*This post is available as a PDF download here.*

# Summary

- The risk-free rate is an important concept in financial theory, but the risk-free rate accessible to most investors can vary significantly in level.
- The variation in risk-free rate not only has an important impact on the theoretically optimal portfolio, but it can have a very real impact upon portfolio returns.
- We demonstrate that recent generational lows in short-term Treasuries had made this less of a problem in recent years.
- With short rates increasing dramatically in recent years, investors should carefully consider the risk-free rate available to them.

**Introduction**

The risk-free rate is often taken for granted in portfolio construction. Allocations for investors may even be determined completely ignoring this rate of return with the assumption that whatever assets are not invested in the primary portfolio of stocks, bonds, and alternatives are simply held in a bank account, money market funds, or short-term Treasuries.

When the risk-free rate is 0% or close to it, this approach makes sense.

While the risk-free rate is by no means a large factor in most investment portfolios, it is coming off its multi-year lows and showing signs that it will continue to increase over the next few years. When the choice is between getting a positive and potentially significant riskless return or zero return for uninvested cash, it helps to understand some of the impacts that falling short of the potential target can have.

**What is the Risk-Free Rate?**

What the actual risk-free rate is can differ in theory and practice.

The Federal Funds rate is used as the risk-free rate in many portfolio calculations. This is the rate that banks lend to each other overnight. There is no rule that says that investors have to earn this rate, but there is not much reason for them not to be able to when we consider that one goal of our fractional reserve banking system is simply for banks to get funds from investors to then lend out at a higher interest rate.

But bank accounts vary considerably in terms of their interest rates and terms (savings, checking money market, CDs, etc.).

For a savings account, getting close to the Federal Funds rate is definitely achievable, especially in the current market environment where a bank’s location has little bearing on whether you can open an account there.

But so is getting *much less* than the Federal Funds rate. In fact, the FDIC reports that the national average rates on savings, interest checking, and money market account rates are 0.09%, 0.06%, and 0.16%, respectively.

*Source: Nerd Wallet. 3 Star and up banks with a $10k minimum deposit. Data as of 12/7/2018.** *

If we remove the filter on bank quality in the above screen, we can find an account for 2.5%, but this is definitely the exception to the rule based on the national statistics.^{1}

Certificates of deposit (CDs) are another route to achieving the risk-free rate. Short-term CDs (or slightly longer term, laddered CDs) can serve as the risk-free investment vehicle as long as liquidity concerns are considered.

In an actual investment portfolio, an alternative to money market or bank account rates is available by actually investing in short-duration U.S. Treasuries, either directly or through an ETF such as the iShares Short Treasury Bond ETF (SHV). SHV’s current yield is 2.27%, which is in line with the Federal Funds risk-free rate.

The downside to this is that there may be commissions associated with moving money in and out of the asset, and advisory fees may be charged on the allocation depending on the account setup.

Practical issues of accessing these options aside, the bottom line is that there exists a large variance in precise rate available to a given investor at any given time. In this rest of this commentary we aim to demonstrate that this creates a non-trivial impact both on portfolio construction and returns.

**Growth of the Risk-Free Asset**

Since 1926, the risk-free rate has fluctuated considerably.

*Source: Kenneth French Data Library. Data as of October 2018.** *

Its median value on a rolling 12-month basis has been 2.9%, but it has ranged from 0% to 15.2%. The multi-year lows of the 2010s had not been seen since the Great Depression era.

When we look at how this translates into compounded growth, there is a sizeable amount of money left on the table when the actual risk-free rate is not achieved.

*Source: Kenneth French Data Library. Calculations by Newfound. Data as of October 2018.** *

In the broader context of a portfolio, these results scale based on the actual cash allocation.

If cash earning the risk-free rate were used as the bond component of a 75/25 portfolio, which is not unrealistic for someone who has a larger liquidity reserve and a smaller asset base, this equates to 20 bps per year.

If rebalancing is considered, then the differential is slightly larger (around 25 bps) because as the risk-free rate is increased, when equities are up, less capital is moved away from stocks at the rebalance, and when equities are down, more capital is available for investing through the drawdowns and realizing the (desired) subsequent recovery.

This benefit may not seem like much, but considering how aggressively investors will pursue reducing fees by the same amount, any incremental return helps.

The analogy with fees breaks down unless the fee reduction is obtained for identical strategies (e.g. two S&P 500 funds). This difference in the return from the risk-free rate is not like switching from one value strategy to another because one has a 20 bps lower expense ratio: money saved can easily be eclipsed by the differences in the strategy dynamics.

Reducing fees by switching strategies is an uncertain savings. Maximizing the potential of the risk-free rate is guaranteed return.

