Lesson 25 of 25 · 7 min

One portfolio, two correlation regimes, one number that changed

$953,600 of unused capacity became a $28,500 deficit, and the only input that moved was an average of twenty-one estimates.

Nothing in this lesson changes except one estimate. The holdings, the prices, the weights and the balance all stay where they are. Only the matrix is re-estimated, and everything downstream of it moves.

A pledged pool of $4,270,000 across seven equally weighted holdings, $610,000 each, every holding with 36 percent annualised volatility. Seven holdings means 7 times 6 divided by 2 = 21 distinct pairwise correlations. Both matrices below are summarised by the average of those twenty-one entries, applied uniformly, which is the arithmetic Track 7 lesson 10 used.

Estimated over a calm period the average entry is 0.29. The bracket is one-seventh plus six-sevenths of 0.29 = 0.3914, portfolio volatility is 36 times the square root of that = 22.52 percent, and effective bets are 7 divided by 2.74 = 2.55. Estimated over a drawdown the average entry is 0.81. The bracket becomes 0.8371, volatility becomes 32.94 percent, and effective bets fall to 7 divided by 5.86 = 1.19. Ten and a half points of volatility, and 1.36 of the 2.55 bets, gone.

An illustrative schedule assigns 68 percent to a pool behaving like two and a half or more independent positions and 45 percent to one behaving like fewer than one and a half. So the calm matrix earns $4,270,000 times 0.68 = $2,903,600 of lending value and the drawdown matrix earns $4,270,000 times 0.45 = $1,921,500 — a gap of $982,100 on a pool whose market value never moved.

Set a balance of $1,950,000 against each. Against the calm figure that is 1,950,000 divided by 2,903,600 = 67.16 percent of lending value, leaving $953,600 unused. Against the drawdown figure it is 1,950,000 divided by 1,921,500 = 101.48 percent, a deficit of $28,500. The two reconcile exactly: 953,600 plus 28,500 is the $982,100 gap. Closing the deficit takes $28,500 of repayment, or $63,333 of further market value pledged at the 45 percent rate.

Nothing was sold, bought, repriced or reweighted. The number that changed was an average of twenty-one pairwise estimates, from 0.29 to 0.81.

Key terms

Re-estimation: Recomputing a matrix from a different window. It changes every figure that depends on the matrix while changing nothing about the portfolio.
Unused capacity: Lending value not yet drawn. It is measured against a lending value that depends on a correlation estimate, so it moves when the estimate does.
Deficit: The amount by which a balance exceeds lending value. Closable by repayment or by pledging more, and the second route is scaled by the advance rate.

Worked example

Seven holdings under two matrices

Seven equally weighted holdings at $610,000 each, pledged pool $4,270,000, each at 36% volatility. Twenty-one pairwise entries averaging 0.29 on a calm window and 0.81 on a drawdown. Illustrative schedule: 68% at two and a half bets or more, 45% below one and a half. Balance $1,950,000.

Calm matrix: effective bets and volatility: 2.55 and 22.52%
Drawdown matrix: effective bets and volatility: 1.19 and 32.94%
Lending value at the 68% tier: $2,903,600
Lending value at the 45% tier: $1,921,500
The $1,950,000 balance against each: 67.16% and 101.48%
Unused capacity, then deficit: $953,600, then $28,500

Seven holdings, seven unchanged prices, one unchanged balance, two matrices. The whole $982,100 came from twenty-one numbers averaged over a different stretch of months.

Check yourself

The same seven holdings and the same two tiers, but the balance is $2,010,000. What is the unused capacity under the calm matrix, the deficit under the drawdown matrix, and do they still reconcile?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.