Margin Loan Leverage Calculator

Purpose and model boundary

This calculator shows what borrowing against securities does to an account. You enter the value of the securities in a margin account, the loan you owe the broker, the maintenance margin, the loan's interest rate and your assumptions for the return and volatility of the securities. The spreadsheet simulates 100 possible monthly price paths over up to 36 months and reports the chance that the account is called within the horizon, how far the value can fall today before a call, the share price that triggers one for a single holding, the leverage, the interest the loan costs over the next year, and the return on your equity if the price falls, stays flat or rises by a fixed move, with the loan and without it.

Every figure on this page is computed by the spreadsheet; the page adds nothing to it. It is an educational estimate from the assumptions you enter. It does not predict markets, it does not tell you whether to borrow, and it is not financial, investment, tax or legal advice. Borrowing to invest can lose more than the money you put in.

Inputs and units

• The value of the securities in the account today, including those bought with the loan, and the loan (the debit balance), in dollars. Enter a loan of 0 for a cash account.
• Price of one share today: optional, for a single holding only. It adds the share price at which the account is called; leave it blank for a portfolio of several holdings.
• The maintenance margin: the smallest share of the position that must be your own equity, as a percentage. FINRA Rule 4210 sets 25 percent as the minimum for long positions, and many brokers ask for more, especially for single or volatile stocks; enter your broker's figure for this position.
• The yearly interest rate on the loan. A twelfth of it is added to the loan at the end of each month, and nothing is repaid.
• The expected yearly return of the securities (an arithmetic mean, with dividends kept in the account) and their volatility (the standard deviation of yearly returns).
• Months to look ahead, from 1 to 36.
• Price move for the scenarios: optional. Blank means 20 percent, so the scenarios are a 20 percent fall, no change and a 20 percent rise over the horizon.
• Random seed: the starting number of the spreadsheet's random-number generator. The page does not show it: each press of Simulate first replaces it with the next seed in the stream, except the first press after a worked example or Reset, which keeps that example's seed. Through the API or MCP the seed you pass is used as given; blank means 42, the seed of the worked examples.

Money is in nominal dollars. Rates are percentages.

Governing relationships

With V the value of the securities, L the loan and m the maintenance margin, your equity is V − L, and the account is below the maintenance margin when (V − L) ÷ V < m, which is the same as

V < L ÷ (1 − m), the margin-call level.

Today the value can fall by 1 − L ÷ (V × (1 − m)) before equity reaches the maintenance margin; for a single holding at share price P, the call price is P × L ÷ (V × (1 − m)). Leverage is V ÷ (V − L). With r the yearly rate, the loan after t months is L × (1 + r ÷ 12)^t, and the interest over the next year is L × ((1 + r ÷ 12)^12 − 1).

Each path draws its monthly random numbers from one seeded generator, the minimal standard generator with multiplier 48,271, x(next) = 48271 × x mod (2^31 − 1). Path r owns its own stretch of 64 steps of the stream, so no two paths share a draw. Each state x becomes a uniform draw u = x ÷ (2^31 − 1), and each draw becomes the month's return through the lognormal distribution matched to the yearly return μ and volatility σ, spread evenly over 12 months, with Z the standard normal value whose probability is u:

1 + R = e^(m₁ + s₁ × Z), with s₁ = s ÷ √12, m₁ = m ÷ 12, s² = ln(1 + σ² ÷ (1 + μ)²) and m = ln(1 + μ) − s² ÷ 2

so twelve months compound to exactly the yearly mean and volatility you entered. The value moves by V(t) = V(t − 1) × (1 + R(t)), and a path is called at the first month end at which V(t) < L(t) ÷ (1 − m); it stays called after that.

Calculation sequence

The spreadsheet first works out the loan with its interest and the margin-call level for every month. It then draws 100 paths of monthly returns, follows each path's value month by month, marks the month ends at which each path is below the margin-call level, and counts the paths called by each month. It takes the percentiles of the value in every month and of the equity at the horizon of the paths never called. Beside the simulation it follows the securities at the average return with no ups and downs, and it works out the three fixed price scenarios.

