return for NRG stock on 12/31/2012?

5.13% Signup and view all the answers

Which formula correctly represents how realized return is calculated?

(Pt+1 + Divt+1) / Pt - 1 Signup and view all the answers

What was the dividend paid for NRG stock on 12/31/2014?

$0.26 Signup and view all the answers

What was the price of NRG stock on 12/31/2014?

$48.50 Signup and view all the answers

How does a negative realized return affect an investor's portfolio?

It decreases the overall value of the portfolio. Signup and view all the answers

What was NRG stock's realized return on 12/31/2013?

4.49% Signup and view all the answers

If an investor bought NRG stock for $58.69 and sold it for $61.44, what was the capital gain?

$3.00 Signup and view all the answers

What is the total return that includes both price change and dividends for NRG stock on 12/31/2015?

-2.86% Signup and view all the answers

What does the variance measure in terms of returns?

The average squared difference between realized and average returns Signup and view all the answers

Which formula represents the calculation of variance?

Var(R) = (1/(T-1)) × Σ(Rt - R)^2 Signup and view all the answers

What is the relationship between standard deviation and variance?

Standard deviation is the square root of the variance. Signup and view all the answers

If the variance of the returns is large, what does it indicate about the actual returns?

They tend to differ significantly from the average return. Signup and view all the answers

Given four realized returns of 0.12, 0.09, -0.07, and 0.06, what is the average return?

0.05 Signup and view all the answers

What does a standard deviation of 8.367% indicate?

Returns will fluctuate significantly. Signup and view all the answers

Which of the following options is true regarding realized returns?

They can be negative, indicating a loss. Signup and view all the answers

In the given example, what is the squared deviation for Year 3’s return of -0.07?

0.0144 Signup and view all the answers

What are the two components of the realized return from an investment?

Income component and capital gain/capital loss Signup and view all the answers

What does the notation $R_{t+1}$ represent in the context of investment returns?

The realized return after one period Signup and view all the answers

Which formula correctly calculates the realized return?

$R_{t+1} = \frac{(D_{t+1} + P_{t+1} - P_t)}{P_t}$ Signup and view all the answers

What is the role of the Capital Asset Pricing Model (CAPM) in finance?

To determine the expected return for a risky security Signup and view all the answers

What is NOT one of the learning objectives mentioned in the material?

Analyze investment strategies for optimal performance Signup and view all the answers

In calculating the expected return on a portfolio, which of the following factors is considered?

The income component and capital gain from stocks Signup and view all the answers

Which variable in the realized return formula represents the price of the asset at the beginning of the period?

$P_t$ Signup and view all the answers

Which of the following computations involves assessing risk via historical performance?

Computing the realized return and variance for an investment Signup and view all the answers

What is the primary characteristic of systematic risk?

It affects all firms and cannot be diversified. Signup and view all the answers

What happens to firm-specific risk when many stocks are combined in a large portfolio?

It averages out and is diversified. Signup and view all the answers

What type of risk is specifically associated with fluctuations due to company-specific events?

Firm-specific risk Signup and view all the answers

Which of the following best describes an efficient portfolio?

A portfolio that contains only systematic risk. Signup and view all the answers

How does the reduction in risk behave as correlation decreases?

Risk reduction becomes greater as correlation decreases. Signup and view all the answers

What represents market-wide news affecting stock returns?

Changes in interest rates and inflation. Signup and view all the answers

Which of the following is NOT a type of risk broken down in the context of stock portfolios?

Psychological risk Signup and view all the answers

What is the primary factor influencing systematic risk?

Broader economic conditions impacting all businesses. Signup and view all the answers

What is a market portfolio?

An efficient portfolio containing all shares and securities in the market. Signup and view all the answers

What does beta (β) measure in the context of systematic risk?

The relative sensitivity of a security's returns to the overall market. Signup and view all the answers

How does volatility differ from beta?

Volatility measures total risk, encompassing both systematic and unsystematic risk, whereas beta measures only systematic risk. Signup and view all the answers

What statistical relationship is used to calculate beta?

