# Risk-Free Interest Rate – Measurement, Proxies, Applications

The risk-free interest rate is a fundamental concept in finance that serves as the baseline for evaluating various investment options.

It represents the return on an investment considered to have no risk (i.e., no default risk), such as a government bond, over a specified period.

This article looks at the measurement and proxies of the risk-free rate, its applications in finance, and the differences between the nominal and real risk-free rates.

## Key Takeaways – Risk-Free Interest Rate

- The risk-free interest rate serves as a benchmark for determining the minimum return an investor should expect when taking on a riskier investment. It is typically associated with government bonds, as they are considered to have minimal default risk.
- The risk-free interest rate is influenced by various factors, including central bank policies, inflation expectations, and economic conditions.
- Changes in these factors can lead to fluctuations in the risk-free rate, impacting the cost of borrowing and investment decisions.
- Investors often use the risk-free interest rate as a reference point to evaluate the attractiveness of different investment opportunities.
- Investments offering higher returns should compensate for the additional risk taken compared to the risk-free rate.
- Understanding the risk-free rate is important for assessing the relative risk and reward of various investment options (e.g., cash vs. bonds vs. stocks).

## Measurement of the Risk-Free Rate

The risk-free rate is typically measured using government securities, such as Treasury bills (duration of less than one year), notes (durations between 1-10 years), and bonds (durations of longer than 10 years).

These financial instruments are considered virtually risk-free because they are backed by the full faith and credit of the issuing government, which is assumed to have the ability to meet its financial obligations.

The time horizon of the investment determines the choice of the security used as a benchmark.

For short-term investments, Treasury bills are most commonly used, while longer-term investments use Treasury notes or bonds.

However, the risk-free rate is not entirely devoid of risk.

There is always some small risk of default, as well as price risk (for bonds, which get larger the longer the duration of the bond) as well as inflation eroding the real return.

Nevertheless, the risk-free rate is considered the closest approximation to a risk-free return in financial markets.

## Proxies for the Risk-Free Rate

In cases where a direct measure of the risk-free rate is not available, proxies can be used to estimate it.

Some of the commonly used proxies include:

### Bank rates

Central banks set a target interest rate for lending to commercial banks, which can serve as a proxy for the risk-free rate.

However, these rates may include credit risk and liquidity risk, making them less than ideal.

### Interbank lending rates

The rates at which banks lend to one another, such as the now-deprecated London Interbank Offered Rate (LIBOR) or Euro Interbank Offered Rate (EURIBOR), can be used as proxies for the risk-free rate.

However, these rates have also been subject to manipulation and can incorporate credit risk.

The Secured Overnight Financing Rate (SOFR) has taken over for LIBOR and represents a broad measure of the cost of borrowing cash overnight collateralized by Treasury securities.

### Swap rates

Interest rate swaps, which involve exchanging fixed-rate payments for floating-rate payments, can be used as a proxy for the risk-free rate.

The fixed rate in a swap agreement can provide an estimate of the risk-free rate.

### Prime rate

The Prime Rate is the interest rate that commercial banks charge their most creditworthy customers, typically large corporations and financial institutions.

While it is not risk-free (companies/individuals can’t print their own money to always be able to pay their obligations in nominal terms), it serves as a benchmark for setting interest rates on various loans and financial products, such as adjustable-rate mortgages and business loans.

The Prime Rate is influenced by factors such as the federal funds rate and market conditions, and changes in the Prime Rate can impact borrowing costs for consumers and businesses.

## Applications of the Risk-Free Rate

The risk-free rate plays a crucial role in various financial applications, including:

### Portfolio management

The risk-free rate is used to calculate the expected return on a portfolio and to assess its risk-adjusted performance.

### Capital asset pricing model (CAPM)

CAPM is a widely used model for pricing risky assets, and it relies on the risk-free rate to estimate the cost of equity and to value securities.

### Discounted cash flow (DCF) analysis

In DCF analysis, the risk-free rate is a key input for determining the discount rate, which is used to estimate the present value of future cash flows.