Outputs and interpretation

The headline is the share of the 100 paths that are called at some month end within the horizon. When it is above 1 in 10, its label says so. It is an estimate: at 100 paths its 95 percent sampling margin is about 9.8 percentage points, which the page reports, so a different seed can move it by several points. Beside it are the fall in value today that triggers a call, the call price when a share price is entered, the leverage, the interest over the next year, the seed used and the workbook's self-check. The return needed to cover a year of interest, the 10th, median and 90th percentile equity at the horizon of the paths never called, the equity at the average return and the number of paths simulated (always 100) are returned to the API and MCP.

The first chart shows the 10th percentile, median and 90th percentile of the value in each month with the margin-call level, which rises as interest is added to the loan; the percentiles include paths that were called, as if the securities had been kept. The second shows the share of paths called by each month; its last point is the headline. The third shows your return on equity in the three scenarios beside the same price move without a loan: the loan magnifies both directions and costs interest even when the price stays flat. In the scenarios the price moves steadily to the horizon, so a call is judged at the horizon, which for a steady move is the same as checking every month. The tables give the scenarios and the month-by-month figures.

Validation and status logic

The workbook evaluates the conditions below from top to bottom and returns the first matching status.

NOT VALID is a refusal, not a numeric answer: every number reads zero and the tables are empty. An account exactly at the maintenance margin today is valid; the call test is strict, so it is called at the first month end unless its value rises in that month by at least the loan's monthly interest rate. CHECK accompanies a computed result but calls for the stated review. The self-check is reported separately as arithmetic-integrity evidence; it does not replace this ordered status chain.

Assumptions and limitations

The margin is checked only at the end of each month. A broker checks every day, so a path that dips below the margin-call level during a month and recovers by its end is not counted, and the chance shown is lower than a daily check would find. Monthly returns are lognormal and independent from month to month, with no fat tails or crash months, which cause most real margin calls. The maintenance margin and the interest rate stay fixed, interest is added to the loan rather than paid, and no dividends are paid out. The model does not follow what happens after a call, a forced sale or a cash top-up, so the equity percentiles describe only the paths that were never called. It has one long position, no short positions, no tiered rates and no taxes. One hundred paths give an estimate with the sampling margin shown, not a forecast.

Restrictions and non-computing states

This calculator enforces its numeric limits before it accepts a result, and the workbook also refuses the combination a single limit cannot express: a loan too large for the position value and the maintenance margin entered. A retained seed remains part of every simulation.

Errors and warnings

A request rejected by the page's input limits is not a computed result. A transport or service failure cannot establish a fresh workbook answer. Review the workbook's References and Disclaimer, and your broker's margin agreement, before using a result for a real decision.

Sources and further reading

The model's amounts, rates and return assumptions come from the inputs, not market data. The workbook's References sheet identifies the calculation sources. The links below explain the rules and ideas behind them; they do not endorse this calculator.

• FINRA Rule 4210, Margin Requirements, sets the minimum maintenance margin for long positions at 25 percent of the current market value and lets brokers set higher house requirements.
• Regulation T, Credit by Brokers and Dealers (12 CFR Part 220), governs the credit a broker may extend to buy securities.
• S. K. Park and K. W. Miller, “Random number generators: good ones are hard to find”, Communications of the ACM 31(10), 1988, and the Park–Miller–Stockmeyer 1993 correspondence describe the generator family. The workbook uses multiplier 48,271 and modulus 2³¹ − 1.
• The NIST/SEMATECH e-Handbook's lognormal distribution section and Microsoft Support's NORM.S.INV and PERCENTILE.INC documentation describe the distribution and percentile functions used by the workbook.

This is an educational estimate, not financial, investment, tax or legal advice. Margin rules, house requirements and interest rates differ between brokers; check your own account agreement before you borrow.