1. FIN 422: Student Managed Investment Fund
Topic 11: Risk Free Rate and Risk Premia 
Larry Schrenk, Instructor

2. Overview Estimating Inputs: Discount Rates Riskfree Rate
Equity Risk Premium

3. Readings
Damodaran. Investment Valuation, Chapter 7

4. 1. Estimating Inputs: Discount Rates

5. Estimating Inputs: Discount Rates
Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation.
At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted.
Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital.
Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated.
Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominal
While discount rates are a critical ingredient in discounted cashflow valuation, I think we spend far too much time on discount rates and far too little on cashflows. The most significant errors in valuation are often the result of failures to estimate cash flows correctly….
As companies increasingly become global, and multiple listings abound (Royal Dutch has six equity listings in different markets). the consistentcy principle becomes very important. The currency used in estimating cash flows should also be the currency in which you estimate discount rates - Euro discount rates for Euro cashflows and peso discount rates for peso cash flows.
Recently, I came across a valuation of a Mexican company, where the cashflows were in nominal pesos but the discount rate used was the dollar cost of capital of a U.S. acquirer…. As a result, the value was inflated by more than 300%….

6. Cost of Equity
The cost of equity should be higher for riskier investments and lower for safer investments
While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investment
Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (I.e, market or non-diversifiable risk)
Re-emphasizes a key assumption that we make in risk and return models in finance. It is not risk that matters, but non-diversifiable risk and the cost of equity will increase as the non-diversifiable risk in an investment increases.
This view of the world may pose a problem for us when valuing private companies or closely held, small publicly traded firms, where the marginal investor (owner, venture capitalist….) may not be diversified.

7. The Cost of Equity: Competing Models
Model Expected Return Inputs Needed CAPM E(R) = Rf + b(Rm - Rf) Riskfree Rate Market Beta Market Risk Premium APT E(R) = Rf + Σj=1bj (Rj - Rf) Riskfree Rate Factor Portfolios Factor Betas Factor Risk Premia Multi E(R) = Rf + Σj=1...Nbj (Rj - Rf) Riskfree Rate Macro Factors Macro Factor Betas Macro Risk Premia Proxy E(R) = a + Σj=1...Nbj bj Yj Proxies Regression coefficients
Lays out the four basic models and how non-diversifiable risk is measured in each model:
The capital asset pricing model makes the most restrictive assumptions (no transactions costs, no private information) and arrives at the simplest model to estimate and use.
The arbitrage pricing model and multi-factor model make less restrictive assumptions but yield more complicated models (with more inputs to estimate)
The proxy model is dependent upon history and the view that firms that have earned higher returns over long periods must be riskier than firms that have lower returns. The characteristics of the firms that earn high returns - small market cap and low price to book value, for example in the Fama-French study - stand in as measures for risk.

8. The CAPM: Cost of Equity
While the CAPM (and the CAPM beta) has come in for well-justified criticism over the last four decades (for making unrealistic assumptions, for having parameters that are tough to estimate and for not working well), it remains the most-widely used model in practice.
In the CAPM, the cost of equity is a function of three inputs
Cost of Equity = Riskfree Rate + Equity Beta * (Equity Risk Premium)
In practice,
Government security rates are used as risk free rates
Historical risk premiums are used for the risk premium
Betas are estimated by regressing stock returns against market returns
While this equation is set up in terms of the capital asset pricing model, the issues raised with the CAPM apply to the more complex models as well -the APM and the multi-factor model

9. 2. Riskfree Rate

10. A Riskfree Rate
On a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return.
For an investment to be riskfree, then, it has to have
No default risk
No reinvestment risk
Time horizon matters: Thus, the riskfree rates in valuation will depend upon when the cash flow is expected to occur and will vary across time. If your cash flows stretch out over the long term, your risk free rate has to be a long term risk free rate.
Not all government securities are riskfree: Some governments face default risk and the rates on bonds issued by them will not be riskfree.
Treasury bills may be default free but there is reinvestment risk when they are used as riskless rates for longer-term cashflows. A 6-month T.Bill is not riskless when looking at a 5-year cashflow.
Would a 5-year treasury be riskfree? Not really. The coupons would still expose you to reinvestment risk. Only a 5-year zero-coupon treasury would be riskfree for a 5-year cash flow.
If you were a purist, you would need different riskfree rates for different cashflows. A pragmatic solution would be to estimate the duration of the cashflows in a valuation and use a treasury of similar duration. (Since the duration is the weighted average of when the cashflows come in, this should be fairly long, especially when you count in the fact that the terminal value is the present value of cashflows forever).