## Nominal Risk-Free Rate vs. Real Risk-Free Rate (Differences and When to Use Each)

The nominal risk-free rate is the observed or stated rate, which does not account for inflation.

On the other hand, the real risk-free rate adjusts for inflation and represents the actual increase in purchasing power resulting from an investment.

The Fisher equation can be used to relate the two rates:

nominal rate = real rate + inflation rate

The choice between the nominal and real risk-free rates depends on the context:

- For investments with nominal cash flows, such as bonds with fixed coupon payments, the nominal risk-free rate is appropriate.
- For investments with cash flows that adjust for inflation, such as inflation-indexed bonds, the real risk-free rate is more suitable.
- In capital budgeting decisions, when evaluating projects with cash flows that are expected to grow with inflation, the nominal risk-free rate is often used.
- For economic analysis and forecasting purposes, the real risk-free rate is often preferred, as it provides a more accurate measure of the underlying economic activity and the real cost of borrowing.

## Risk-Free Rate & Risk Premiums

Understanding risk premiums is important for making capital allocation decisions for various reasons.

In finance, the risk premium is the expected return on an investment beyond the risk-free return.

Different types of investments have different risk profiles and thus offer different risk premiums.

Some basic principles:

- Stocks must yield above bonds, which must yield above cash, and by the appropriate risk premiums.
- When risk premiums compress, capital tends to go down the risk curve into safer investments.
- When risk premiums rise, it tends to go up the risk ladder.

Here’s a general look at the risk-return profiles for cash, bonds, equities, private equity, and illiquid investments:

**Cash:**Cash or cash equivalents like short-term government bonds have the lowest risk and, as a result, offer the lowest returns, also referred to as the risk-free rate. This is the baseline return an investor expects without taking any risk.**Bonds:**Bonds have higher risk than cash as they are dependent on the issuer’s ability to pay back the debt. Bonds are a promise to deliver cash over time. Therefore, they usually offer a higher return than the risk-free rate. The difference between the return on the bond and the risk-free rate represents the risk premium for holding the bond.**Equities:**Equities or stocks carry higher risk than bonds because, in the event of a company’s bankruptcy, bondholders are paid before stockholders. This risk is offset by the potential for much higher returns, especially for companies that perform well. Stocks can be thought of as nominal bonds with uncertain coupons.**Private Equity:**Private equity involves investing in companies that are not publicly traded. The risk here is even higher as these investments are often illiquid (hard to sell quickly), and the companies may be less established or in a restructuring phase. They may also be more indebted due to the nature of the funds used to take the company private in cases of leveraged buyouts. For the additional risks, investors in private equity expect a higher return or risk premium.**Illiquid Investments:**Illiquid investments can include real estate, collectibles, private business investments, and others that can’t be quickly converted to cash. These carry higher risk because of their lack of liquidity, and the market for these investments may fluctuate a lot, meaning an investor could potentially lose a substantial part of their investment or not be able to buy or sell. They may also require specific skills to operate well. However, the potential returns are often higher, justifying a higher risk premium.

Understanding these risk premiums allows investors to construct a portfolio that aligns with their risk tolerance and investment goals.

For instance, conservative investors may prefer cash and bonds, accepting lower returns for lower risk.

More aggressive investors may prefer equities, private equity, and illiquid investments, accepting higher risk for the potential of higher returns.

Additionally, understanding risk premiums is important for diversification, which is a strategy to manage risk by investing in a variety of assets.

By understanding the risk and return characteristics of different assets, investors can select a mix that could potentially yield higher returns for a given level of risk.

Risk premiums can also be used in the Capital Asset Pricing Model (CAPM) mentioned above, a tool to calculate the expected return on an investment given its risk relative to the market.

## Conclusion

Understanding the risk-free interest rate is important for making informed investment decisions and analyzing financial markets.

The risk-free rate serves as a benchmark for evaluating various investments and plays an important role in several financial applications, including portfolio management, capital asset pricing, and discounted cash flow analysis.

Additionally, it is important to distinguish between the nominal and real risk-free rates, as the appropriate choice depends on the context and the nature of the cash flows involved.