Leverage in a portfolio: return, risk, costs and margin calls

In depth12 min read · 12 sources

Leverage in a portfolio means investing more money than you have yourself: with a securities-based loan, with leveraged ETFs or with derivatives. Leverage multiplies gains and losses, costs interest and slows long-term growth as soon as the fluctuations become too large. Here you will learn how to calculate leverage, at what price fall a margin call looms and why a portfolio financed with a loan behaves differently from a leveraged ETF that is reset daily.

What leverage does

A leveraged portfolio has two sides: securities with a value H, the gross exposure, and an account C, which is negative with leverage (the loan). Your equity is E = H + C, the leverage factor L = H / E. With L = 2 and $10,000 of equity, you hold $20,000 of securities, financed with a $10,000 loan; with L below 1, part of the money sits alongside as cash.

Return and volatility grow with L, and the borrowing rate acts as a hurdle: the borrowed part only pays off if the securities earn more than the loan costs. The Sharpe ratio stays the same as long as you borrow at the risk-free rate; any spread on top lowers it. Losses, on the other hand, hit in full: in a loan-financed portfolio with L = 2, a price fall of 50% means a total loss (see maximum drawdown).

Growth: why double leverage does not bring double the return

Over many years, what counts is not the average annual return but the growth of wealth, the geometric return (see CAGR). It lies roughly half the variance below the arithmetic mean. That is volatility drag. With leverage, the variance grows with the square of L. If leverage is continuously held at L, the following applies approximately:

Assumptions: μ = 7%, σ = 16%, borrowing at 3%, cash at 2%. Growth is highest at L* = (μ − r_K) / σ² = 0.04 / 0.0256 ≈ 1.56, at around 6.1%. That is a good 0.4 percentage points more than without leverage, with just over one and a half times the fluctuation. At double L*, a little over 3.1, growth falls back to the borrowing rate. L* is the allocation according to the Kelly criterion; full Kelly buys the highest growth at the price of very large interim losses (MacLean et al. 2010).

The formula assumes constant leverage and prices without jumps. Real markets have fat tails and jumps. With leverage, rare large losses weigh more heavily than the formula shows.

Margin loan or leveraged ETF: who resets the leverage?

With a securities-based loan, or a margin loan at your broker, the lender lends against your portfolio: you buy additional securities with borrowed money, the loan stays the same in dollars and only the interest is added. If prices rise, your equity grows faster than your holdings and the leverage falls. If they fall, it rises. A leveraged ETF, by contrast, resets its leverage to the target value every trading day: after a winning day it buys more, after a losing day it sells.

The table shows both forms with leverage of 2 over two days, without interest or costs:

Over the whole period, the loan-financed portfolio delivers exactly double the index return, but its leverage drifts: after the first day to 1.83 or 2.25. The daily leverage reset keeps the leverage at 2 but makes the result path-dependent: it gains in trends and loses in a zigzag market, just like a CPPI with a floor of 0 and a multiplier of 2.

According to Cheng and Madhavan (2009), the return on leveraged and inverse ETFs contains a path-dependent option that, under certain conditions, harms buy-and-hold investors; daily releveraging can also amplify volatility before the market close. Avellaneda and Zhang (2010) derive an exact formula and confirm it on 56 leveraged funds. Without interest and costs, it reads:

In 2008, according to Avellaneda and Zhang, most leveraged ETFs lagged behind the corresponding static strategies. If you want to achieve a fixed multiple of the index over a longer period with a leveraged ETF, you have to adjust it yourself; in their data, about one adjustment a week was enough. Factor certificates are similarly reset daily.

Margin call: when selling becomes compulsory

With a securities-based loan, the lender sets a lending value for each security, and the account must maintain a maintenance margin: equity must make up at least a share m of the securities held. FINRA Rule 4210 (2026) requires US brokers to keep at least 25% of market value for stocks bought on credit. If equity falls below that, a margin call follows, a demand for additional funds: pay in more money or sell securities, otherwise the lender sells them itself.

Without rebalancing and interest, the margin call comes when prices have fallen by more than d since purchase:

With m = 25%, the limit is L = 4: at that point, any price fall immediately triggers a margin call. The example shows how expensive a forced sale is.

