How much of a fixed-price retail margin does the load shape take?
A retail book hedged with a flat block reports a margin on the annual forward. Its customers do not consume at the annual forward, and the difference is almost the whole margin.
A supplier sells 4,200,000 MWh a year at a fixed 78.50, buys a flat block at the forward to cover it, and books a margin of 25,883,698.63. Once the customers’ consumption is priced in the hours it actually happens, the same book earns 3,601,531.82. The load shape takes 22,282,166.81, which is 86.0857 per cent of the booked margin, and nothing in the flat-block report shows it.
No price view is needed to get there. The annual forward is set equal to the time-weighted average of the year’s 8,760 hourly prices, 70.1872, so the flat block is priced fairly by construction. The whole effect comes from the fact that customers use more power when power is dear, and the block buys the same amount in every hour.
The book as booked, and the book in its hours
The retail book has four lines. Revenue is 4,200,000 MWh at 78.50. The cost to serve is 2.15 per MWh. The power cost is the only line that changes between the two readings: once as a flat block at the forward, once as the customers’ load bought hour by hour on the same price curve.
Flat block at the forward
Load in its hours
Revenue
329,700,000.00
329,700,000.00
Power cost
294,786,301.37
317,068,468.18
Cost to serve
9,030,000.00
9,030,000.00
Price paid per MWh
70.1872
75.4925
Margin per MWh
6.1628
0.8575
Margin
25,883,698.63
3,601,531.82
Same customers, same volume, same curve. The difference in power cost, 22,282,166.81 or 5.3053 per MWh, is the shape cost.
The price the book is really exposed to is the load-weighted 75.4925, not the time-weighted 70.1872. The premium of 5.3053 per MWh is the shape cost expressed as a price, and it is 86.0857 per cent of the 6.1628 the desk thinks it is earning. What remains is 0.8575 per MWh, on a book that sells at 78.50.
The flat-block report is not wrong about anything it measures. The block is bought at a fair price, the volume matches the contract to the megawatt-hour, and the margin is correctly computed. What it measures is a customer who consumes the same amount in every hour of the year, and no retail customer does.
Where the 22,282,166.81 comes from
A flat block at an average load of 479.45 MW delivers exactly the contracted 4,200,000 MWh over the year, but not in the right hours. In the dearest hours the customers take more than the block delivers, and the supplier buys the difference at spot. In the cheapest hours they take less, and the supplier sells the surplus back. The shape cost is that trade, row by row down the price duration curve.
Hours
Price
Load, MW
Load less block, MWh
Bought (sold) at spot
100
260
772.21
29,275.57
7,611,648.94
250
155
705.47
56,505.43
8,758,341.75
550
105
633.97
84,986.55
8,923,587.86
1,100
85
572.01
101,809.08
8,653,771.95
1,900
72
505.27
49,057.44
3,532,135.60
2,400
63
452.84
(63,873.98)
(4,024,060.56)
1,700
50
390.87
(150,588.46)
(7,529,423.11)
760
34
338.44
(107,171.64)
(3,643,835.62)
8,760
479.45
0.00
22,282,166.81
The flat block is 479.45 MW in every hour. Positive rows are bought at spot to cover load above the block; bracketed rows are the surplus sold back.
The volumes net to zero, as they must: the block and the load are both 4,200,000 MWh. The money does not. In the dearest 3,900 hours the supplier buys 321,634.08 MWh for 37,479,486.10, an average of 116.53. In the cheapest 4,860 it sells the same 321,634.08 MWh for 15,197,319.29, an average of 47.25. A spread of 69.28 on 7.66 per cent of the volume is the whole shape cost.
Concentration does the rest. The 100 dearest hours, 1.14 per cent of the year, carry 34.16 per cent of the shape cost on their own. The dearest 350 hours carry 73.47 per cent. The top 900 hours cost 113.51 per cent of it, more than the total, and the cheap hours hand part of it back.
A slightly peakier customer takes all of it
The shape is an input: eight multipliers on average load, from 1.62 in the dearest hours to 0.71 in the cheapest, normalised so the year still adds up to the contracted volume. The obvious question for anyone pricing a new customer book is how much more peaked the load could be before the margin is gone. Chapter 9 answers it by dividing the booked margin by the shape cost, which gives 1.1616. The Amplitude sheet solves it and gets 1.1627.
