by Corey Hoffstein, Rodrigo Gordillo & Team, Return Stacked Portfolio Solutions

- This article explores the relevance of leverage in investment strategies amid higher interest rates. The decision to use leverage should be based on the expected returns of assets rather than current interest rates. By emphasizing the importance of understanding risk premiums, the article highlights that leverage can remain beneficial even in environments with higher interest rates.

### Introduction

Coming out of a decade-long low interest rate environment, many investors are questioning whether utilizing leverage remains a prudent idea now that interest rates are meaningfully above zero.

Our answer is that the level of interest rates should not impact the decision to utilize leverage. If leverage makes sense in a low-interest rate environment, then it should make sense in a high interest rate environment.

### Risk Premiums and the Risk-Free Rate

At the foundation of any discussion about return is the risk-free (RF) rate, which is the rate of return earned for investing in a theoretical, riskless asset. Although the risk-free rate doesnāt actually exist, a typical proxy is the yield of U.S. Treasuries, since those are as close to ārisk-freeā as an investor can get.

Intuitively, for any investor to make an investment in anything that is not riskless, they would require the expected return on that investment to be higher than the risk-free rate (this is not strictly true, as insurance instruments offer an obvious counter-point, but is sufficiently true for most investments). Put simply: the investor expects to get paid to be willing to bear the risk. As we have been known to say, āNo Pain, No Premiumā. Generally speaking, if a risky asset has an expected return lower than the risk-free rate, the price of that asset should come down such that the expected return goes up and properly compensates the investor.

For any asset, the expected return above the risk-free rate is called a ārisk premium.ā For example, in equities we have the āEquity Risk Premiumā (ERP) and in bonds, we have the āTerm Risk Premiumā (TRP) (there are many other risk premiums that we could list, but to keep this article succinct, we will focus on the ERP and TRP).

Expected Return = Risk-Free Return + Expected Risk Premium

In Figure 1, we provide a stylized decomposition of expected returns of equities and bonds into their individual components.

From Figure 1, we can see that the expected returns for bonds and equities are composed of both the risk-free rate, as well as their respective risk premiums. These risk premia are defined as the expected excess return of the asset above the risk-free rate.

### Applying Leverage to an Asset

If an investor wants to gain exposure to the S&P 500 index, most investors will operate in the cash market, using cash to purchase a share of the SPDR S&P 500 ETF Trust (ticker: SPY) or the underlying stocks themselves.

Another method, however, could be to borrow money (using leverage) to purchase the exposure. If we borrow the money, we will have to pay back the borrowed amount plus the interest accrued, but we would keep whatever we madeĀ *in excessĀ *of that amount. So, if the S&P 500 returns more than the interest we must pay, we came out ahead by borrowing. In this scenario, the excess return of the S&P 500 is what we expect to make by borrowing, so long as the investor can borrow close to the risk-free rate.

This latter method is effectively how a S&P 500 futures contract works.

One minor difference that we would be remiss to mention is the interest rate. If an investor goes to a bank to borrow money, the interest rate charged would likely be significantly higher than the yield on U.S. Treasury Bills, while futures contracts embed an interest rateĀ remarkably closeĀ to the yield on 1-3 Month U.S. Treasuries.

Taken together, an investor who purchases an S&P 500 futures contract expects to earn theĀ *equity risk premiumĀ *of equities and their realized return will be equal to the return of the S&P 500 minus the risk-free rate (assuming the embedded borrowing cost in S&P 500 futures equals the risk-free rate).

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### Why Does that Matter

Since return stacking inherently uses leverage (typically via futures contracts) to stack returns into a portfolio, the risk premium of the assets in the portfolio is of great interest to investors. However, what the section above hopefully illuminates is that the actualĀ *levelĀ *of interest rates does not.

In fact, since the return of every asset can be decomposed into the risk-free rate and its excess return, and futures contracts effectively isolate the excess return, the choice whether to use leverage based upon the level of the risk-free rate implies that there is a relationship between the level of the risk-free rate and the size of the expected risk premium.Ā In other words, itās a market timing decision!

To further illustrate this, in Figure 2, we build a 100/100 stock/bond portfolio to analyze how the expected returns change as we introduce leverage to the portfolio.

From Figure 2, we can surmise, that stacking bonds on an equity portfolio leaves the portfolio with three things: the risk-free rate, the ERP, and the TRP. Even though we are implicitly incurring borrow costs by applying leverage, we clear that hurdle so long as the ERP and/or the TRP are positive. Since we would expect risky assets to have a positive excess return, a logical conclusion is that the level of interest rates is inconsequential to applying leverage.

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### Do We Even Need to Talk about Leverage Here?

While we tend to apply the lens of leverage due to our affinity for return stacking, does this conversation even require the application of leverage?

The short answer is āno,ā but the long answer utilizes a concept that we already applied earlier in this article.

If we assume that the risk-free rate is 5%, for us to holdĀ *any*Ā allocation to a risky asset then we need to have the expectation that that risky asset will returnĀ *greater than*Ā 5%, or at least properly compensate the investor for the risk taken.

To further develop this intuition, letās detail two potential investments:

- An investment that will return 5% in one year, guaranteed.
- An investment that will return a maximum of 5% in one year, with a 50% probability of losing 5%.

No rational investor would select the second option, as the first is guaranteed and provides the same maximum gain.

Without even applying leverage, the investor is better off allocating to the risk-free asset, since it is irrational to allocate to the second choice.

If an investor has the view that equities or bonds will underperform cash (i.e. the ERP and TRP are negative), then that investor should allocate to cash. This decision is trueĀ *regardlessĀ *of whether the position is levered or not.

If, however, the risk-free rate goes up and we believe that it is no longer prudent to use leverage, what weāre actually saying is, ābecause the risk-free rate went up, we believe the risk premia of our assets has gone down.āĀ Again, this is inherently a market timing decision based upon the level of the risk-free rate.Ā (That is not to say that there isnāt a potential relationship between the risk-free rate and levels of risk premia due to aggregate investor risk preferences, but they should be contemplated explicitly.)

### Conclusion and Tying it All Together

To concretely summarize this post, we posit the following:

- Levered exposures should earn (approximately) the excess return of the asset class.
- The choice of whether to invest in an asset should be driven by its expected risk premium and potential benefit to the portfolio as a whole.
- For higher interest rates to imply that leverage is no longer attractive, it must mean there exists a relationship between the level of interest rates and expected risk premiums. In other words, we must believe we can use the level of interest rates as a market timing signal!

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