Worked example of Long Term Risk (with assumptions)

Definition: what “Long Term Risk” means

Long Term Risk is the risk that remains meaningful when a position (or exposure) is held for a long time. In forex, “long time” usually implies that more than one effect can matter: price changes over time, ongoing costs (such as financing/holding costs), and the possibility that real execution differs from the assumptions used in the example.

It helps to separate two ideas:

• Market uncertainty over time: exchange rates can move in either direction.
• Accumulation of frictions: when you hold, you continue to incur costs and your realized prices may differ from the prices used in forecasts.

A worked example is useful because it forces explicit assumptions about position size, costs, and plausible exchange-rate moves.

Mechanism: how a worked example can quantify it

A simple way to quantify long term risk (without predicting the future) is to compute a range of outcomes for a hypothetical holding period, then describe the downside relative to an initial reference.

Use these components:

1. Initial exposure and size: how much base currency you control and how large the notional is.
2. Price move assumption: pick a plausible minimum and maximum exchange rate for the period.
3. Ongoing costs assumption: estimate an average holding cost rate for the period (as a simplified number).
4. Execution and slippage assumption: decide whether you assume trades execute at the reference rate or whether you include a buffer.

A key limitation is that these inputs are assumptions. The goal is verifiable arithmetic, not a forecast.

Worked numerical example (scenario with explicit assumptions)

Assume an investor opens a forex position and holds it for many weeks. The exact quoting convention varies, so this example uses a simplified payoff expressed in account currency.

Assumptions

• Entry price (reference): 1.1000 (exchange rate units per base currency).
• Holding period outcome range: exchange rate could be as low as 1.0500 or as high as 1.1500.
• Position notional (simplified): 100,000 base units.
• Contract-to-account conversion is simplified so that a change in the exchange rate of 0.0001 corresponds to $10 of P/L. (This is a made-for-arithmetic conversion factor used only to show calculation steps.)
• Average holding cost over the period: $200 total.
• No additional slippage beyond what is implied by the conversion factor (so slippage risk is not included yet).

Compute downside scenario

1. Price change to the downside:
   • From 1.1000 to 1.0500 is a change of -0.0500.
2. Convert price change to P/L using the conversion factor:
   • 0.0500 / 0.0001 = 500 units of the 0.0001 step.
   • P/L from price move = 500 × $10 = -$5,000.
3. Add holding cost:
   • Total outcome = -$5,000 - $200 = -$5,200.

Compute upside scenario

1. Price change to the upside:
   • From 1.1000 to 1.1500 is +0.0500.
2. P/L from price move:
   • +0.0500 / 0.0001 = 500.
   • P/L from price move = 500 × $10 = +$5,000.
3. Add holding cost (still negative):
   • Total outcome = +$5,000 - $200 = +$4,800.

What the example shows as “Long Term Risk”

• In this scenario, the downside over the long holding period is -$5,200, given the assumed price range and holding cost.
• The reason long term risk is relevant is that you cannot treat the problem as only “one price move.” The costs (here modeled as $200 total) and the realized path/execution differences can materially change the realized result.

Limitations and risks (what could break the example)

At least one material limitation is usually present in any worked example like this:

1. Cost and financing uncertainty

   • Holding costs can vary across time and conditions. If your real average holding cost is higher than the assumed $200, the downside grows.

2. Execution and slippage

   • The example assumes the conversion factor already captures the mechanics. In reality, execution can be worse than reference prices, especially when liquidity is lower.

3. Model mismatch for the “plausible range”

   • Choosing 1.0500–1.1500 is subjective. A different range changes the calculated downside immediately. Historical volatility does not guarantee future outcomes.