Elm Wealth - Leverage: Sense and Non-Sense

November 20, 2025

Investing 101

Leverage: Sense and Non-Sense

By Victor Haghani and James White¹
ESTIMATED READING TIME: 9 min.

Introduction

There’s a lot of leverage in the US stock market right now. Margin debt at retail brokerage firms is at a record $1.2 trillion, leveraged ETFs add another $250 billion to that total, and those figures are dwarfed by the notional value of stock options and futures, which are regularly hitting new records.

There are a variety of rationales behind these different forms of leverage, including, but not limited to, pure speculation. But all this leverage raises a question at least about a potentially productive use: when does it make sense to borrow so you can own more stocks (or similar risky assets) than the value of your wealth? An often-heard but incorrect answer is: “when the expected return of stocks is higher than the cost of leverage.” Another answer we don’t find convincing is to decide to leverage because, historically, it would have delivered higher risk-adjusted returns. One problem with these answers is that they don’t tell you how much to leverage, or to the extent they do, they suggest taking on as much leverage as you can get. This is because perhaps more fundamentally, they fail to incorporate any concept of risk.

Risk-adjusted Return and the Merton Share

We think a better answer is to take on leverage when it increases your expected risk-adjusted return, and it follows that the optimal amount to leverage (if at all) is that which gives you the highest expected risk-adjusted return. But what is risk-adjusted return, and how can we calculate it?

To make things more concrete, let’s start with a stylized case in which the only two assets you can invest in are either stocks or relatively safe US Treasury obligations, and we’ll also assume that all of your wealth is financial capital (we’ll be discussing human capital below). With a few more simplifying assumptions,² we can write risk-adjusted return (RaR) for a portfolio as the expected return minus a “cost of risk,” which is proportional to both the variance of portfolio returns and to your coefficient of risk aversion:

\[\text{RaR} = r_\text{port} – \frac{1}{2} \gamma \sigma_{\text{port}}^2\]

where $r_\text{port}$ is the expected portfolio return, $\gamma$ is your personal coefficient of risk aversion, and $\sigma_\text{port}$ is the annual standard deviation of portfolio returns.

From this, we can deduce the “Merton share” as the answer to the question: “what fraction of wealth invested in risky assets maximizes your expected risk-adjusted return?” The result: the optimal fraction of your wealth to invest in stocks is proportional to expected stock returns in excess of safe asset returns – called the risk premium – and inversely proportional to both the risk of stocks (measured as variance of returns) and your personal degree of risk-aversion. In symbols:

\[ \hat{\kappa} = \frac{r_\text{stocks} – r_\text{safe}}{\gamma \sigma^2} \]

where $\hat{\kappa}$ is the optimal fraction to invest in the risky asset.

A Merton Example

For the remainder of the article, we’ll use the Merton share for sizing calculations, but always remembering it’s a rule-of-thumb based on specific assumptions, not a fully general result.

Let’s say you have a fairly low degree of risk-aversion (we’d say $\gamma = 2$), and you’re pretty bullish on stocks, expecting they’ll return 10% per year compared to 4% for safe assets. You also feel that stocks will have about 15% return variability per year, considerably less risky than they’ve been over the past century. Under these pretty optimistic views of the future, the Merton share says you should borrow 33% to invest 1.33 times your wealth in stocks:

\[ 1.33 = \frac{0.10 – 0.04}{2 * 0.15^2} \]

But this is implicitly assuming you can borrow at the same rate as the safe asset return – in reality, your borrowing rate is going to be higher, and dramatically higher in some cases. Let’s say that your cost of borrowing is 5.5%, 1.5% higher than the safe asset return. We can still use the Merton share, we just have to make the safe asset rate, $r_\text{safe}$, equal to the borrowing rate of 5.5%. Now the Merton share says to invest 100% of your savings in stock, with no leverage.

\[1.0 = \frac{0.10 – 0.055}{2 * 0.15^2}\]

So to decide whether it makes sense to leverage and by how much, we can use the Merton share while being careful to include the cost of leverage in the risk premium calculation in the numerator.

The leverage kink

In the chart below (and sticking with our assumptions above), we show the optimal wealth fraction to hold in stocks as a function of the risk premium, assuming the cost of leverage is 1.5% higher than the safe asset return (i.e. $r_\text{leverage} – r_\text{safe} = 1.5%$). We can see the cost of leverage puts a “kink” in the curve, creating a range where risk premium is increasing, but the optimal fraction to invest in stocks remains constant at 100%.³

Getting real with the inputs

Let’s discuss reasonable ranges for the current inputs to decide whether it makes sense to take on leverage in your investing.

Risk premium: our estimate (here) of the excess return of the global stock market (US plus non-US) is just under 3%, with US stocks alone at about half that level. Our estimate is roughly in line with the average expectations of a broad sample of investment firms.
Stock market risk: taking into account long-term historical volatility along with information from the long-dated options market gives us an estimate of around 18% for future long-horizon stock market volatility, measured as annual standard deviation of returns. Let’s assume an investor who sees equities in a low volatility state expecting stock market variability of 16%.
Cost of leverage in excess of the safe asset return: here we don’t have a single number. Standard margin rates at the biggest discount brokers – Fidelity, Schwab, E*trade and Vanguard – are more than 5% higher than T-bill rates, while they can be as low as +1.5 – 2% on $1 million at Interactive Brokers and Robinhood. The wholesale cost of leverage above T-bills implied by stock futures, options markets, and hedge fund prime brokerage terms is around 1%.⁴
Investor risk-aversion: in our experience, the degree of risk-aversion of most affluent investors falls in a range of 2 – 3. Such investors would be indifferent to flipping a fair coin where heads would increase their wealth by 33% – 50% while tails would reduce their wealth by 20%. Our clients’ average risk aversion is closer to 2.

