View Carlson-Titman-Tiu Paper - The Paul Merage School of Business

Taking expectations:
dR R t
dR P t
In particular, from (11),
= r eq
t dt + σLdW L t + σr(r eq
= r ∗ dt + σLdW L t .
E dR R t
= r eq
t dt
E dRP
t = r∗dt. E dR P ∗ P
t = r dt + E dRt t − µL) ˆ φ ′ 1 (req t )
ˆφ1(r eq
t )dW r t
11
(10)
(11)
eq
− rt dt. (12)
Equation (12) implies a particular link between the returns of REITs and property: specifically,
equation (12) suggests that the returns of real estate E dRP
t can be explained by the returns
E dRR
t of REITs, however not completely. In order to fully explain the returns of private compa-
nies we would need to add the public discount rates r eq
t dt as an explanatory variable in a regression
of private returns on public returns. This result suggests that when regressing private returns
P REret on public returns REIT ret and the public discount rate P UBrate:
we should have:
P RErett = a + bREIT rett + cP UBratet + ɛt, (13)
a constant term with positive sign, namely, a = ∗ dt above.
the coefficient of public b returns will be positive.
the coefficient of public discount rates r eq , c, will be negative.
3.5.3 Return Correlations
The instantaneous conditional correlation between REIT and Private Real Estate returns is given
by: