Question

Your fund is considering trading 10-year bonds issued by the UAE government, and you see that at 9:30 a.m. their lowest ask price is $102.31 and their highest bid price is $99.50. Five seconds later a buy order for a block of $10 billion is executed at $102.76. At 10:30 a.m. you check the market again and see that the lowest ask price is $102.55 and their highest bid price is $100.02.

a. Compute the (absolute and relative) quoted spread at 9:30 and at 10:30.

b. Compute the (absolute and relative) effective ask-side half-spread at 9:30.

c. Compare the quoted half-spread with the effective (relative) ask-side half-spread at 9:30. What may explain this difference between them?

d. Compute the (absolute) realised spread in the 9:30-10:30 interval.

e. Compare the realised spread computed under (d) with the (absolute) effective spread at 9:30 computed under (b). What may explain the difference between them?

Answer 1

Given information:
Time	Lowest Ask	Highest Bid
09:30	102.31	99.5
10:30	102.55	100.02

a. At 9:30 the absolute spread is 2.81. and the relative spread (that is equal to the absolute one divided by the mid quote) is 2.78%. At 10:30 the absolute spread is 2.53 and the relative spread is 2.5%

					Quoted Spread
a)	Time	Lowest Ask	Highest Bid	Midprice	Absolute	Relative
	09:30	102.31	99.5	100.905	2.81(102.31- 99.5)	0.027847976(2.81/100.905)
	10:30	102.55	100.02	101.285	2.53(102.55- 100.02)	0.02497902(2.53/101.285)

b. At 9:30 the absolute effective ask-side half-spread is 1.85, and the relative effective ask-side half-spread is 1.84

					Effective Ask-Side Half Spread
Time	Lowest Ask	Highest Bid	Trans. Price	Midprice	Absolute	Relative
09:30	102.31	99.5	102.76	100.905	1.855(100.905-102.76)	0.018383628(1.855/100.905)

c. At 9:30 the relative quoted half-spread is 2.78%/2 = 1.39%, while the relative effective spread is 1.84%. The difference may be explained by the fact that the buy order associated with the transaction price of 102.76 is very large, and therefore “eats” up several limit orders on the buy side of the LOB (if the market is organized as an order-driven market) or equivalently induces dealers to require a higher ask price than the quote one to supply the desired amount. In other words, the difference between the two spreads tells us that, on the ask side, the market for these bonds has limited depth.

d. The realized ask-side half-spread is 1.475.

					Realized Ask-Side Half Spread
Time	Lowest Ask	Highest Bid	Trans. Price	Midprice	Absolute	Relative
10:30	102.55	100.02	102.76	101.285	1.475(101.285-102.76)	0.014562867(1.475/101.285)

. e. The realized half-spread is lower than the effective one. The difference is due to th large buy order at 9:30:05, both the bid and the ask prices have increased, reflecting the informational content of the order. As usual in these cases, the realized spread (which measures the profits of the market maker, benchmarked against a later price) is lower than the effective spread (which measures the trading cost to a trader placing a market order).

The reason is that after the order execution, the market price “turns against” the dealer who has filled the buy order.