How to use the market-neutral portfolio calculator
- List the positions. Enter each one with a name or ticker, its market value in dollars and its beta. Longs take a positive value and shorts a negative one: +400000 for a $400,000 long, −350000 for a $350,000 short. The six defaults are a fictional book of three longs and three shorts. Betas are on the stock pages or can be measured with the beta calculator.
- Enter the capital. The fund’s equity, used to show leverage and exposure as a share of capital.
- Set the hedge instrument’s beta. 1 for an index fund or index future on the benchmark the betas were measured against. Use a different value for a sector fund or another index.
The results show the net beta exposure, net and gross dollars, the average beta of each side and the adjustments. The second table lists each way to neutralize the book side by side.
How the exposures are calculated
Net beta exposure = Σi xi βi = Lβ + Sβxi is the signed dollar value of position i and βi its beta. L and S are the long and short books (S is negative); Lβ and Sβ are their beta-weighted totals. Net beta exposure divided by 100 is the expected gain or loss for each 1% market move.
The adjustments, with H the beta of the hedge instrument:
Short-book scale for dollar-neutral: kD = L ÷ |S|
Short-book scale for beta-neutral: kB = Lβ ÷ |Sβ|Scaling multiplies every short position by the same factor k. A positive h means buy the index; a negative h means sell it.
To be both dollar- and beta-neutral, the calculator solves two equations for the short-book scale k and an index trade h:
A worked example
The book holds $1,000,000 of longs with an average beta of 1.060 and $900,000 of shorts with an average beta of 1.275. Gross exposure is $1,900,000, 1.90× the $1,000,000 of capital. The book is net long $100,000 in dollars, but its net beta exposure is -$87,500: the high-beta shorts outweigh the longs, so the book is slightly net short the market.
Each fix solves one problem and worsens the other:
- Buy $87,500 of the index to remove the beta exposure. The book is then net long $187,500 in dollars.
- Scale the shorts by 1.111 to $1,000,000 to be dollar-neutral. Net beta exposure deepens to -$215,000.
- Scale the shorts by 0.924 to $831,373 to be beta-neutral. The book is then net long $168,627.
Making it both at once means cutting the stock shorts to $218,182 and selling $781,818 of the index: most of the short side becomes an index hedge, which gives up much of the stock selection on that side.
Why the two neutralities conflict
Dollar neutrality balances money; beta neutrality balances market sensitivity. They agree only when a dollar of longs carries the same beta as a dollar of shorts. Long/short books rarely look like that, because the stocks a manager likes and dislikes tend to differ systematically: shorts often cluster in speculative, high-beta names, and longs in steadier businesses.
When the shorts carry more beta, as in the example, a dollar-neutral book is net short the market. It will lose in a broad rally even if the longs beat the shorts after adjusting for beta, and gain in a sell-off for the same reason. The P&L then reflects a market bet the manager may not intend. When the longs carry more beta, the opposite happens:
| Example book | Longs with higher beta | |
|---|---|---|
| Average beta, longs | 1.060 | 1.145 |
| Average beta, shorts | 1.275 | 0.950 |
| Net dollars | $100,000 | $100,000 |
| Net beta exposure | -$87,500 | $290,000 |
| Net beta after dollar-neutral scaling | -$215,000 | $195,000 |
| Net dollars after beta-neutral scaling | $168,627 | -$205,263 |
In the second book the longs average more than the index beta and the shorts less. Scaling the shorts and trading the index cannot then achieve both neutralities with a positive short book, so the calculator reports it as not possible. Fixing it means changing the names, using a hedge with a beta above the long book’s or below the short book’s, or choosing which neutrality matters more.
Which one to aim for
Beta neutrality is the one that removes the market’s direction from returns, so it is usually the primary goal of a market-neutral strategy. Dollar neutrality still matters for financing: margin requirements, borrowing costs and short rebates all depend on dollar amounts, not betas. Some funds run beta-neutral with a modest dollar tilt; others hold dollar-neutral books and hedge the residual beta with index futures, the first adjustment in the table.
A beta-neutral book is not risk-free. It still carries sector, size, value, momentum and other factor exposures, plus stock-specific risk. Beta is also an estimate: a book that is neutral on two-year betas may not be neutral during a sell-off, when correlations and betas tend to change. Re-estimate betas regularly and treat neutrality as a range rather than an exact point.
What this calculator does not include
- Other factors. Only market beta is balanced; sector and style exposures are not measured.
- Beta uncertainty. Betas are taken as exact. A beta calculator shows how wide their confidence ranges can be.
- Costs and financing. Borrow fees on shorts, the cost of index futures and margin requirements are not modeled.
- Volatility. Dollar and beta neutrality say nothing about how volatile the book is; VaR attribution shows where the risk sits.
- Rebalancing drift. Prices move every day, so exposures drift away from neutral between rebalances.