1. A lower beta is required to support either the liquidity argument, or the "tax option" argument -that increased volatility adds a tax option value and thus lowers the stock's expected or required rate of return. Christopher G. Lamoureux and Percy Poon "The Market Reaction to Stock Splits;The Journal of Finance,1987
2. Bid-ask spreads, as a percent of stock price, increase after a stock split proportionally to the decrease in stock price due to the split. However, firms may use splits as a favorable signal effect;The Effects of Splits on Bid-Ask Spreads,1990