Portfolio risk and correlations

This lesson explains how to calculate the risk of a portfolio in which positions react to the same factors: sector, currency, interest rates, or asset type. It is for someone who has already mastered a limit per single transaction and wants to know why a sum of positions that each comply with that limit can still surprise. The starting point is correlation understood as a common factor, not as a single number from a tool.

Why several positions are sometimes one position

A limit per single position answers the question how much can I lose on this one entry. It does not answer the question how much can I lose if all my entries turn out to be the same bet. Three companies from one sector, two pairs quoted in dollars, or an index contract plus a stock from that index are, at the risk layer, one decision made several times. The 1-2% rule still works correctly for each position separately, but it does not protect against repeating the same bet five times. It is also worth knowing what an index contract exactly contains and how it differs from a commodity contract — the lesson Indexes and commodities compares them.

The consequence is arithmetic, not psychological. If each of five positions carries 1R of risk and all depend on one factor, then in a scenario that hits that factor the account behaves as if it held a 5R position. A day on which nothing happened on any single chart can therefore bring a drawdown equal to five planned losses.

What correlation is and what one coefficient does not say

Correlation takes values from -1 to +1. A positive value means the assets move in the same direction, a negative one means the opposite. A value close to zero does not mean independence under all conditions; it means no clear relationship in the data window from which you calculated the coefficient. The same coefficient calculated on different intervals and in different periods can come out differently, which is why you always record the time window and data frequency in the sheet.

The coefficient is an auxiliary tool, not the answer. In practice the more important thing is the common factor that can be named: sector, settlement currency, rate level, asset class. A named factor allows a decision even when the tool does not calculate correlation for your combination of instruments. The settlement currency can also be a stablecoin if you hold capital on a crypto exchange — and its risk is not limited to the exchange rate, which the lesson on stablecoins and depeg risk describes.

How many independent bets you really have — the formula

Assuming every position contributes the same risk and every pair of positions has one common correlation ρ, the number of independent bets is approximated by:

effective_bets ≈ N / (1 + (N - 1) x ρ)
risk_multiplier ≈ sqrt(N x (1 + (N - 1) x ρ))
total_risk_in_R ≈ risk_per_position_in_R x risk_multiplier

The formula’s behaviour is visible at the extremes. At ρ = 0 you have N independent bets, and risk grows with the square root of N, that is, more slowly than linearly: five independent positions come to about 2.2R, not 5R. At ρ = 1 you have one bet repeated N times, so the multiplier equals N and five positions at 1R give exactly 5R — the same situation described in the paragraph about five entries depending on one factor. Watch the direction of the relationship: the number of independent bets falls as correlation rises, while risk rises. The table below shows the same five-position portfolio under different assumptions; all numbers in it are illustrative, chosen only to show the shape of the relationship.

The formula is a model, not a forecast. It assumes equal risk size and one common correlation for all pairs, while a real portfolio has varied correlations. Treat the result as an order-of-magnitude measure: its job is to show that five independent positions at high correlation behave closer to one than to five.

How to calculate total exposure in one currency

Notional values in different currencies must be brought to a common denominator before you compare them with any limit. The calculation is short but requires consistency:

exposure_in_account_currency = Σ (position_value_i x currency_rate_i)

Example with illustrative numbers: a position worth 1,000 USD and a position worth 800 EUR, rates of 4.00 PLN/USD and 4.30 PLN/EUR (all figures illustrative, not quotes). The sum is 4,000 + 3,440 = 7,440 PLN (Polish złoty) (illustrative figure).

Two things are easy to confuse. First: notional is not risk — a position with a large notional and a tight stop contributes less risk than a small notional with a wide stop. Notional serves to control leverage and liquidity, while risk in R serves to control the limit. Second: the rate used for conversion is itself an exposure, so you record its source and the date it was read. If your position is already a currency pair settled in one of those currencies, you convert it once and do not add the same exposure a second time in another row.

A limit per factor alongside a limit per position

A limit per factor does not replace a limit per position — it adds a second dimension of control. Setting it comes down to four steps:

1. Name the factors. Sector, settlement currency, rate level, asset class. Each position gets one main factor and, if necessary, one additional.
2. Sum risk in R per factor. Position A at 1R, position B at 1R, position C at 1.5R give 3.5R on one factor.
3. Compare with the limit per factor. A limit recorded in the plan, for example 2R per sector, is a number, not a guideline.
4. Decide before entry. You either reduce an existing position or do not open a new one. A decision after the fact is only a description of an exceeded limit.

