Chapter 2.1 Finance: Discount Rates and Risk-Free Rate

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