11. Riskfree Rate in US dollars
If you are valuing a company in US dollars, you need a US dollar risk free rate.
In practice, we have tended to use US treasury rates as risk free rates, but that is built on the presumption that the US treasury is default free.
If you accept the premise that the US treasury is default free, you still have several choices, since the US treasury issues securities with differing maturities (ranging from 3 months to 30 years) as well in real or nominal terms (Inflation protected treasuries (TIPs) or nominal treasuries)
In valuation, we estimate cash flows forever (or at least for very long time periods) and in nominal terms. The correct risk free rate to use should therefore be a long term, nominal rate. The thirty-year treasury bond rate is the longest term rate that you can find and there is a good case to be made that it should be the risk free rate. However, given how difficult it is to get the other inputs for the discount rate (default spreads & equity risk premium) over thirty year periods, you should consider using the ten-year US treasury bond rate as your risk free rate for US dollar valuations.
Since we are valuing cashflows for the long term, we want a long-term riskfree rate (so, rule out the 6-month T.Bill rate). Since the valuation is in US dollars (a nominal rate), we can also rule out the TIPS rate. In theory, the 30-year rate should be the best choice. In practice, I would go with the 20-year bond for the following reasons:
It is the most liquid of the treasuries and there is always a fresh auction rate from the previous Monday,
Getting other inputs such as equity risk premiums and default spreads is easier with a 10-year rate than a 30-year rate
The term structure flattens out by the time you get to the 10-year rate…..

12. Riskfree Rate in Euros
The only reason for differences in rates across these securities is default risk. Consequently, it makes sense to use the lowest of the rates (Germany) as the rsikfree rete, if you are valuing a company in Euros.

13. Riskfree Rate in Nominal Reais
The Brazilian government had 10-year BR$ denominated bonds outstanding in January 2013, with an interest rate of 9%.
In January 2013, the Brazilian government had a local currency sovereign rating of Baa2. The typical default spread (over a default free rate) for Baa2 rated country bonds in January 2013 was 1.75%. The risk free rate in nominal reais is therefore:
Riskfree rate in Reais = Nominal 10-year BR$ rate – Default spread
= 9% % = 7.25%
The government bond rate is not riskfree. To get to a riskfree rate, you would subtract out the default spread of 2.55% from the bond rate to get to a riskfree rate of 8%.

14. Sovereign Default Spreads: Two Paths to the Same Destination…

15. And a Third – Average Default Spreads: January 2013
Rating
Default spread in basis points
Aaa
Aa1 25
Aa2 50
Aa3 70 A1 85 A2
100 A3
115
Baa1
150
Baa2
175
Baa3
200
Ba1
240
Ba2
275
Ba3
325 B1
400 B2
500 B3
600
Caa1
700
Caa2
850
Caa3
1000

16. Riskfree Rates in Different Currencies: January 2013

17. 3. Equity Risk Premium

18. Equity Risk Premiums: Intuition
The equity risk premium is the premium that investors charge for investing in the average equity. For lack of a better description, think of it as the price of bearing a unit of equity risk.
It is a function of
How risk averse investors are collectively
How much risk they see in the average equity
The level of the equity risk premium should vary over time as a function of:
Changing macro economic risk (inflation & GDP growth)
The fear of catastrophic risk
The transparency or lack thereof of the companies issuing equity

