Suppose there is a mean-variance optimizer looking to invest for two periods in bonds. They can invest in a two year bond with annual yield y2 or they can invest in the one year bond at r1 and then, a year later, invest in another one year bond at currently uncertain rate r2. What must be the liquiditiy premium in order for them to be indifferent between the two options?
Now suppose they are looking to invest for three years. What is the liquidity premium to make them indifferent between the three year bond or getting a two year bond, then a one year bond after?
What if they want to invest for n years. Derive the liquidity premium to make them indifferent between then year bond and the n − 1 year bond followed by a one year bond.