Such sales also move the market. According to Brunnermeier and Pedersen (2009), traders provide liquidity as long as they can obtain funding; but their margins themselves depend on market liquidity. If margins rise, selling follows and prices fall further. This creates a liquidity spiral:

Geanakoplos (2010) calls the pattern the leverage cycle: without intervention, leverage becomes too high in the boom and too low in the crisis, and so do prices. Bad news increases uncertainty, lenders demand more collateral, and the most highly leveraged have to sell (deleveraging). The maintenance margin can therefore rise exactly when your portfolio is falling anyway.

What the research shows: leverage aversion and betting against beta

In the CAPM, everyone can borrow at the risk-free rate; anyone who wants more return leverages the market portfolio. If that is not possible, the security market line becomes flatter (Black 1972). Frazzini and Pedersen (2014) build a model with leverage and margin constraints on this: because constrained investors buy high-beta assets instead of leveraging safe ones, these assets have a low alpha. Their betting against beta factor, which buys low-beta assets with leverage and sells high-beta ones, delivered clearly positive risk-adjusted returns, but little when funding conditions tightened.

Asness et al. (2012) apply leverage aversion to asset classes: if many investors do not use leverage, safe assets have to offer more return per unit of risk, and those who can use leverage can exploit this. Risk parity does exactly that: it overweights low-volatility assets such as bonds and leverages the whole portfolio to a higher level of risk. Whether this works depends on funding. If credit becomes more expensive or scarcer, the advantage shrinks. The article on the low-volatility anomaly describes the same idea for equities.

Leverage over the life cycle

Ayres and Nalebuff (2008) make an unusual proposal: young savers have little capital but decades of income ahead of them. Even with 100% equities, they bear little equity risk in dollar terms at first and a great deal shortly before retirement. With leverage in their younger years and more cautious investments later, they spread it more evenly. This is called diversification across time. In their calculation with US equity data from 1871, expected wealth at retirement was 90% higher than with life-cycle funds and 19% higher than with a pure equity investment; the approach was published as a book in Ayres and Nalebuff (2010).

In theory, this fits Merton (1969): the optimal equity allocation depends on the excess return, risk and risk tolerance, and is not capped at 100%. In practice, objections remain: private investors borrow at higher rates than the money market rate, an early crash can force a sale at the bottom via margin calls, and the data come from a market that was very good for equities. The article equity allocation by age covers the topic without leverage.

Costs

• Borrowing rate: securities-based loans usually cost a reference rate plus a borrowing spread. Every additional percentage point lowers the result at L = 2 by one percentage point a year, because it is charged on (L − 1) × equity.
• Leveraged ETFs: the financing is inside the fund, plus the ongoing charges and the trading for the daily reset. Cheng and Madhavan (2009) cite high transaction costs as an additional drag for long-term investors.
• Futures and options: leverage without a loan; for futures and written options, with margin (collateral) and an obligation to post additional margin. The financing is built into the price of the future (cost of carry).

Limits and common mistakes

• Leverage on the wrong risk: what matters is the volatility of the whole. Leverage of 1.5 on a portfolio of equities and bonds can fluctuate less than a single stock without leverage.
• Underestimating drift: without rebalancing, the leverage in a loan-financed portfolio rises after losses. If you start at 1.5, you are already at 1.71 after a 20% fall.
• Jumps and gaps: prices can jump overnight or over a weekend. The margin call threshold is then not touched but skipped over, similar to the gap risk of a CPPI.
• Backtests flatter: monthly values do not show slumps within a month, and historical data only contain crises that have already happened. Sequence risk shows how much the order of returns matters.

As a general principle: leverage is not a promise of return but an amplifier of return, risk and mistakes alike. This article is not investment advice.

How Portfolio Lab calculates it

In the Backtest, each security in a portfolio can optionally be given its own leverage between 0.1 and 5. The app then treats it like a leveraged ETF that is reset daily: in each period (daily with daily prices, monthly with asset classes), L times the return applies; the portion L − 1 costs the money market rate from the Settings plus a spread (default 1% p.a.), with no floor for the rate, and below 1 the rest sits as cash earning the money market rate. If the return for a period reaches −100% or less, the security is worthless. The leveraged price applies in all portfolios that hold the security; the benchmark remains unleveraged. The Leverage tab compares CAGR, volatility and max. drawdown without and with leverage. The backtest does not model a loan-financed portfolio with drifting leverage, maintenance margin and margin calls. For that, the calculations above apply. Formulas and examples are in the backtest methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.