19. Equity Risk Premiums: The Historical Risk Premium
The historical premium is the premium that stocks have historically earned over riskless securities.
While the users of historical risk premiums act as if it is a fact (rather than an estimate), it is sensitive to
How far back you go in history…
Whether you use T. bill rates or T. bond rates
Whether you use geometric or arithmetic averages.
While everyone uses historical risk premiums, the actual premium in use can vary depending upon
How far back you go in time
Whether you T.Bills or T.Bonds
Whether you use arithmetic or geometric averages
This table was developed using data that is publicly accessible on the S&P 500, treasury bills and 10-year treasury bonds on the Federal Reserve of St. Louis web site.
Dataset: histretSP.xls
An interesting issue that has been raised by some researchers is that there may be a selection bias here. The U.S. stock market was undoubtedly the most successful equity market of the 20th century. Not surprisingly, you find that it earned a healthy premium over riskless rates. A more realistic estimate of the premium would require looking at the ten largest equity markets in the early part of the century and estimating the average premium you would have earned over all ten markets. A study at the London Business School that did this found an average equity risk premium of only 4% across these markets.

20. The Perils of Trusting the Past…
Noisy estimates: Even with long time periods of history, the risk premium that you derive will have substantial standard error. For instance, if you go back to 1928 (about 80 years of history) and you assume a standard deviation of 20% in annual stock returns, you arrive at a standard error of greater than 2%:
Standard Error in Premium = 20%/√80 = 2.26%
Survivorship Bias: Using historical data from the U.S. equity markets over the twentieth century does create a sampling bias. After all, the US economy and equity markets were among the most successful of the global economies that you could have invested in early in the century.
The noise in stock prices is such that you need years of data to arrive at reasonably small standard errors. It is pointless estimating risk premiums with years of data.
The survivorship bias will push historical risk premiums up, if you use the US as the base market.

21. Updated Equity Risk Premium
On January 1, 2013, the S&P 500 was at , essentially unchanged for the year. And it was a year of macro shocks – political upheaval in the Middle East and sovereign debt problems in Europe. The treasury bond rate dropped below 2% and buybacks/dividends surged.
The key lesson I would take away is that equity risk premiums are unstable and that globalization has made them more unstable. The other is that there seems to be mean reversion in the process – implied premiums, when abnormally high or low, move back towards a longer term average.

22. Implied Premiums in the US: 1960-2012
As the index changes (and it is the input most likely to change by large amounts in short periods), the implied premium will change. Note that as premiums rise, stock prices drop. Notice two historical phenomena: (1) Equity risk premiums spiked in the 1970s as inflation increased in the US (2) Equity risk premiums bottomed out at 2% at the end of 1999 at the peak of the dot-com boom.
Would you settle for a 2% premium? If your answer is no, you believe that stocks are overvalued.

23. Why Implied Premia Matter
In many investment banks, it is common practice (especially in corporate finance departments) to use historical risk premiums (and arithmetic averages at that) as risk premiums to compute cost of equity. If all analysts in the department used the geometric average premium for of 4.2% to value stocks in January 2013, given the implied premium of 5.78%, what were they likely to find?
The values they obtain will be too low (most stocks will look overvalued)
The values they obtain will be too high (most stocks will look under valued)
There should be no systematic bias as long as they use the same premium (4.2%) to value all stocks.
Everything will look cheap…
Using any premium higher than the implied premium today will bias values downwards (and most stocks will look overvalued). This is why risk premiums used in equity research departments tend to be different than those used in corporate finance.
So, how do analysts compensate for this bias?
They make unrealistic estimates of growth and reinvestment to arrive at what they feel are reasonable values. They then put pressure on management to deliver these unrealistic numbers. Managers bend the accounting rules to pull this off… and we have the makings of accounting scandals.