$rac{Cov(R_i, R_{Mkt})}{Var(R_{Mkt})}$ Signup and view all the answers

Which statement accurately describes stocks in cyclical industries?

They usually exhibit higher betas due to their sensitivity to economic conditions. Signup and view all the answers

What does the Capital Asset Pricing Model (CAPM) express?

The expected return on a security is determined by its beta and the market risk premium. Signup and view all the answers

If the risk-free rate is 5% and the market risk premium is 7%, what is the expected return for a share with a beta of 1.2 according to the CAPM?

11.4% Signup and view all the answers

What would happen to the expected return if a share's beta doubles while the risk-free rate and market risk premium remain unchanged?

The expected return would increase proportionally to the change in beta. Signup and view all the answers

Study Notes

Copyright Notice

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Chapters 10 and 11

Topic: Capital Markets and the Pricing of Risk
Topic: Optimal Portfolio Choice and the Capital Asset Pricing Model

Learning Objectives

Compute the realized return and variance for an investment.
Compute the expected return, variance, and standard deviation (or volatility) of returns.
Compute the expected return on a portfolio given a portfolio of stocks and the variance of the portfolio.
Use the Capital Asset Pricing Model (CAPM) to calculate the expected return for a risky security.

Historical Returns of Stocks and Bonds

Realized Return: The gain or loss from an investment over a specific time period.
Components of Return:
- Income component (cash received directly)
- Capital gain/loss (change in asset value)
Formula for Realized Return (Rt+1): Rt+1= (Divt+1+Pt+1−Pt)/ Pt
Where:
- Pt = share price at beginning of period
- Pt+1 = share price at end of period
- Divt+1 = dividend received at end of period

Example 1

A stock purchased for $10 is sold for $11 with a dividend of $0.50.
Realized return = 5% + 10% = 15%

Alternative Example 10.2

This example shows how to calculate annualized returns for a stock (NRG) in 2012 and 2014, using price and dividend data.
Formulae for calculating the return is provided in this example.

Table 10.2

Table of S&P 500, Microsoft, and Treasury Bill realized returns annually.
Data spans 2002-2014.
Includes percentage returns for each year.

Average Annual Return

The average annual return is calculated by summing the realized returns for each year (t = 1 to T) and dividing by the number of years (T).
Example values for different investments are provided in a table (Small stocks, S&P 500, Corporate bonds, Treasury bills)

Variance and Volatility of Returns

Variance: Measures the average squared difference between actual returns and the average return.
Larger variance indicates greater returns that differ from average returns.
Standard Deviation (or Volatility): The square root of the variance, describing the range of returns.
Formula for Variance (Var(R)): Var(R) = (1/T) Σ(Rt-R)^2; where R is average return and Rt is actual return in year t
Formula for Standard Deviation (SD(R)) or volatility (σ): SD(R) = √Var(R)

Variance and Volatility Example

An example table demonstrates how to calculate variance and standard deviation.
Data on realised returns and average return in each year is included.
Results include the standard deviation.

Table 10.4

Return Volatility (Standard Deviation) is displayed for various investments (small stocks, S&P 500, Corporate Bonds, Treasury Bills).
Data is for 1926-2014.
Standard deviation is compared to quantify risk.

The Historical Trade-Off Between Risk and Return

Excess Return/Risk Premium: The difference between the average return of an investment and the average return on T-Bills (a risk-free investment).
Risk-Free Return (T-Bills): Government bills that are virtually free from default risk.
Data from the table on various investments with their return volatilities (Standard Deviations) are provided.

Common Measures of Risk and Return – Expected Return

Expected Return (E[R]): The weighted average of possible returns, where weights correspond to their probabilities, representing the anticipated return of a risky asset in the future.
Formula for Expected Return (E[R]): E[R] = Σ (PR × R); where PR is the probability of return R

Expected Return Example

An example table presents probabilities of different economic states (Recession, Boom) and their associated returns for JO's Secretarial service and Tracey's Educational Supplies for each state.

