Chapter 2.1 Finance: Discount Rates and Risk-Free Rate

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the implied equity risk premium (ERP) based on the information provided?

4.60% (correct)

8.32%

Cannot be determined from the information provided.

3.72%

If analysts are using the arithmetic average historical equity risk premium for the period of 1928-2023, what can we say about the equity risk premium used?

It accurately reflects the current market conditions.

It is too low, resulting in overvalued stocks.

It does not account for the forward-looking nature of the equity risk premium. (correct)

It is too high, resulting in undervalued stocks.

How does the implied equity risk premium relate to the risk-free rate?

The risk-free rate is subtracted from the implied equity risk premium to determine the expected rate of return on stocks. (correct)

The implied equity risk premium is subtracted from the risk-free rate to determine the expected rate of return on stocks.

The risk-free rate is multiplied by the implied equity risk premium to determine the cost of equity.

The risk-free rate and the implied equity risk premium are independent of each other.

What is the relationship between the implied equity risk premium and bond default spreads?

They are directly related - as bond default spreads increase, the implied equity risk premium increases. (C) Signup and view all the answers

In corporate finance departments, which type of equity risk premium is commonly used?

Historical equity risk premium (A) Signup and view all the answers

What is the impact of using an outdated equity risk premium when valuing stocks?

It may result in overvalued or undervalued stocks, depending on the difference between the historical and current equity risk premium. (D) Signup and view all the answers

What is the relationship between the cost of equity and the implied equity risk premium?

The cost of equity is equal to the implied equity risk premium. (B) Signup and view all the answers

Using a constant historical equity risk premium to value stocks, irrespective of market conditions, could lead to what outcome?

Misinterpretation of risk assessments, leading to potentially biased investment decisions. (B) Signup and view all the answers

What is the main limitation of using historical risk premiums in valuation?

It can have substantial standard error based on historical data. (A) Signup and view all the answers

Which factor does NOT significantly affect the calculation of historical risk premiums?

The performance of international markets. (B) Signup and view all the answers

What is indicated by a standard error in premium greater than 2% when using data stretched over 90 years?

Considering volatility in annual returns affects accuracy. (C) Signup and view all the answers

How is a country's equity risk premium typically estimated?

Through the default spread of its sovereign bonds. (C) Signup and view all the answers

Which method is NOT suitable for estimating the default spread for a country?

Assessing the country’s equity market performance. (A) Signup and view all the answers

What potential bias may affect the historical data used for estimating risk premiums?

Survivorship Bias. (A) Signup and view all the answers

Which of the following is the default spread based on a Ba2 rated sovereign as of January 2024?

3.28% (C) Signup and view all the answers

What is the historical risk premium primarily a measure of?

The difference in returns of stocks versus bonds. (A) Signup and view all the answers

What is the implied risk-free rate used in the Sensex computation?

6.76% (A) Signup and view all the answers

In the context of the provided information, what is the most likely interpretation of "Default Spread based premium"?

The premium associated with the risk of default on a company's debt. (B) Signup and view all the answers

According to the table in slide 47, which of the following has the strongest correlation with the actual return over the next 10 years?

Current implied premium (D) Signup and view all the answers

What does the term "Lambda" refer to in the context of the content provided?

The expected rate of return on the market. (A) Signup and view all the answers

Identify the formula used for calculating the cost of equity when solving for the expected return on stocks, as described in the text.

Cost of Equity = Risk-Free Rate + (Expected Growth Rate - Risk-Free Rate) (A) Signup and view all the answers

What is the implied equity risk premium for India, as calculated in the Sensex computation?

4.42% (D) Signup and view all the answers

What is the purpose of using a historical equity risk premium (ERP) for the Sensex?

To provide a baseline comparison against the observed implied ERP. (B) Signup and view all the answers

The content mentions "Market makes mistakes even in the aggregate but is correct over time." What does this statement suggest about the use of implied equity risk premium?

That the implied equity risk premium is a volatile measure, but it should converge towards its historical average over time. (A) Signup and view all the answers

Study Notes

Discount Rates

Discount rates are crucial in valuation
A risk-free investment's actual return equals its expected return, meaning no variance.
Risk-free investments lack default and reinvestment risk.
Estimating a risk-free rate requires considering time horizons and currency differences—different rates exist for different time frames and currencies.
Government securities are not always risk-free; some governments face default risk.

The Risk-Free Rate

Actual return = expected return on a risk-free investment
No variance around expected return
Criteria for a risk-free investment: no default and no reinvestment risk
Factors influencing risk-free rate estimation
- Time horizon: risk-free rates vary across time periods for cash flows.
- Currencies: risk-free rates are specific to each currency.
- Not all government securities are risk-free: some governments face default risk.

Sovereign Default Spread

Three approaches to determine sovereign default spread:
- Using sovereign dollar or euro denominated bonds: Default spread = Emerging Govt Bond Rate - US Treasury Bond rate (same maturity).
- Using CDS spreads: Default spread = Sovereign CDS spread (adjusting for market frictions).
- Using sovereign rating-based spread: Use average spread of similar-rated countries.

Approach 1: Default Spread from Government Bonds

Data for selected countries provided
Calculations illustrate how government bond rates, risk-free rates, and default spreads relate.

Approach 2: CDS Spreads

Data, presented in a table format, displays CDS spreads for various countries.

Approach 3: Typical Default Spreads

Standard & Poor's and Moody's give sovereign rating correlations.
Default spreads for different sovereign ratings.