24. Estimating a Risk Premium for an Emerging Market 1
Approach 1: Build off a mature market premium
Assume that the equity risk premium for the US and other mature equity markets was 5.8% in January You could then add on an additional premium for investing in an emerging markets.
Two ways of estimating the country risk premium:
Default spread on Country Bond: In this approach, the country equity risk premium is set equal to the default spread of the bond issued by the country. Brazil’s default spread, based on its rating, in September 2011 was 1.75%.
Equity Risk Premium for Brazil = 5.8% % = 7.55%
Adjusted for equity risk: The country equity risk premium is based upon the volatility of the equity market relative to the government bond rate.
Standard Deviation in Bovespa = 21%
Standard Deviation in Brazilian government bond= 14%
Default spread on Brazilian Bond= 1.75%
Total equity risk premium for Brazil = 5.8% % (21/14) = 8.43%

25. Estimating a Risk Premium for an Emerging Market 2
Approach 2: Estimate an implied equity risk premium for Brazil

26. Estimating a Risk Premium for an Emerging Market 2
Belgium
1.05%
6.85%
Germany
0.00%
5.80%
Portugal
4.88%
10.68%
Italy
2.63%
8.43%
Luxembourg
Austria
Denmark
France
0.38%
6.18%
Finland
Greece
10.50%
16.30%
Iceland
3.00%
8.80%
Ireland
3.60%
9.40%
Netherlands
Norway
Slovenia
Spain
Sweden
Switzerland
Turkey UK
W.Europe
Albania
6.00%
11.80%
Armenia
4.13%
9.93%
Azerbaijan
3.00%
8.80%
Belarus
9.00%
14.80%
Bosnia & Herzegovina
Bulgaria
2.63%
8.43%
Croatia
Czech Republic
1.28%
7.08%
Estonia
Georgia
4.88%
10.68%
Hungary
3.60%
9.40%
Kazakhstan
Latvia
Lithuania
2.25%
8.05%
Moldova
Montenegro
Poland
1.50%
7.30%
Romania
Russia
Slovakia
Ukraine
E. Europe & Russia
2.68%
8.48%
Country Risk Premia
January 2013
Bangladesh
4.88%
10.68%
Cambodia
7.50%
13.30%
China
1.05%
6.85%
Fiji Islands
6.00%
11.80%
Hong Kong
0.38%
6.18%
India
3.00%
8.80%
Indonesia
Japan
Korea
Macao
Malaysia
1.73%
7.53%
Mongolia
Pakistan
10.50%
16.30%
Papua New Guinea
Philippines
3.60%
9.40%
Singapore
0.00%
5.80%
Sri Lanka
Taiwan
Thailand
2.25%
8.05%
Vietnam
Asia
1.55%
7.35%
Canada
0.00%
5.80%
USA
N. America
Argentina
9.00%
14.80%
Belize
15.00%
20.80%
Bolivia
4.88%
10.68%
Brazil
2.63%
8.43%
Chile
1.05%
6.85%
Colombia
3.00%
8.80%
Costa Rica
Ecuador
10.50%
16.30%
El Salvador
Guatemala
3.60%
9.40%
Honduras
7.50%
13.30%
Mexico
2.25%
8.05%
Nicaragua
Panama
Paraguay
6.00%
11.80%
Peru
Uruguay
Venezuela
Latin America
3.38%
9.18%
Updated country risk premiums.
Angola
4.88%
10.68%
Botswana
1.50%
7.30%
Egypt
7.50%
13.30%
Kenya
6.00%
11.80%
Mauritius
2.25%
8.05%
Morocco
3.60%
9.40%
Namibia
3.00%
8.80%
Nigeria
Senegal
South Africa
Tunisia
Zambia
Africa
4.29%
10.09%
Bahrain
2.25%
8.05%
Israel
1.28%
7.08%
Jordan
4.13%
9.93%
Kuwait
0.75%
6.55%
Lebanon
6.00%
11.80%
Oman
Qatar
Saudi Arabia
1.05%
6.85%
United Arab Emirates
Middle East
1.16%
6.96%
Australia
0.00%
5.80%
New Zealand
Australia & NZ
Black #: Total ERP
Red #: Country risk premium
AVG: GDP weighted average

27. From Country to Corporate Equity Risk Premia
Approach 1: Assume that every company in the country is equally exposed to country risk. In this case,
E(Return) = Riskfree Rate + CRP + Beta (Mature ERP)
Implicitly, this is what you are assuming when you use the local Government’s dollar borrowing rate as your riskfree rate.
Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk.
E(Return) = Riskfree Rate + Beta (Mature ERP + CRP)
Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales)
E(Return)=Riskfree Rate+ b (Mature ERP) + l (CRP)
Mature ERP = Mature market Equity Risk Premium
CRP = Additional country risk premium
The differences between the three approaches lie largely in what you do with the CRP. In the first approach, you just add it to the company’s cost of equity and treat it as different from all other macro economic risk exposure. In the second, you assume that beta measures exposure to country risk exposure as with all other macro economic risk. In the third approach, you estimate a different exposure to country risk, assuming that it is different from all other risk.

