Question 2. (Liquidity Premium) (7 Points) You recently found out that when the market is in recession, ALL assets seem to suffer from some degree of liquidity problems as there are less trades than usual, and thus it is hard to sell an asset without losing some of its fair value. So, you concluded that at least some portion of liquidity risk must be systematic in nature and therefore it must be compensated by the market. To verify this, you cut the market portfolio in half by the illiquidity measure developed by Amihud (2002) [So that you have one relatively liquid portfolio and one relatively illiquid portfolio. Assume that this measure is reliable.] and calculated the market liquidity risk premium as follows: Market liquidity risk premium = Expected return on the illiquid portfolio - Expected return on the liquid portfolio = [E(RIL) - E(RL)] Then you formed 5 portfolios from the entire market based on liquidity (Amihud measure) and estimate the factor loading f (called liquidity beta) of each portfolio using [Rn - RL] as the factor in a factor model and got the following results: Portfolio on Liquidity Low 2 3 High Liquidity Beta (factor loading) 0.7 1.3 0.9 1.5 1.1 Return 8.3% 7.5% 6.7% 4.1% 2.4% (a) Assuming that all your estimations are correct, determine whether your measure of liquidity risk can be a systematic risk factor from the above table. (Prove a brief explanation) [2 points] After looking at the above results, (b) you conjecture that market liquidity should be closely related to firm size and liquidity risk will matter more for big firm stocks. To further verify whether the above liquidity factor can be a measure systematic risk, you formed 15 portfolios on firm size and liquidity factor loading (numbers in % are portfolio returns): Portfolio on (firm Size \\ Liquidity factor loading) Low 2 3 High Small 11.4% 9.2% 6.4% 4.9% 1.1% Medium 7.2% 4.5% 7.1% -2.3% -1.9% Big 2.3% 3.8% 5.0% 5.7% 6.1% (b) From the above table, verify whether your conjecture seems to be correct or not. (Prove a brief explanation) [2 point] (c) Assuming that all your estimations are correct, determine whether your measure of liquidity risk can be a systematic risk factor from the above table. (Prove a brief explanation) [3 points]