Ideal price

The ideal price is the workbook's name for the single "fair" price hiding inside a two-sided quote. It is defined as the average of the best bid and offer price.

Nobody necessarily trades at it. A buyer who wants shares now pays the ask, which is above the ideal price; a seller who wants out now receives the bid, which is below it. The workbook puts it this way: in an infinitely liquid market, it would be possible to execute large transactions on both the buy and sell side at prices very close to the ideal price. In a real market you pay more than the ideal price when buying and receive less when selling.

That gap is the point of defining it. The ideal price is the yardstick — the zero line — from which the cost of trading in size is measured.

Impact cost is the percentage degradation experienced vis-à-vis the ideal price when shares are bought or sold. Two properties follow, and the workbook states both: impact cost varies with transaction size, and it is different for the buy side and the sell side.

The workbook's first illustration uses a book with a best bid of Rs 4.00 and a best ask of Rs 4.50, so the ideal price is (4 + 4.50) ÷ 2 = Rs 4.25. Its second uses a best bid of 9.80 and best ask of 9.90, giving an ideal price of Rs 9.85; buying 1,500 shares costs an average of Rs 9.9333, and the impact cost is printed as 0.84%.

Because the ideal price sits exactly midway, the bid-ask spread is always twice the distance from the ideal price to either best quote. That is why the spread "conveys the transaction cost for a small trade", while the ideal price lets you measure the cost of any trade size on either side.

Ideal price  = (Best bid price + Best offer price) ÷ 2

Impact cost (buy)  = (Average buy price − Ideal price) ÷ Ideal price × 100
Impact cost (sell) = (Ideal price − Average sell price) ÷ Ideal price × 100

The workbook's options order book (Chapter 6, section 6.5):

Ideal price = (16.60 + 16.80) ÷ 2 = Rs 16.70

Buy 5,700 at market (illustrative quantity). 2,850 at 16.80 and 2,850 at 16.85:

Average buy price = (2,850 × 16.80 + 2,850 × 16.85) ÷ 5,700 = Rs 16.825
Impact cost (buy) = (16.825 − 16.70) ÷ 16.70 × 100          = 0.75%

Sell 5,700 at market. The best bid has 19,950 waiting, so all 5,700 go at 16.60:

Impact cost (sell) = (16.70 − 16.60) ÷ 16.70 × 100 = 0.60%

Same book, same quantity, different impact cost on each side — because the ideal price is fixed but the depth behind the bid and the ask is not.

A rounding note on the workbook's figure. In the 9.85 example, (9.9333 − 9.85) ÷ 9.85 × 100 = 0.846%, which the workbook prints as 0.84%. If a question gives options of 0.84% and 0.85%, the workbook's own printed answer is 0.84%.

Chapter 2, section 2.4 (Attributes of an Index), defines the ideal price while introducing impact cost, because low impact cost is a mark of a liquid, investable index. Chapter 6, section 6.5, returns to impact cost and the bid-ask spread as trading costs "not actually paid by market participants". The ideal price itself is the first step in every impact cost calculation the paper sets.

• Ideal price is the mid-point of the best bid and best offer — not the last traded price, not the best ask, not the closing price.
• Impact cost is measured from the ideal price, so using the best ask as the base for a buy order understates it.
• Impact cost differs on the buy and sell sides even though the ideal price is the same for both.
• The spread is twice the distance between the ideal price and either best quote.
• The ideal price assumes infinite liquidity; real trades land on either side of it.