How to Estimate the Risk-Free Rate for Stock Valuations

The risk-free rate (r_f) is one of the most important inputs in finance. It's the baseline return investors expect from an investment with "zero risk," and it feeds directly into the capital asset pricing model (CAPM), which is central to absolute valuation models.

If you get the risk-free rate wrong, every downstream calculation is off.

For most U.S.-focused investors, the risk-free rate is the 10-year U.S. Treasury yield. But the concept gets more nuanced when you're valuing companies in different currencies, dealing with governments that carry default risk, or deciding between real and nominal terms.

Below, we'll break down what the risk-free rate actually is, why the 10-year maturity is preferred, how to find it across different scenarios, and the most common mistakes investors make.

What Is the Risk-Free Rate?

The risk-free rate is the expected rate of return on an investment with "guaranteed" returns. It serves as the baseline against which every investor measures expected risk and return.

For an asset to qualify as truly "risk-free," it must satisfy two conditions:

1. No default risk: There must be zero chance the issuer will fail to make promised payments. U.S. Treasury bonds are considered to have no default risk because the U.S. government can always print dollars to service its debts. In contrast, even a very mature company like Microsoft (MSFT) has some tiny risk of defaulting on its bonds.
2. No reinvestment risk: The returns must be guaranteed for your entire analysis period. If you use a short-term bond (e.g., 3-month T-bill), you face reinvestment risk because you'd need to reinvest at potentially different rates when it matures. That uncertainty disqualifies it from being truly "risk-free" over a long investment horizon.

Both conditions must be met. A bond that satisfies one but not the other doesn't qualify.

When Default Risk Isn't Zero

The "no default risk" condition has nuances worth understanding. It may not hold when:

• Governments cannot honor claims made by prior governments and/or when governments borrow in currencies other than their own.
• Multiple countries share a common currency (e.g., the Eurozone), since none of them individually have the power to print currency at will.

The primary ways to determine whether a country's government bonds carry default risk are:

• Sovereign credit ratings: Check ratings from Moody's, S&P, and Fitch. Countries rated AAA are generally considered default-free for local currency borrowings.
• Control over currency: Countries that can print their own currency are less likely to default on local currency debt. This doesn't apply to countries sharing a currency (e.g., Eurozone members).
• Historical precedent: Assess whether the country has ever defaulted on its local currency debt.
• Credit default swap (CDS) spreads: CDS spreads provide a market-based, real-time assessment of default risk. Lower spreads suggest lower perceived default risk. Near-zero spreads indicate very low risk.

Note: It's the country's risk of default on its local currency obligations that matters, not the currency itself. The currency is the medium, but the focus is on the issuing government's ability and willingness to meet its debt obligations.

Why the 10-Year Treasury?

For absolute valuations (e.g., DCF), even if your forecast period is only 5 or 10 years, cash flows extend into perpetuity (assuming you're using a perpetual growth method for terminal value, which is the standard approach).

The 30-year rate might seem like a better match for a company's indefinite life, but the 10-year government bond rate is generally preferred for three reasons:

1. Duration matching: Duration refers to the weighted average time of all future cash flows, including the terminal value. This duration often falls closer to 10 years than to very short-term periods or 30 years. The 10-year rate better aligns with the average timing of cash flows.
2. Consistency with other inputs: Other inputs in DCF valuation, such as corporate bond maturities used when calculating the cost of debt (i.e., with the yield to maturity approach), are often based on 10-year terms. Using the 10-year government bond rate maintains consistency across inputs in the valuation model.
3. Liquidity and market efficiency: The 10-year government bond is typically more liquid and efficiently priced than longer-term bonds like 30-year bonds. This makes the 10-year rate a more reliable benchmark.

If using an exit multiple approach for terminal value or based on investor discretion, a shorter or longer risk-free rate may be more appropriate.

Where to Find the 10-Year Treasury Rate

For U.S. valuations, you can find the current 10-year Treasury yield on FINRA or the U.S. Department of the Treasury's Daily Treasury Par Yield Curve Rates page. These rates are updated regularly.