Amplitude
Shape cost
Per MWh
Share of booked margin
Margin left
0.00 (flat)
0.00
0.0000
0.00%
25,883,698.63
0.25
5,594,877.33
1.3321
21.62%
20,288,821.30
0.50
11,173,483.73
2.6604
43.17%
14,710,214.90
1.00 (the book’s shape)
22,282,166.81
5.3053
86.09%
3,601,531.82
1.1627
25,883,698.63
6.1628
100.00%
0.00
1.50
33,326,611.33
7.9349
128.76%
(7,442,912.70)
1.5721
34,913,698.63
8.3128
134.89%
(9,030,000.00)
Amplitude scales every multiplier’s distance from 1.00; the load is re-normalised to 4,200,000 MWh at each step. At 1.5721 the margin before the cost to serve is zero.
A customer book whose multipliers sit 16.27 per cent further from 1.00 than this one earns nothing after the cost to serve. That is a modest change in the mix of customers, and the mix is usually decided by whoever is winning the business, not by whoever is hedging it.
The shortcut and the solve differ because the shape cost is not proportional to the amplitude. The raw multipliers average 1.0058333 across the year’s hours, not 1.00, and the normalisation that restores the contracted volume moves as the amplitude moves. Half the amplitude costs 11,173,483.73, which is 43.17 per cent of the margin rather than half of 86.09; twice that half is 64,800.65 more than the full shape costs. The gap between 1.1616 and 1.1627 is small, and the workbook shows both rather than smoothing it over, because the shortcut is exactly the proportional reasoning the chapter warns against three sentences earlier.
What the plant does and does not cover
The tempting reply is that the group also owns a power station, and a power station earns most in exactly the hours the retail customers cost most. It does, and it earns 19,599,440 of convexity over its must-run block priced on its own hours. That covers 87.96 per cent of the shape cost, not all of it.
Flat reading
Hour by hour
Effect of the hours
Plant gross margin
41,192,800.00
60,792,240.00
19,599,440.00
Retail margin
25,883,698.63
3,601,531.82
(22,282,166.81)
Group
67,076,498.63
64,393,771.82
(2,682,726.81)
Chapter 15. The flat reading overstates the group by 2,682,726.81, or 4.00 per cent.
The netting hides two effects, each more than seven times the size of the net. And the physical cover is thinner than the annual totals suggest. Over the 3,900 hours the plant runs, it produces 226,502.91 MWh more than the retail customers take. In the three dearest rows of the curve, the customers still take 44,274.40 MWh more than the plant produces, and 2,008,502.91 MWh of retail load falls in hours when the plant is not running at all. A plant that is long over the year can be short in precisely the hours that cost the most.
What to do with it
Report the retail margin at the load-weighted price, not the annual forward. On this book that single change moves the margin per MWh from 6.1628 to 0.8575, and it needs nothing a supplier does not already hold: a price curve and a load profile. Beside it, three numbers belong in any retail pricing paper:
The shape cost per MWh, set against the margin per MWh the tariff is built on. Here 5.3053 against 6.1628.
The amplitude at which the shape takes the whole margin, solved rather than divided. Here 1.1627.
The share of the shape cost sitting in the dearest hundred hours. Here 34.16 per cent, which is also the share a peak-hour hedge or a demand-response clause could address.
A shape premium of 5.3053 on a tariff is not a margin. It is the price of the customers’ timing, and a book that reports it as margin has counted a cost it has not yet paid as a profit it has already made.
Reproducing it in the workbook
Everything above sits in Shape_and_the_Retail_Book.xlsx. On the Shape sheet the booked margin is B26, the cost hour by hour B29, the shape cost B30, the load-weighted price B32 and the share of the booked margin B36; column J gives the block less load by row, and multiplying it by the price in column B, with the sign reversed, gives the row-by-row table above. The shape multipliers are the blue cells C10:C17: set them all to 1.00 and the shape cost falls to zero.
On the Amplitude sheet the input is B4, which ships at 0.5; type 0.25, 1 or 1.5 to reproduce the table. B17 and B18 give the shape cost and its share, B23 the shortcut of 1.1616, B24 the solved 1.1627 and B26 the 1.5721 at which the cost to serve goes too. The Group sheet carries the plant in B4:B7 and the three-column comparison in B27:D29, with the coverage figures in B37:B41. The Checks sheet sets every one of these beside the figure the book prints, 44 of 44 OK.
The workbook behind this article
Every figure above is a live formula in the free companion files for
Energy Trading: the curve, the shape, the amplitude and the group, with a Checks sheet
setting the printed figure beside the computed one. No account and no email address.
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