Variance and Standard Deviation

Formula for Variance: σ2 = Var(R) = E[(R − E[R])^2] = Σ PR × (R − E[R])^2
Formula for Standard Deviation: σ = √Var(R)

Textbook Example 10.1

Example calculation of expected return and volatility of AMC stock, given equal likelihood of 45% return or -25% return.

The Expected Return of a Portfolio

Portfolio Weights: Fraction of total investment in each asset in a portfolio. Portfolio weights add to 1.
Formula for Portfolio Weights: xi = Value of investment i / Total value of portfolio
Expected Portfolio Return (E[Rp]): Weighted average of the expected return of each asset in the portfolio.

Textbook Example 11.2

Portfolio expected return calculation example using $10,000 in Ford stock and $30,000 in Tyco International stock.

Determining Covariance and Correlation

Covariance: Expected product of deviations of two returns from their means. Measures the degree to which returns move together.
Formula for Covariance: Cov(Ri, Rj) = E[(Ri − E[Ri])(Rj − E[Rj])]
Correlation: Measure of common risk shared by stocks without depending on volatility.
Formula for Correlation: Corr(Rᵢ, Rⱼ) = Cov(Rᵢ, Rⱼ) / (SD(Rᵢ) * SD(Rⱼ))
Positive covariance/correlation: Two returns tend to move together.
Negative covariance/correlation: Two returns tend to move in opposite directions

Table 11.2

Calculations for covariance and correlation of returns between pairs of stocks (North Air, West Air and Tex Oil).

Computing a Portfolio's Variance and Volatility

Portfolio Variance (Var(Rp)): The variance of a two-stock portfolio is calculated by considering individual variances, covariances and weights of the stocks in the portfolio.
Formula for Portfolio Variance: σ²p=x²Var(R₁) + x₂Var(R₂) + 2x₁x₂Cov(R₁,R₂)
Explains how correlation affects portfolio risk. Lower correlation leads to a lower portfolio standard deviation.

Textbook Example 11.6

Calculation of portfolio volatility for various combinations of stocks (Microsoft, Hewlett-Packard, and Alaska Air). Includes correlation coefficients of stock pairs, demonstrating calculations based on correlation data.

Diversification in Stock Portfolios

Total Risk: Composed of firm-specific risk and systematic risk. Total risk is measured by variance or standard deviation
Firm-Specific Risk (Non-Systematic): Fluctuations due to company- or industry-specific news (e.g., introduction of competition, strikes)
Systematic Risk: Fluctuations related to market-wide news, like economic trends, affecting all firms (e.g., interest rates, inflation)
Diversification effect: Firm-specific risk is reduced in larger, diversified portfolios. Systematic risk, however, remains undiversifiable.

Figure 11.2

Shows how the volatility of an equally weighted portfolio decreases as the number of stocks in the portfolio increases. Illustrates the effect of diversification.

Measuring Systematic Risk

Efficient Portfolio: A portfolio containing only systematic risk. Reducing volatility requires lowering potential/expected return.
Market Portfolio: Portfolio holding all shares and securities in the market. The S&P 500 is a frequent proxy.
Beta (β): Measures systematic risk of a security relative to the overall market. Beta, unlike volatility, measures only systematic risk.
Formula for Beta: β₁ = Cov(Rᵢ, Rмkt)/ Var(Rмkt)

Table 10.6

Table showing beta values for individual stocks relative to the S&P 500 index, based on monthly stock data (2010-2015).

Capital Asset Pricing Model (CAPM)

CAPM: Equilibrium model describing the relationship between the risk and return. Expected return is based on Beta.
Formula for Expected Return (using CAPM): E[R] = rf + β × (E[RMkt] − rf). Where: rf = risk-free return ; β=beta, E[RMkt] is expected return on the market portfolio.

Example - CAPM

Example application of the Capital Asset Pricing Model (CAPM) to find expected return given risk-free rate, market risk premium, and beta value.

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Description

Test your knowledge on Capital Markets and the Pricing of Risk, along with Optimal Portfolio Choice and the Capital Asset Pricing Model. This quiz covers key concepts such as realized return, variance, and expected returns for investments and portfolios. Ideal for students studying finance and investment strategies!