28. Estimating a Risk Premium for an Emerging Market 3
Approach 3: Estimate a lambda for country risk
Source of revenues: Other things remaining equal, a company should be more exposed to risk in a country if it generates more of its revenues from that country.
Manufacturing facilities: Other things remaining equal, a firm that has all of its production facilities in a “risky country” should be more exposed to country risk than one which has production facilities spread over multiple countries. The problem will be accented for companies that cannot move their production facilities (mining and petroleum companies, for instance).
Use of risk management products: Companies can use both options/futures markets and insurance to hedge some or a significant portion of country risk.
This is not meant to be an all inclusive list. While there are undoubtedly other factors to consider, you also have to be able to obtain this information not only on your firm but on other firms in the market. In fact, of the three items listed above, revenue sources may be the only publicly available information on companies.

29. Estimating Lambdas: The Revenue Approach
The easiest and most accessible data is on revenues. Most companies break their revenues down by region.
l = % of revenues domesticallyfirm/% of revenues domestically avg firm
Consider, for instance, Embraer and Embratel, both of which are incorporated and traded in Brazil. Embraer gets 3% of its revenues from Brazil whereas Embratel gets almost all of its revenues in Brazil. The average Brazilian company gets about 77% of its revenues in Brazil:
LambdaEmbraer = 3%/ 77% = .04
LambdaEmbratel = 100%/77% = 1.30
Note that if the proportion of revenues of the average company gets in the market is assumed to be 100%, this approach collapses into the first one.,
There are two implications
A company’s risk exposure is determined by where it does business and not by where it is located
Firms might be able to actively manage their country risk exposure
This is a simplistic approach, but it is the easiest one to use. You can usually get the percent of revenues that your firm gets in the country from its annual report.
Notice that Embraer has a lambda close to zero since it gets so little of its revenues in Brazil. Since its factories and work force are still in Brazil, this estimate seems to be too low.

30. Approaches 1 & 2: Estimating Country Risk Premium Exposure
Location based CRP: The standard approach in valuation is to attach a country risk premium to a company based upon its country of incorporation. Thus, if you are an Indian company, you are assumed to be exposed to the Indian country risk premium. A developed market company is assumed to be unexposed to emerging market risk.
Operation-based CRP: There is a more reasonable modified version. The country risk premium for a company can be computed as a weighted average of the country risk premiums of the countries that it does business in, with the weights based upon revenues or operating income. If a company is exposed to risk in dozens of countries, you can take a weighted average of the risk premiums by region.

31. Operation Based CRP: Single versus Multiple Emerging Markets
Single emerging market: Embraer, in 2004, reported that it derived 3% of its revenues in Brazil and the balance from mature markets. The mature market ERP in 2004 was 5% and Brazil’s CRP was 7.89%.
Multiple emerging markets: Ambev, the Brazilian-based beverage company, reported revenues from the following countries during 2011.
In the case of Embraer, its limited revenues in Brazil give it a low equity risk premium.
In the case of Ambev, the computation is messier because it has revenues in many Latin American markets. We use revenue weights to weight the CRP.

32. Extending to a Multinational: Regional Breakdown
Coca Cola’s revenue breakdown and ERP in 2012
With a multinational, it is often too messy to do individual countries, either because of the logistics of computing dozens of CRP or because the information is not provided. You can use the regional breakdown to get an approximate ERP. I applied the GDP weighted average from the map to arrive at the ERPs and CRPs for each region.
Things to watch out for
Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia
Obscure aggregations including Eurasia and Oceania