Real vs. Nominal Risk-Free Rates

Before estimating the risk-free rate, you need to decide whether your valuation is in real or nominal terms.

This choice must be consistent: real cash flows require a real discount rate, and nominal cash flows require a nominal discount rate.

The definitions are straightforward:

• Real: Adjusts for inflation to reflect the actual purchasing power of money over time. Typically uses inflation-indexed government bonds (e.g., TIPS in the U.S.) as the risk-free rate.
• Nominal: Represents monetary values without adjusting for inflation, meaning it includes inflation effects. Uses standard government bonds (e.g., 10-year Treasury bonds in the U.S.) as the risk-free rate.

When deciding between the two:

• Use real terms when inflation is high or unpredictable, or when you want to isolate the impact of inflation on value. This is often relevant in emerging markets or during periods of economic instability.
• Use nominal terms when cash flows are expected to include inflation, which is typical in most business environments where actual currency values are used. This approach is more practical for long-term forecasts in stable economies.

In practice, converting to real cash flows is uncommon and complex (it requires stripping out inflation expectations from all forecasts). Most investors prefer nominal cash flows and discount rates for this reason.

How to Find the Risk-Free Rate

Finding the right risk-free rate depends on where the company operates, what currency you're valuing in, and whether the local government is considered default-free. Below are the three main scenarios.

Scenario #1: Default-Free Government Bond Available

This is the simplest and most common case. If a long-term government bond exists in your chosen currency and the government is considered default-free, use the yield on that bond directly.

For a valuation in U.S. dollars, use the 10-year U.S. Treasury bond yield. Other countries where currencies have historically been considered default-free include Japan, Switzerland, Australia, Canada, Singapore, and Norway.

For multinational companies that do business worldwide, you can use the U.S. 10-year Treasury rate as the global risk-free rate. The USD is considered the global reserve currency, and U.S. Treasuries are the most liquid and widely traded securities globally.

For Euro-denominated valuations, use the yield on the lowest-yielding 10-year government bond among Eurozone countries. This focuses on the absolute lowest risk in the Eurozone. You can also use the long-term government bond yield benchmark for the Eurozone if you want a broader measure.

Note: For non-U.S., non-Euro government bond yields, the OECD long-term interest rates page is a useful resource for finding 10-year yields across countries.

Scenario #2: Government Bond Available but Government Has Default Risk

When the local government bond exists but the government is not considered default-free, you need to strip out the default risk from the bond yield. The approach depends on whether a local currency rating is available.

Local Currency Rating Available

Use the long-term government bond rate less the default spread to estimate the risk-free rate. The steps are:

1. Identify the long-term government bond yield in the local currency.
2. Find the local currency rating for the country (e.g., from Moody's, S&P, or Fitch).
3. Determine the default spread associated with this rating.
4. Subtract the default spread from the government bond yield to estimate the risk-free rate.

This method assumes the default spread captures all the additional risk in the government bond compared to a truly risk-free asset. It's a way to "strip out" the default risk from the observed bond yield.

Brazil example:

Let's apply this with Brazil:

• Brazilian 10-year government bond yield is 12%.
• Brazil's local currency rating is Ba2 from Moody's.
• From Damodaran's country default spread and risk premiums table, the default spread for Ba2 is 3.28%.

The estimated risk-free rate is 8.72% (12% - 3.28%).

CDS Spreads Alternative

Instead of using credit ratings (which can lag markets), you can use CDS spreads as a more real-time measure.

Instead of step #3 above, find the CDS spread for the country's local currency rating. In step #4, subtract the CDS spread from the government bond yield.

This approach provides a more current estimate, especially in volatile markets or for countries with rapidly changing economic conditions.