With these “base case” inputs, the Merton share yields an optimal stock allocation of about 60%.⁵ How much would these inputs have to change for leverage to make sense? At a risk premium of 4%, with 15% volatility, 1.5% cost of leverage, and risk aversion coefficient of 1, the optimal stock allocation is about 110%. Yet even in this case where leverage formally pencils out, the difference in risk-adjusted return between holding 110% stocks and 100% stocks is a mere 0.01% pa.

Additional gains are small near optimality

Let’s assume you’re able to build a portfolio as risky as the stock market but with an expected return high enough to justify 1.5x leverage, including a leverage cost of 1.5%. Then 5/6ths of the extra expected return you’d get from the leverage would get eaten up by a higher cost of risk, and only 1/6 would remain to increase your risk-adjusted return. The relatively small additional gain in expected risk-adjusted return may not justify the added complexity and extra attention required to manage a leveraged portfolio.

Leveraging a low Beta stock portfolio

Low Beta stocks (those with low co-movement with the broad stock market) have historically generated higher returns relative to risk than theory would suggest. Fans of “low Beta” stock investing believe they can build portfolios that have a lower expected return than the broad stock market, but with risk that is proportionally even lower.

Could it make sense to leverage such a portfolio? With expected excess return of the broad market at 3%, let’s assume that you could buy a low Beta portfolio with expected return of 2.5% and risk of just 10% (an increase in Sharpe ratio of 50%). Plugging these numbers into the Merton share, we find that even an investor on the low end of the risk-aversion spectrum should not leverage an attractive low Beta stock portfolio.

Human Capital, Financial Capital, and Leverage

Human capital is the value of your lifetime earnings from work, after taxes and beyond basic living expenses. For young people, human capital usually far outweighs their financial capital. Understanding not only its size but also how it moves with the stock market and the broader economy is key.

Economist Moshe Milevsky, in Are You a Stock or a Bond? frames the issue this way: if your earnings rise and fall with the economy (say, in finance or construction), your human capital is more like a stock. If your earnings are steady and less tied to economic cycles (like doctors or tenured professors), your human capital is more like a bond. Knowing whether your human capital is “stock-like” or “bond-like” helps guide how much risk you should take with your financial capital.

Barry Nalebuff and Ian Ayres, in Lifecycle Investing, argue that young investors with little financial capital but significant, bond-like human capital should consider using leverage to invest more heavily in stocks early in their careers. They recommend buying call options on the stock market (instead of margin borrowing) and suggest gradually reducing stock exposure as human capital declines relative to financial wealth with age. They also advise limiting leverage to about 2x to keep risks manageable.

How much does leverage help? Take a young investor whose human capital is six times his savings and resembles a risk-free bond. Using our base-case assumptions, and a 1.5% cost of leverage above the risk-free rate, the Merton share suggests holding twice his savings (excluding his human capital) in stocks. Compared to being 100% in stocks, his expected return (in excess of the safe asset return) is 50% higher, and his risk-adjusted return is improved by 45%.

It may be worthwhile to leverage if he is confident he’ll experience a financing friction of 1.5% or less. This benefit shrinks if borrowing costs are higher, if human capital is smaller or more correlated with the market than assumed, or if the leverage isn’t rebalanced efficiently. These risks mean that even with the promise of higher risk-adjusted returns, young investors should approach leverage with caution.

Mortgage Borrowing

A house is a long-lived asset, and the most common purpose of a mortgage is simply to spread out paying for it over time. We do know people who have considered taking out a home equity line of credit to invest in stocks because it was a cheap and stable source of borrowing, and in this case the same logic applies as we’ve discussed above.

Connecting the dots

There are many strategies involving leverage which are regularly in the news these days: “buy-borrow-die” estate planning, leveraged ETFs, “portable alpha”, “return stacking”, etc., and without digging into each one, we suspect none of these will, absent special situations, withstand a full analysis which includes the utility dynamics and the various costs– including the cost of leverage, management fees and transactions costs. In general, we’re hard-pressed to think of a case where it is sensible to leverage stocks if the cost of leverage is more than 2% over the safe asset return, and 2% is lower than the going rate at the main discount brokerages.

Even assuming a cost of leverage of around 1%, in the current market environment, we find it unlikely that investors late in their careers with substantial savings relative to their remaining human capital would be able to noticeably improve the expected risk-adjusted return of their savings by leveraging investments in stocks or other similar and related risky assets.

For investors early in their careers, whose human capital is much larger than their savings, holding a leveraged stock portfolio may be worth the extra costs, risks and complexity – but it’s a close call.

Note:

In the section “Connecting the dots,” we’ve updated the term “risk stacking” to “return stacking.” Our thanks to Corey Hoffstein for this correction.

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Leverage: Sense and Non-Sense

Introduction

Risk-adjusted Return and the Merton Share

A Merton Example

The leverage kink

Getting real with the inputs

Additional gains are small near optimality

Leveraging a low Beta stock portfolio

Human Capital, Financial Capital, and Leverage

Mortgage Borrowing

Connecting the dots

Note:

Further Reading & References

Leverage: Sense and Non-Sense

Introduction

Risk-adjusted Return and the Merton Share

A Merton Example

The leverage kink

Getting real with the inputs

Additional gains are small near optimality

Leveraging a low Beta stock portfolio

Human Capital, Financial Capital, and Leverage

Mortgage Borrowing

Connecting the dots

Note:

Further Reading & References

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