Equilibrium Interest Rate And Liquidity Premium Under Proportional Transactions
Equilibrium Interest Rate And Liquidity Premium Under Proportional Transactions
Dimitri Vayanos
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J with 6 = and r = R — r' . Given the investors total wealth «> = "f + -4, . The vahu-s of the liquid and illiquid portfolios over time are given by At = Wt and at — {or t < tau[ At = to, ;e^<'-"''' and a, = xvt - uv;f'''-"i'' for r^ < t < t* + A* At = ivt and Oj = for r* + A' < t.
It follows that the values of r^ and A* can be calculated by noting (i) that total financial wealth Wt grows by fxp(AA*) between r* and t' + A* i. E.
UV; + A- = uv;e^^* (4. 11) and (ii) that aggregate liquid financicd wealth must equal the supply of hquid assets i. E.
/ \e-''atdt= Ae-''(u-, -ti;.. E'"-^''Hi = (l-A. -)-- (4. 12) Using the expression for w, from equation 3. 5 as well as equations 4. 11 and 4. 12 above we obtain the values of r, * and A*.
4. 2. 2 Liquidity Premium In appendix C we show that the first order effect of transactions costs on the liquidity premium, in, is given by 1 + e-'"^* '"* = '' \. E-'^' - ^^-^^^ It is fairly easy to understand the determination of m*. Equation 4. 6 imphes that if m* were different from its value in equation 4.
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