**Portfolio Construction and the Risk-Free Rate**

One of the primary uses of the risk-free rate in portfolio construction is within a mean-variance framework where the goal is to maximize the expected Sharpe ratio. The effect of changing the risk-free rate is illustrated in the chart below.

The efficient frontier is shown in black, the different capital market lines are shown as the colored lines, and the corresponding circles indicate the tangency portfolios.

All else held equal, a higher risk-free rate moves the tangency portfolios further out on the efficient frontier. From an implementation standpoint, an investor desiring to target a specified volatility level would hold some mix of the tangency portfolio and the risk-free asset.

A practical issue comes into play when we consider the assumptions behind modern portfolio theory: namely that borrowing and lending are done at the same rate.

Investors outside of larger institutional investors generally pay a premium for borrowing funds, and as we have seen from bank account data, receive potentially much less for lending.

As such, the borrowing line is likely to be more set in stone. For example, a larger account at Interactive Brokers would pay about 100 bps over the Federal Funds rate to borrow.

In the example above, if we assume that borrowing is done at 4% – the orange line – and lending (i.e. savings) is done at 0% – the blue line – then the capital market line actually is kinked along the efficient frontier.^{2}

When you move up the blue line to the blue tangency portfolio, you then move along the efficient frontier because you cannot borrow at 0% and because of the risk-free rate being used, either by choice or not, you cannot lend at 4%. You move up the efficient frontier until you hit the orange tangency portfolio, at which point you begin to move along the orange line as you borrow at 4%.

Increasing your risk-free rate as much as possible shapes the capital market “line” as more of an actual line, which is desirable in the Sharpe-optimal framework.

**The Practical Impact of the Risk-Free Rate **

Using a cross-section of asset classes (including global equities, government bonds of various maturities, and commodities) going back to 1973, we can use different fractions of the risk-free rate and construct the implied long-only mean-variance optimal portfolios (using resampling to account for estimation noise). To obtain expected return and covariance estimates, we will use a 3-year forward crystal ball and form the portfolio each month. Even though we are using a crystal ball over a longer time horizon, the shorter holding period still may deviate considerably (a topic we discussed in a different context in God, Buffett, and the Three Oenophiles).

As of late, there has not been much difference in the rolling returns, which is expected given the extremely low risk-free rates. The largest benefit was in the 80s and 90s when rates were regularly above 5%.

Over the whole period, the annualized rates of return were 9.9%, 10.7%, and 11.8%, depending on whether a 0% risk-free rate, half of the risk-free rate, or the full risk-free rate was assumed.

Note that this analysis assumes that the investor will simply hold the mean-variance optimal portfolio with no regard to its volatility level. This means that the rolling returns may not compare apples-to-apples, as one portfolio may bear significantly more risk than another. In an effort to more accurately isolate the impact upon returns, we can attempt to hold volatility levels constant among the portfolios.

Since the borrowing rate for all portfolios is assumed to be the same, we will add cash in with the higher volatility portfolios to bring their forecast volatilities in line with the 0% risk-free rate portfolio. This avoids using leverage, which is in line with many investor processes. This results in a generally conservative portfolio (overall volatility of 7.5%).

A similar effect emerges, where the full risk-free rate portfolio gains ground when risk-free rates are high and loses ground when rates are lower.

Over the 2000s, the portfolio with the full risk-free rate has been lagging the 0% risk-free rate portfolio, mainly because of the difference in the tangency portfolios’ performance for the two rate scenarios. The lower volatility portfolio has done well, and for much of the time, the tangency portfolios have been close to identical, as shown in the following chart.

Positive numbers indicate that the full risk-free rate portfolio had a higher allocation to that asset class, and vice versa.

**Conclusion**

The risk-free rate is commonly used and discussed in portfolio discussion without much definition or consideration beyond the fact that it exists.

There is no set risk-free rate, but there is a generally accepted ceiling that can be earned without taking any significant risk. There is however the unfortunate opportunity of earning 0% as your own personal risk-free rate.

In a mean-variance framework, the selected risk-free rate will have some bearing on the optimal portfolio and will affect the resulting mix of this portfolio and the risk-free asset. These effects have been most pronounced when the risk-free rate is higher.

With rates still low from a historical perspective, the impact of not achieving the full risk-free rate may not be extreme, but with how simple it is to deploy cash in a more effective manner, setting up a process in the current increasing rate environment is a sensible way to maximize returns in a guaranteed way when other assets are facing headwinds of uncertainty.

- Services like Max My Interest aim to make this bank account selection process simpler, especially for accounts above the FDIC coverage limit.
- See Lee M-C. and Su, L-E. Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate. Universal Journal of Accounting and Finance 2(4): 69-76, 2014. http://www.hrpub.org/download/20140801/UJAF1-12202421.pdf

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