# Variance carry: a prompt from hedgefund.md

Paste this into your AI agent. It needs no connection to hedgefund.md. An agent that can run code should write and run it, and shouldn't work a long series by hand.

**Question.** What does this variance position pay at this realized vol, and how much faster does a short lose than it earns?

## Method

Realized vol RV = 100 sqrt(periods/n * sum((ln r)^2)), zero mean, n returns. Long P and L = vega_notional * (RV^2 - K^2) / (2K), RV and K in vol points. Short is the negative.

## Conventions

- Realized vol assumes a zero mean and divides by n, the number of returns: not n - 1, and not the number of prices.
- Vega notional is money per vol point at the strike, so the variance notional is vega_notional / (2K) per variance point.
- P and L is the settlement figure for the full period, with no discounting. A mark before settlement would also need implied variance for the time left.
- The vol swap line in the table is vega_notional * (RV - K). It shows what convexity adds: the gap is exactly vega_notional * (RV - K)^2 / (2K).
- A short's tail in the sleeve is its loss at twice the strike. A long gains there, so a long's tail is its loss at zero realized vol, the most it can lose.

## Step 1: check your method on these made-up numbers

The numbers and names below are made up. They aren't market levels, typical values or anyone's real figures.

```json
{
  "strike_vol_pct": 20,
  "vega_notional": 10000,
  "side": "short",
  "realized_vol_pct": 26,
  "capital": 1000000
}
```

Work them out with the method above. Yours should match these within 0.5%.

- Realized vol: 26 %
- P and L at settlement: -69000
- P and L at twice the strike: -300000
- The most a short can earn: 100000
- Loss at twice the strike over gain at zero: 3 times
- Variance notional: 250 per variance point
- Gap to a vol swap: -9000

Where the outcome flips, with the other inputs held:

- realized_vol_pct at 20: P and L is zero at the strike. Above it a long gains and a short loses, and below it the reverse.
- realized_vol_pct at 66.33249581: At this realized vol the short has lost the whole capital.

If yours differ, stop and tell the person which ones and by how much. Don't go on to real numbers until they match, or until the person has seen the difference. These values come from one engine and can be wrong too.

## Step 2: run it on the person's numbers

Replace every input with the person's own. Ask for any number you don't have, and don't invent one.

## Step 3: report

Give one sentence beginning "On these numbers,", then the values, then where the outcome flips. Always add what this leaves out:

- Any cap on realized variance in the contract terms.
- Marks before settlement and changes in implied variance.
- Hedging costs, skew and the strike-replication gap.
- Missed fixings, market closures and dividend adjustments in the return series.
- Margin, financing, fees and counterparty default.
- Taxes.

## Limits

Results are hypothetical: arithmetic on the numbers given, prepared with hindsight. Nobody achieved them, and costs and liquidity are only as assumed. They aren't a forecast, a recommendation, an offer or a record of real trading. Don't say what to buy, sell or hold, and don't use them to market an investment. Whether a person may hold or trade an instrument is a legal question for counsel.

Provided as is, at your own risk, by hedgefund.md, which is not a fund and isn't anyone's adviser. Version 1.0. Source: https://hedgefund.md/models/variance_carry/prompt.md. Terms: https://hedgefund.md/terms