Order matters: first you calculate the sum per factor, then you check the limit, and only at the end do you look at the chart of the new instrument.

Where to get a correlation coefficient for your own sheet

The coefficient is not given once and for all, so you need a procedure for reading it, not a single value. The simplest way to work:

1. Choose a window and interval. For example daily returns from the last few months — you record the period and interval in the sheet together with the result.
2. Calculate the pair you actually compare. The correlation of an index with a single stock is sometimes different from the correlation of two stocks from the same sector.
3. Repeat the calculation on a second window. If the result changes significantly, treat the relationship as uncertain and fall back to the common factor named in step one.
4. Verify in your own tool. You read values from an analytical platform or a sheet you maintain yourself; never take a number from memory or from someone else’s post.

If you have no access to a coefficient, you can still work: name the factor and apply a limit to it, assuming conservatively that positions from the same factor behave similarly.

Correlations change under stress

In market panic, many assets move in the same direction, because investors reduce risk across the whole portfolio, not just in one company. Relationships that looked weak in a calm period can strengthen markedly then. The conclusion for the plan is concrete: do not assume that a measured correlation will hold on the worst day, and leave a buffer in the limit per factor. The context of these changes is described in the lesson on risk-on and risk-off, and the way correlated losses add up over time in the material on expectancy and drawdown.

For the same reason, drawdown is calculated for the whole portfolio, not for a single position. One successful transaction does not compensate for five losses that occurred at the same moment and for the same reason.

When the portfolio says do not trade

1. You cannot name the factor you are entering. A missing name means you do not know what you are summing risk with.
2. The sum of R per factor exceeds the plan’s limit. The limit concerns the whole exposure, not each position separately.
3. The new position is the same thesis as a position already open. A different instrument does not change the direction of the bet if it reacts to the same factor.
4. The coefficient calculated on a second window comes out significantly different and you have no buffer. Then you either reduce size or postpone entry until you set a limit per factor.

Exposure sheet (fill in before your next entry)

Typical mistakes

• Counting positions instead of bets. Six rows in a sheet do not mean six independent decisions.
• Assuming a different instrument is a different factor. Two pairs quoted in dollars are one factor, even if the charts look different.
• Treating a measured correlation as a constant. A coefficient from one window describes that window, not the future.
• Summing notional values without a rate and a date. Exposure in one currency requires a rate; without the read date the number loses meaning after a few days.
• Setting the limit per factor after opening a position. Then it is not a limit, only a description of a state that already exists.
• Omitting leverage when calculating notional. Instruments with margin allow building a large notional on a small deposit, and that affects exit liquidity.

Measurable exercise

Take the last month of your transactions or ten example positions. For each, record the main factor, the notional in account currency, and the risk in R. Complete the exposure sheet and calculate the sum of R for each factor. Then choose the set of positions with the largest sum and plug it into the formula for the effective number of bets, assuming two correlations: moderate and high. Record both results. The conclusion should be one sentence: how many independent bets you had in that period and under what limit per factor they fit the plan. If you hold index funds in the portfolio, also check how strongly their components overlap — the material on ETFs in practice helps here.

Common questions

How do I check the correlation of two assets?

You calculate the coefficient from historical data or read it from an analytical tool, recording the time window and interval. Treat the value as a description of that window, not as a permanent property of the pair. When the result changes between windows, it is better to base the limit on a named common factor: sector, currency, or asset class.

Does a limit per factor replace the 1-2% rule per position?

No, they are two different levels of control. The per-position rule guards the size of a single entry, and the per-factor limit guards the sum of exposure to one bet. You record both numbers in the plan and check them before entry, not after.

Are two currency pairs with dollars always one factor?

Broadly yes, because both react to the same currency. Different quote currencies give partial diversification, but the common factor remains. You calculate the sum in R per factor and only then check the limit.

Why calculate the effective number of bets when the formula is a simplification?

Because without that number you cannot see the difference between a portfolio of five independent positions and a portfolio of one thesis repeated five times — both look identical in the sheet and in the order list. The formula is a model, so it does not give precision to a tenth of an R, but it shows the order of magnitude of exposure. That knowledge changes the decision about size and about the number of simultaneous entries, and those two decisions determine portfolio drawdown.