**Quantitative Finance Collector**, and kindly contributed to R-bloggers)

All else equal, investors should require higher returns on assets whose liquidity is lower, in other words, investors demand a higher expected return, and hence larger liquidity premium, by holding a less liquidity asset. Risk & return co-exist.

Is this really true for corporate bonds? I run a simple regression using R to test my data, where US corporate bonds are downloaded from TRACE (Trade Reporting and Compliance Engine), CDS data from Datastream, Treasury / Swap interest rate from Federal Reserve Bank, the total number of bonds in my sample is 2409 from year 2004 ~ 2010. Liquidity of a corporate bond is measured as in the paper *Corporate Yield Spreads and Bond Liquidity* by Chen, Lesmond, and Wei (2007), Journal of Finance,

where alpha1 & alpha2 represent bid & ask spread, respectively, by using maximum likelihood estimation we could estimate the transaction cost alpha2-alpha1 for each bond, obviously the higher the transaction cost, the lower the liquidity.

Then I estimate the long-term liquidity premium by

here y, r, lambda and l are corporate bond yield, risk free rate, credit risk premium and liquidity premium. Finally I rank the corporate bonds by their liquidity premium, and scaled the ranking to be between 0 ~ 1, the higher the number, the lower the liquidity premium. What we would expect is a negative relationship between liquidity & liquidity premium, that is to say, investors would expect a lower liqudity premium by holding a larger liquidity bond, and vice versa.

Below is a simple univariate regression of liquidity on liquidity premium, where swap.liquidity is the liquidity premium estimated using swap rate as risk free. Not only the liquidity premium is significant enough, but also its coefficient sign is intuitive and same as expected

the regression result shows the liquidity premium is highly significant even after controlling for those typical bond characteristics such as coupon rate, issue amount, age, maturity and the rating, where rating is expressed as from 1 to 7, with 1 being the highest rank “AAA”. The larger issue amount, the lower transaction cost (and the higher liquidity); also the higher rating, the lower transaction cost. Overall there is a 140 basis point different in transaction costs between the lowest and highest premium.

I think by now we can draw a conclusion based on this empirical analysis: **investors do demand a higher return for less liquidity corporate bond in the market.**

Tags – bond , liquidity**Read the full post at Liquidity Premium vs Liquidity of Corporate Bonds**.

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