Kyle’s Lambda

Introduction

Kyle (1985) Lamdba can be interpreted as the cost of demanding a certain amount of liquidity over a given time period. Following Hasbrouck (2009) and Goyenko, Holden and Trzcinka (2009), we can estimate Kyle’s Lambda for stock \(i\) as the slope coefficient \(\lambda_{i}\) in the following regression model:

(1)\[r_{i,n} = \lambda_{i}\cdot S_{i,n} + \varepsilon_{i,t}\]

where for the \(n\)-th five-minute period, \(r_{i,n}\) is the (percentage) stock return and \(S_{i,n}\) is the signed square-root dollar volume, i.e., \(S_{i,n}=\sum_k sign(v_{k,n}) \sqrt{|v_{k,n}|}\), and \(v_{kn}\) is the signed dollar volume of the \(k\)-th trade in the \(n\)-th five-minute period.

References

• Kyle (1985), Continuous Auctions and Insider Trading, Econometrica, 53(6), 1315–1335.

• Hasbrouck (2009), Trading Costs and Returns for U.S. Equities: Estimating Effective Costs From Daily Data, The Journal of Finance, 64(3), 1445–1477.

• Goyenko, Holden and Trzcinka (2009), Do Liquidity Measures Measure Liquidity, Journal of Financial Economics, 92(2), 153–181.

API

frds.measures.kyle_lambda(returns: ndarray, signed_dollar_volume: ndarray) → float

Kyle’s Lambda

Parameters:

• returns (np.ndarray) – (n,) array of stock returns

• signed_dollar_volume (np.ndarray) – (n,) array of signed dollar volume

Returns:

Kyle’s lambda (*1000000)

Note

The return value is the estimated coefficient of \(\lambda\) in equation (1) multiplied by 1,000,000.

Return type:

float