# The Risk-Free Rate

The risk-free rate is a foundational element of investing. It’s the theoretical rate of return you can get investing in something that is guaranteed and has no risk. It’s a reference point in investing as it makes sense to understand what type of return you can achieve without risk before investing in something risky.

Let’s make this more clear with an example:

If you can invest your money risk-free at a 2% rate of return, you would charge a higher return for investing your money in an asset where the return is not guaranteed. Let’s say you demanded an additional 4% return for investing in the risky asset. This 4% return is your risk-premium. Adding both the risk-free rate and your risk premium gives you a total return of 6%. If the risk-free rate increased from 2% to 4%, the risky asset would become less attractive as the risk-premium you now receive would only be 2% instead of 4% even though your total return stayed the same. At least some of the investors who hold the asset would choose to sell and purchase the risk-free asset causing the price of the risky asset to drop. With the basics down, let’s discuss what it means for an investment to be risk-free.

Two conditions must exist for a risk-free investment:

- No default risk
- No uncertainty about reinvestment

Only entities that control the printing of their currency can be considered risk-free. The rationale is if they need to pay you for loaning them money, they can simply turn on the printing presses.

If you have a 5-year time period, you would need a 5-year default-free bond. You couldn’t use a 2-year bond and then purchase a 3-year bond to fill the gap as there would be reinvestment risk.

There are three key insights when understanding the risk-free rate:

- There’s only one real risk-free rate
- The real risk-free rate is equal to real economic growth
- It affects the future more than the present

Risk-free rates vary across currencies due to inflation. Higher inflation currencies will have higher risk-free rates, and lower inflation currencies will have lower risk-free rates. This fact also means there’s only one real risk-free rate, which makes sense because if capital can flow freely to economies with the highest real returns, it will, and this will arbitrage away any additional return.

The real risk-free rate is equal to the real rate of economic growth. An economy can only promise a return relative to the amount it grows over the long term.

Since growth delivers cash flows in the future, the value of future growth will increase more than currently owned assets as risk-free rates fall and vice versa. This asymmetry sheds light on one reason why “growth stocks” have beaten “value stocks” in the current low-interest environment.

## How to Determine the Risk-Free Rate

When valuing a business whose cash flows are potentially perpetual or is a going concern use a:

- Long-term risk-free rate that is practical
- Risk-free rate that is in the same currency as the cash flows.

### USD Risk-Free Rate

For a company whose cash flows are in U.S. dollars, use the 10-year U.S. Treasury bond rate instead of a longer-term instrument. 10+ year data is hard to find, and we’ll need it for the equity risk premium and other calculations.

Secondly, the company location does not affect the risk-free rate. All that matters is the currency the cash flows are stated in.

The only time it would make sense to use year-specific risk-free rates is if the yield curve is sloping significantly upward or downward by more than 4-5%. This process is time consuming as default spreads need to be year consistent.

### Currencies with default-free entities

If there is a default-free government or entity in your currency, use that rate. For example, many governments use Euros and have different 10-year bond rates. Use a default-free government bond rate such as Germany’s in this case, or better yet the ECB’s rate. We’ll bring in the default spread for risky bonds later.

### Currencies without a default-free entity

There are three methods to determine the risk-free rate:

- Adjust the local currency
- Change the currency
- Do the analysis in real terms

#### Adjust the local currency using a ratings agency

Net out the local currency default spread from the government bond rate. The default spread can be estimated by using the credit rating from a rating agency or using CDS spreads. Aswath Damodaran provides a list of country default spreads and risk premiums.

For example, if the Indian 10-year government rupee bond rate is 7% and it’s rated at baa2, which has a default spread of 2.64%. The risk-free rate in rupees (INR) would be:

$% RupeeRiskFreeRate = 7.01\% - 2.64\% = 4.37\% $%

#### Change the currency

Currencies are just a unit of measurement. A company has the same intrinsic value regardless of what currency the financials are stated in. Calculate the discount rate and then convert to another currency by using purchasing power parity based on expected inflation. This will ensure that inflation in the growth rate stays consistent with inflation built into the discount rate:

$% CurrentInflationRateUSD * \frac{(1 + ExpectedInflationRateLocalCurrency)^t}{(1 + ExpectedInflationRateUSD)^t} $%

#### Do the analysis in real terms

As discussed above, there’s only one real risk-free rate. The only difference between risk-free rates between currencies is due to inflation. We can determine the inflation rate of the local currency by using the CDS markets. If you do not have access to CDS market information, check to see if the local government issues a risk-free bond in its local currency. For instance, if India issues a 10-year U.S. bond in rupees, you can subtract that rate from the equivalent USD issued bond to determine the inflation rate.

## Additional Reading

If you want to learn more about risk and the risk-free rate, I suggest the following two resources:

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