Getting to a Risk-Free Rate in Brazilian Reais

Three approaches are used.
- Approach 1: Government bond spread
  - Default Spread = Brazil $ Bond Rate - US T-Bond Rate
  - Risk-free rate in $R = 10.35% - 1.87% = 8.48%
- Approach 2: CDS Spread
  - Riskfree rate in $R = 10.35% - 1.81% = 8.54%
- Approach 3: Rating based spread
  - Riskfree rate in $R = 10.35% - 3.28% = 7.07%

Why do risk-free rates vary across currencies?

Shows examples across markets
Risk-free rates vary considerably based on factors like local sovereign ratings.

Risk-Free Rate: Don't Have or Don't Trust the Government Bond Rate?

Scaling risk-free rate: adjusting for country-specific inflation.
Formula presented: Risk-free rate(Currency) = [ (1 + Riskfree rate(base currency)) / (1 + Expected Inflation(Base Currency))] - 1
Example calculation for Egyptian pounds using US dollars as the base.

The Equity Risk Premium

Historical premium: premium earned by stocks over risk-free securities.
Sensitivity: how far back in history the data is taken and the type of risk-free rate used influences accuracy.
US average historical calculations (arithmetic and geometric) displayed for the period 1928-2023.

The Perils of Trusting the Past

Noisy estimates: historical data on risk premiums has standard errors, so it is an estimate rather than a hard fact.
Survivorship bias: historical data often includes only successful firms and not necessarily a representative sample.

The Country Default Spread

Default spread is set equal to the default spread for the country .
The sovereign CDS spread is for the country in US dollars.
Default spread based on local currency rating (e.g., Brazil's Ba2 rating)
Calculation examples for Brazil show the derivation of country risk premium and total ERP.

An Equity Volatility Based Approach to Estimating the Country Total ERP

Approach to calculate total ERP using the volatility of emerging-market and US markets:
- Total Equity Risk Premium = Risk Premium(US) * (σ(Country Equity)/σ(US Equity))
- Example calculation for Brazil's total ERP (using Bovespa and S&P 500 standard deviations).

A Melded Approach to Estimating the Additional Country Risk Premium

Country ratings measure default risk.
Default spread * (Country Equity Volatility /Country Bond Volatility)
Example calculation for Brazil's risk premium.

A Template for Estimating the ERP

Procedure steps for calculating ERP, including mature market premium, country risk assessment, conversion of risk measures, and ERP estimation.
Formula for ERP for country vs. US.
Considerations like ratings, whether sovereign ratings are or aren't available, methods for estimating ERP if no sovereign rating is available.

Implied Equity Premiums

Using asset prices and cash flow estimates, the implied return rate can be calculated.
Calculating the required discount rate which equates present value to the paid price estimates the expected equity return.
Subtracting the risk-free rate yields the implied equity risk premium.

Equity Risk Premium: January 2020

Calculation of implied equity risk premium using last 12 months of cash flow, and the expected earnings growth over the next five years.

Estimating a US Dollar Cost of Equity for Embraer - September 2004

Cost of equity for Embraer based on different calculation methods, considering beta, CRP, and exposure across locations. (Location CRP, and Operation CRP).

Valuing Emerging Market Companies with Significant Exposure in Developed Markets

Conventional practice for valuing emerging-market companies assumes equal exposure to country risk.
Determining the consequences of applying an emerging equity risk premium calculation method.
Constructing an investment strategy to profit from the misvaluation (if it exists).

An Updated Estimate: ERP in 2024

Calculation of implied ERP using cash flow from last 12 months, and expected earnings growth for 5 years from now.

Implied Premiums in the US: 1960-2023

Visualization of implied equity risk premiums.

Implied Premium versus Risk-Free Rate

Visualization of implied ERP versus Risk-Free Rate over time.

Equity Risk Premiums and Bond Default Spreads

Visualization of equity risk premiums and bond default spreads over time.

Equity Risk Premiums and Cap Rates (Real Estate)

Graph illustrating equity risk premiums and real estate risk premiums over time.

Why Implied Premiums Matter?

Common practice in investment banks to use historical risk premiums.
Potential outcomes when analysts use a historical average equity risk premium from other periods.

Which Equity Risk Premium Should You Use?

Correlations between various equity risk premium predictors and actual returns.

An ERP for the Sensex

Calculation and process to estimate ERP of the Sensex in a given time.

The Evolution of Emerging Market Risk

Data table shows changes in key metrics over time, such as PBV, PBV, ROE, US T-Bond Rate, Growth Rate, Cost of Equity for developed markets and emerging markets, and the differential between them for each year.

Relative Risk Measures

Discussion of relative risk measures
Statistical concept of beta

The CAPM Beta: The Most Used (And Misused) Risk Measure

Standard procedure for estimating beta using regression analysis.
Problems associated with using historical beta.

Unreliable, when it looks bad...

Data limitations and issues impacting the usefulness of using a single beta number
Visualization examples of beta regression analysis over periods across markets

Or When it Looks Good...

Example of a historical beta calculation and results
Example of chart

One Slice of History...

Example illustrating volatility of GME
Example illustrating stock market volatility over a period

Studying That Suits You

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

Description

This quiz covers essential concepts related to discount rates and the risk-free rate in finance. It delves into the characteristics of risk-free investments, the factors influencing their rates, and the implications of sovereign default risk. Test your knowledge on these critical elements of financial valuation.