Scenario #3: Government Bond Available but No Local Currency Rating

When the government is not considered default-free and no local currency rating is available, use one of three alternative estimation methods:

Method #1: Build-Up Approach

The build-up method combines a real risk-free rate with expected inflation:

r_f = r_f,real + π_e

where:

• r_f = nominal risk-free rate
• r_f,real = real risk-free rate
• π_e = expected inflation

The steps are:

1. Estimate the real risk-free rate. Typically, use the yield on U.S. TIPS as a global real risk-free rate.
2. Estimate expected inflation for the country in question. Use economic forecasts or historical averages.
3. Sum these components to get the nominal risk-free rate.

Pakistan example: With a U.S. TIPS yield (10-year) of 1.54% and expected inflation in Pakistan of 10.0%, the nominal risk-free rate is 11.54% (1.54% + 10.0%).

Method #2: Forward Exchange Rates

The forward exchange rate approach uses currency forward rates to imply the risk-free rate differential between two currencies. This is useful when currency markets are liquid and efficient:

F^t = S × (1 + r_f,d)^t / (1 + r_f,f)^t

where:

• F^t = forward exchange rate (at time t)
• S = spot exchange rate
• r_f,d = domestic risk-free rate
• r_f,f = foreign risk-free rate

The steps are:

1. Obtain the spot exchange rate and forward rate for the currency pair (local currency vs. USD).
2. Use the known risk-free rate for USD (i.e., U.S. Treasury yields).
3. Solve for the implied foreign (local) risk-free rate.

Taiwan example: With a spot rate of 33.3500 THB per USD, a 1-year forward rate of 33.3539 THB per USD, and a U.S. 1-year Treasury yield of 3.99%, solving for the implied local risk-free rate yields ~3.97%.

Method #3: Discount Rate Conversion

The discount rate conversion approach converts a known risk-free rate from one currency to another using expected inflation differentials. Useful when you have reliable inflation forecasts for both countries:

r_f,local = (1 + r_f,USD) × (1 + π_e,local) / (1 + π_e,USD) - 1

where:

• r_f,local = local currency risk-free rate
• r_f,USD = USD risk-free rate
• π_e,local = expected inflation in local currency
• π_e,USD = expected inflation in USD

Pakistan example: With a U.S. risk-free rate (10-year) of 3.65%, expected U.S. inflation of 2.0%, and expected Pakistan inflation of 10.0%, the estimated local risk-free rate is ~11.78%.

Common Risk-Free Rate Mistakes

The most common mistake with the risk-free rate is adjusting the current rate (e.g., the 10-year U.S. Treasury) when it deviates from what the investor considers "normal." There are three problems with this approach:

1. "Normal" is subjective and varies by investor perspective.
2. Adjusting the risk-free rate artificially affects company valuations.
3. Using a "normal" risk-free rate without adjusting related fundamentals leads to inconsistent valuations.

Other common mistakes include:

• Using a short-term government bond yield for valuations. Short-term instruments introduce reinvestment risk and don't match the duration of a DCF's cash flows.
• Not matching real/nominal risk-free rates with real/nominal forecasted cash flows. If your cash flows include inflation (nominal), your discount rate must also be nominal.
• Not subtracting the default spread for long-term government bonds that are not considered default-free. Using the raw bond yield overstates the risk-free rate.

The Bottom Line

The risk-free rate is the foundation of every cost of equity and WACC calculation in absolute valuations.

For most U.S. investors valuing domestic companies, it's as simple as using the current 10-year U.S. Treasury yield.

The 10-year maturity is preferred because it matches the average duration of projected cash flows, maintains consistency with other valuation inputs, and benefits from high liquidity.

The concept gets more complex when valuing companies in currencies where the local government carries default risk.

In those cases, you either subtract the default spread from the local bond yield (if a credit rating exists) or use alternative methods like the build-up approach, forward exchange rates, or discount rate conversion.

The key rule is consistency: match real cash flows with real discount rates, and nominal with nominal. And don't adjust the risk-free rate to what you think is "normal." Use the current rate and let the rest of your model adjust accordingly.